e oK gg Hreman # the Hb 
i Fleet-ſtreet.. 
bs 3 a, : Or the Treaſury of the Ma- 
thematicks: Containing Variety of Uſetul Practices 
pan Arichmetick, Geometry, Trigonometry, Aſtronomy, 
Geography, Navigation, and Surveying. As alſo the 
eaſuration of Board, Glaſs, Tiling, Paving, Timber, 
Stone and Irregular Solids, Likewiſe it teacheth the Art 
of Gauging, ialling, Ren aalen, Military Orders 
aud Gunnery: Explains the Logarithms, Sines, Tangents 


ad Secants, ſheweth their Uſe in Arithmetick, &c. To 
Ewhich is annexed, a Table of rxo000 Lo arithms, Log 


Lines and Tangents, Illuſtrated * Sculptures 
per. Originally compos d b Ta, Gent. 3 
Enow carefully Neri d and Corre To which is ad- 


ed, che Beſeription and Uſe of both Globes, and ſome of 

che chiefeſt Mathematical Inſtruments both for Sea 

and Land: Wich many other conſiderable Additions 
a Improvements throughout the Whole Work. By 
. Alingham,Teacher of the Mathematicks. Price 6s. 6 I 

The Elements of Euclid, explain d in a New but moſt 
| als Method: By that Excellent Mathematician F. C. F. 
1 the Socieryof of Feſus: Now made Engliſh. Pr. 4.. 
A New Method of Fortification; by Monſieur de hos 

"ay Engineer General of Fance. Done into Engliſh, and 

Eilluftrated: with 32 Copper-Plates. Price 6s. 

© The Gentleman's Dictionary: Explaining all the $1 
Terms relating to the Riding and Manage of the Great- ' | 
ore; the Military Art, Artillery, ee. the Art of Nas | 

| vigation and Naval Affairs. Written by M. Guillet, and 

Eedicated to the Paupbine, with large Additions and 

y _—c Price 5s. 

= Recreations, Mathematical and Phyſical ; ſolving 

many profitable and delightful Problems of Arithmerick, = 

Geometry, Opticks, Gnomonicks, Coſmography, Me- 
13 Ph ſicks and Pyrotechny. By AM. 2 ol 

b Profeſſor of the Mathemaricks in Paris. Done into Eng- 

bs. and illuſtrated wich many Cuts. Price 6 


e oK gg Hreman # the Hb 
i Fleet-ſtreet.. 
bs 3 a, : Or the Treaſury of the Ma- 
thematicks: Containing Variety of Uſetul Practices 
pan Arichmetick, Geometry, Trigonometry, Aſtronomy, 
Geography, Navigation, and Surveying. As alſo the 
eaſuration of Board, Glaſs, Tiling, Paving, Timber, 
Stone and Irregular Solids, Likewiſe it teacheth the Art 
of Gauging, ialling, Ren aalen, Military Orders 
aud Gunnery: Explains the Logarithms, Sines, Tangents 


ad Secants, ſheweth their Uſe in Arithmetick, &c. To 
Ewhich is annexed, a Table of rxo000 Lo arithms, Log 


Lines and Tangents, Illuſtrated * Sculptures 
per. Originally compos d b Ta, Gent. 3 
Enow carefully Neri d and Corre To which is ad- 


ed, che Beſeription and Uſe of both Globes, and ſome of 

che chiefeſt Mathematical Inſtruments both for Sea 

and Land: Wich many other conſiderable Additions 
a Improvements throughout the Whole Work. By 
. Alingham,Teacher of the Mathematicks. Price 6s. 6 I 

The Elements of Euclid, explain d in a New but moſt 
| als Method: By that Excellent Mathematician F. C. F. 
1 the Socieryof of Feſus: Now made Engliſh. Pr. 4.. 
A New Method of Fortification; by Monſieur de hos 

"ay Engineer General of Fance. Done into Engliſh, and 

Eilluftrated: with 32 Copper-Plates. Price 6s. 

© The Gentleman's Dictionary: Explaining all the $1 
Terms relating to the Riding and Manage of the Great- ' | 
ore; the Military Art, Artillery, ee. the Art of Nas | 

| vigation and Naval Affairs. Written by M. Guillet, and 

Eedicated to the Paupbine, with large Additions and 

y _—c Price 5s. 

= Recreations, Mathematical and Phyſical ; ſolving 

many profitable and delightful Problems of Arithmerick, = 

Geometry, Opticks, Gnomonicks, Coſmography, Me- 
13 Ph ſicks and Pyrotechny. By AM. 2 ol 

b Profeſſor of the Mathemaricks in Paris. Done into Eng- 

bs. and illuſtrated wich many Cuts. Price 6 


* 5 4 2 4 =" 2 ſu 9 R 9 * 

a b 8 * WWW 2 1 r 
R hd c — = bg ks * 5 > * 8 2 * : SE i” 2 3 
* 1 - 8 _ N " 7 8 = 
"2 þ : : E 
* e 1 +. I , 
* 3 "a. N * 
- "4 N 
4 * 
© nt * ” £27 
o 
. L , 
* 
- 
" 8 . 


_— 


| EE "A NEW. 


TREATISE 


_——— — 


i. Three Parts, 


a 
9 * OE . 


The F r e all ds Comte __ 
of ARITHME I CK, inwhole Num- 
bers and Factions, both Vulger and Decimal. 


| 
| 8 
| 


— 


1 


II The Second, The Demonftrazion of thoſe. 


Rates. 


The Third, The Uk and A licaria of i it 
in the Exchequer, Cuſtom-Houſe, Exciſe, Pay- 


4 


W not hitherto Publiſh d. 
E etl Ain my Teacher of 
| the 2 e 


LONDON: 


Printed for I. Freeman, at the Bible agaiclt 
the . in hs. . — 


n 


ARITHMETICK. | 


N. &c. with ſome Practical Rules, Notes, 


— 9 


4 
Me — — 
* 
— a 


2 At 


pains 


N 


err ns 


r On ww IAEA Ree 7 


8 
8 
3 


6 
— PPP 


R 
f s 
+ 


_ 


„ eo r . s 


e 


r 
* "Fn +4 1 
* 


8 


$ 


an Ae woe AN 
: 
. A A 
7 
7 


17 i 

* *-4 

* 
& * 

PL + Ren 

E 


— 


* 


». as 


5 i tes, v . nn ani 


* 
* 
* 


3 
— * 4 
-— 1 N * 
l 
po 6 40 ; — 4 x 


4 4 
* 
3 1 
18 


* 
8 * 
„ 
7 
A 
* 4 F 
0 


7 
ft 


1 


Me ann ae n 


* 


— a. i at 


* 3 pr 
wt 12 
+ : 
* 
ht 
© as 
* * 2 k 


ö e n 


2 
* 


3 


a «> 
2 


2 It 7 2 
Ae 


. 
ba; # 


Gs 


* 
* „ 


ͤ ² “ 


i 
7 


4 
* 
* 


* wi 


. 
Ma 
hs 8, 
N 


* 
4 gd * 
9 4 
A hs ai 
n+ on Ad 
* $a + 
1 


* 
— 


* Y 


- 
"i 1 
043% +7 
, *4 


SS. 
4 


en I 
* 


* 


9 


* 
* 


is gn A 
ii 435% 


Ne 


Coty A I. tt» 


- [3 
Femmes - 


= 


unn — — —̃ — : 
* eee r Wen r #4 We 


. 


- 


- 


* 
ta ia babe 


—— rt + OA +> ae 


* 
rn rears 


* 


$29 * 


- == BY % 1 \ Ad We s 


2 


- 
— 
4 
5 
F * 
" 
4 
* 
R 
5 
4 
. 
— 
£& 
« 
* 
4 *% 
I ds 
WE 3 
* — 
4 
. 
- 
7 
” 
CY 
. 
* 
1 
$448 
+ 5 * 
% 
$"< 4 
1 " . * 
— N and * 
+ 2 
» * 1 x 
4 N * 
«4 * by 
* * \ I 
6 
£ 
5. <a 
A 
1 
* 
my" 
* * 
N & ; 
. 
* 
5 
- - 
. 
7 PL 
i 
. 
# 
BY 


4s 


* 


I humbly deſire, may be as the 


46 


Dedication, 


* 


* 


to preſe ent 30 with this Trea- 
tiſe o, etick; which, 


.. 


- 


HA | 


- 


- aide ? 11 oy 24 


; 8 


*. 


. 


Tele 
3 e 
dinigend: Paling; 


* 
— 
\ * 
A * 
1 Fg 
af 
* 


179192 1970 mn sbb 1 
of the Excellericy 
Wy eee will benicefels, 
ing of Tach imme 
| Aal Uſes ro el 
7 wranlacted“ Hebo Jom RDO). 
therein 5 för tis not” only 
neveflary f6rithoſe who = 
Ait th all kind f Tra- 
x bits alfShigh- - 
I requiſite for Perſons of all 
10 Plato kells um, wirkout 


areand 


0 11493 A 


© Arich- 


_ Thetick, Heuer Science or F - : 


lick could: ſubſiſt, and 


" — 


. 


ub 
FR and Reaſon would be 


1 | 


baniſh | 


— chmarladgad® > 


Arithmetick, that renders- Men 
reaſonable, and gives them Fs 
tration, QOtiler and 13 in her 
| Ideas; Sal 0 ly -| caſes. 
Wenns che Nacue, by "Is 
Aubtille reaſoning whe ere che Senſes 
| Mark, r 1417 90 Nom? 10 2015 ; 2p 1 
«i Wherefore I fhall no dounger 
inſiſt upon che Excellency of A- 
rithmetick, but nanu give 5 
the Readęf a 


the following Bobks A 


hich 1. 3 


A ave Entitufd, ob Ds | HA. 15 p 


baagech mund {A amb} br: Ft 


W. herein 1haverndeavo uni od 
enhibie: the firſt Printiples there: 
af, bet in whale Numbers amt 


Fractionꝭ, aſter fuck-method-asT 


8 > & 5 


hackfoundinmy Practiſabf I eacn-- 
ig, ro: be moſt ſhor it arid «ah. 5 : . 1 
eee e, 


Dae RNEADER. | 
Walgorand Decimul, (themoſt knot- 
part) Iwill be bold to ſay, are 
oricthodicall yDigeſted andINu- - 
ad, erwi render them intel- 
Agible to the meaneſt Capacity. 
An the Second part oft lic 
: ae, have Moen the Demonſtra- | 
tion of moſt of thoſe Rules, both 
 mywholeNacbersand Fractions, | 
andi have alſo fliown you! Grada- 
rig hñowi to taiſe ſeveral Theor 
_ Gy>which/moſt' Queſtibns, bob 
iniSunple and Com Antereſt 
are ſolvd ; à8 likewiſe for buying l 
=: a ſelling Eſtates, Annuities'and 1 © 
—_— Panſunr, alſo: Tinin ig off Rats, Cc. | 4 
1 919 l I hoes yd icto Pra- ; 
Ctiſez not olyin Rramples drawn 
Ifromcommn Commodities; but 
Alſo in chings of another Nature, 
pac in Relationrofeveral Of. | 
Particul \\the'-Bxchequer, | 


rr 


Tode ED 


5 Exciſe, with che man- 

Computing Seldiers and 

ages. lle Bote 

Deductions of Sandee „ O 

VWecteniigb, Royal Hoſpital acid Agency, 

— drveakenardacobumed orzineath 1 
| f which 3 17-4 


4% I: — 
v Queſtions; which will be as 
lafant i Knowing and Read- 
9 b Arichme- 
. ho es — NI 
taken tem Hiſtor 
ke wich means «rw Aden. 
blj Mond 22ithei fame dime, 
which Attempt will make" chis 
Book rom all _— 
ubliſhed in Engl: | 
EG are, 5 ha, the Princi- 
7 pal things herein contain'd, — 


— Cours Wel 


Frauty the. lacers 3 


In db NEHADER. 


Thave elſe to £ ay, 15, That if in 
hat is here delivefed, any mi- 
ſtake be Committed, or ſome | 


ings not ſocleat expraſi; as they 
2 have been, F 


40 
ever attending the gr 


doubtedly Ii Wilb meet with 


e 


mus, yet I hope there ate lame will 
kindly accept 995 hy arr] 5 


ho oe | 


fertd, ee pardon he 
rors, rememhring hey 
mans. 1 lin — 9 8 


24 No 2111 13112. i Ile On ib 100 ; 
| \ Aut bortids n 
* 8 ee rde 


F117 © 2 43 oy Oc a7 441 218 2150 


25151 b 2:22709d 029750 2831 laq | 1 


J deſite my 
Ader to conlidery. that. (heli 
may troubleſome buſineſs gf:Keach- 
ang, While I Was Writing this) 
the Preſs, and our Natures are al- 
Quſes of ſuch ieee 
and 


INS ww A. A. A Aa 


„5111 gs ib... 


10 3 ST 


| "The | Contents." 


OILY EN ; 


ae 6 UE 4A 

5 F Arithimetich,. N NN 
Of oor \ nd 8 den t e 

Of Setractias int wk r ug A 


Of. Multiplication, I Yoo © 1 lus 
Of Di viſion,” . x, 3 4 s e wh * * N 28 


EN * 
dra 


Of Re Reduction, "> 558 1 \ } 39 
Of the Golden N or * of 1b, r 
The Rule of Three Iaverſs, * 


The Doctrine of Vulgar Fractionn, 7 
To reduce a hole 3 to 4 beh. ard. 


contrary, > Io fi S350 6 R 855 
To Fedice 4 eee practio to a Simple, 58 


To reduce Fractions of * nn 10 


ehe Denominatin, 6 Wan r 
Ta _ a Fradtion | into: another,” el 
Pal ue, IL Key kv +165) 


32 the Value of a FraGjon-ints Rn" 
arts of Coin, Weight, Ge. A 
þ ition of Fra ions, 8 Ns ct Logon I 


Su 8 action Fractions, Nas Ann SN Fe 
Multiplication. of Fraftions, 31 ye 
Diviſion of Frattions, , 
Rule 225 of Three Direct in Frackions, 3 DT. 56: 
Three Reverſe in Fracfiuu, 578 
Keats ion of Queſt ions, fo 8 rhe Rules 

Df Fal Vulgar Frattions, 4344 LS : 


Th Doctrine 0 fDecimals, Ke W . 
Wien - ug. 


5 
ba >” Dp * 
2 * * u — — „ — 
e — 2 — — * . — — : 
b „1 = i ran. Atom — — 
af 25 N - — — — — — 3 w 3 — wm 
nnn p ** * k 2 . — . 
, " * , Pres 5 \ — 3 — 2 — — — Eos a 
F ; „ . " 1 — —_— 2 — . . ne II. 
x * 2 * 7 ** N < NN N 8 EI No 9 RE? ” 
\ vo Y . > TR” WT 1 7 0 7 - 1 P ods im * K „ * 


2 1 o 
— 7 
9 N 

; 


* pon, - — — cy ——— 
— „„ „ 
W * MP *** 

, 

* 4 


— 


2 


2 4 
* INE 
_— — III — 
W * N th 
* By lg 2 * 88 
=_ 


Mehta of 5 ; 4 a AX. 92 
Di viſon of Decimals, © A 
Reduttion of Decimals, 1 
To find the value of a ET) N in the 
uon Parts of Money, Meigbr, 
Apratica! Rule, for finding the 7. a BY 
eimal of a pound Sterling, TINA 2670 
A Table, ſhewing the Dee! of any gart 30 
Pound S, 2 + was an 
Prat? ice, Shs f vx WE \- m 112 
re and e e „1241 
Torfind: Be Tren N ee 1% 
The compound Rule of Tires Died Rn : 
8 7 S ed $2 nne ae Kin v2) 2355 


Siniple lurereſ F. 17 id 1 Du N * 


7 wo Rules for 8 the Inpei Ws * 

ws Rae for Slag the Bo fall f 
Rebate or Diſcompr, _ aß by 

. eee 1 D d ae dl 130 
OF Annuities at Simple Intereſtsiio , 150 
Of compound ble. ABI * Wonen 
Off Annuities at compound. Iureriſt, > ROT 
Ib find the preſent worth of Amy, 31 

Fellowſhip Single, wa A Fo os 175. 
Fellowſhip Done: 7 n B wed . | IG 1 | 
Aligation Ae en N 
Aligation\ Altena, e Jo Nor Well 
The Rule of Poſit ion Single wang 19 
ion Double, IRE d IR 00 Ne 5 
Extradtion of the [quare NC {worth 
Extraction of the ſire Root of a Decimal, 204 
| Extrattion 


=. 


try. 


88.0 8898880 


een bh: 


” LS „ * _— —_—_— —_— —— 1 


The CON TENT-ST 


Estractim of the Jquare Root bf \w"Valjar Fran 


E107, Set ©! pagerives 
Extracfion tbe Cube Roos; Fla. ig ad 5 
Extraction of the cube Root Fes Cn 
of Barter (Exchange, and Loſy' ond Gino 

219 to 227.2 * N Rwe 34. an 
Definirions 5. Coroll aries, Axiom uni Pr 

3 fer Demonſtratiet; 29497 3n IC 
Of Number and it: Notation 10092 
Demonſtration of the Rule 7 Three Dir" 
Demonſt ration of The Rule of Three Reverſe, 

Demonſtratiow of the compiund Rule F Tae 

Direct, ert GI O55 mt 
eee bp the purer | Rite" "Reverſo," 

anus Ii, A* . W 2 * "24 2 
Opec aft A rite e. [oils 


ere. 
* Nos. 2 4 


25 

me, 

260 

3 Alba with Time, 261 


The Demonſtration of Aligation Medial, 263 


. The Demonſtration of Aligation Alternate, 264 


The Demonſtration of vulger Fradions, from 
268 10 274. 


The Demonſtration of Decimal Frattions, from 
274 10 279. 

Uſe of Arithmetick in the Exchequer and Tres 

un, from 283 to 290. 


Uſe 


A IN RN r 55 
er -Arithwetick in tbe Cuſtom-Houſe,. 


rom 291 to 300. 
Uſe; of Arithmetich.. in the. Exciſe: Office, 
from 301 10 305. We ON 
Of ithings relating to the Computing, Soldiers. 
and Seamens Wages ; ſhowing the Nature "of 
Agents Accounts, and their manner of com 
puting Poundage, Royal. Hoſpital; Off. 


Reckonings and Agency, allo, a Cyllefti> . 


en of Queſtions relating to the Jame MR i 
rom zos to 322 
| Sin Propoſitions For En airel * an. NA 
from 1 29 8 331. 
Of Mea ing; from 332 tO, "EN 
A Table Fe the Eng lim ae For, 
- with the Standard Fes of. l ot ber 
Countries, by Mr. Greaves, N ds 
A Collettion of 11 to Exerciſe muſt of, 
the Preceding Rules, AN iat 1 


8 EST 1 80 ' XY (348% hay. Wach 
Gin ASS tay, 2 *\ 8 Y > 5 * 
7 EY, "y 7 « 2 N Nord * * Na x 3 A a. 

282 * 3 
1 ; | {Lat 
By by * | »* \ * q >: 

2 & . S443 33 N. 0 Watt Mes 9 \ 

- {. * S * 
* ; 21 * INI N e eee Sar 


ö Batt eee * Kato SG 


s „  þ©4 00 VIC. + 
0:1! tn Ned d 
„ 44 tn * Nö NN H 
. Q7L 01 ** $ 
vl den ages XA 202 vi : Addis, G 
8 0! ES: mon * * 


. 


92 


* 


4 


* 


r — 
— - 


3 


M x * 8” 2 — A , 8 . 5 
nnn A) eis. 
„ „ 1 8 T i. 


all defined indivilible, i. e. not. ro be 


£ { TY . 8 Mi ** 1 x 4 *. 
1 9 5 % * -*y , G 0 f 1 A % — : F ”F S228 ig 
#7; £4,514 Wo. IL OSLO 44 F,X SZ 4 


þ <4, *p 


' Rithpaiick, is 15 the: At k F right t. can, 
true Reckoning, the. "Sub 
which is Number, and is b u. 
to which all tr e Precepts of Computation 
hath relation. | 

Number is chat by which the, Quantity | 

of. any thing 1 18 expreſſed, ; as. the Unite, 18 

the quanticy by which one thing, is cxpref, 


ſed, and Two the e OY; Which ty 


7241871 


named two” Ge. nk vs an” bc 
Hence the eforc- tis ev ident bow 
Ancients Were Mmiſtaken, WHO ſaid, That 
Unity was the beginning of 6 Wa 

yet of it ſelf no Number, 11 8 altoges., 2 
chick diſagreeable' ro the Princip es of Gee, | 

mittry, Mute k, Time, &. WiN begipnipgs, 


are 1 Post. a Sound, a Momint, & "CG. and? oo Fo 


5 


ded into patts; but an Unite may be di- 
5 . 


I * „ 4 * „ 
0 * * a5 a *; 
1 . 


35 
vided into parts, and therefore cannot be f 
the beginning of number. So that if what is va 
diviſible cannot be the beginning of number, 
then it muſt be (o) a Cipher or Noth; pri 

for whatever is greater than nothing is di- N. 

viſible; And as a Point in Geometry is 

defined to be the beginning of Magnitude, 
yet of it ſelf no Magnitude; ſo may a Ci- 
her be ſaid to be the beginning of Num-. 
r, yet of it ſelf no une Wy 
Now an Unite is a number (as before 
was noted ) for tis part of the ſame mat- 

ter that is the whole, and by it, and it a- 

ne, ſeveral things are numbred, as One 

God, One Morld, & c. Therefore it cannot he 


— 


che beginning of number. 
But here Note, that chotgh Unity be 
not the beginning of Number, yet tis the 
beginning of Multitude, For Multitude is 
only a Collection of Unites. 30 
Number is either whole or broken,. 
whole numbers we call Pitegers, and bro- 
ken Numbers Factions. A whole Number 
cConſiſts of one or many Unites; a broken 
number or Fraction, of part or parts of an 
The Common Notes or Characters, by 
which we expreſs Numbers, whether whole 
or Broken, are one of theſe following, vix. 
123456789 o, The later of which, tho 
of it elk it ſigniſieth nothing, yet when join · 
ed on the right hand e Of OTE, 
TD GO PAs IT” 2 OA CIT; 8 


Bag 
4 


5 155 
of the aforeſaid Figures, encreaſeth their 


Value ten times. 
In numbers of any ſort, have are two 
princi pal things to be conlidered, vir. 
Notation, arid Numeration. 
Notation is, what the Vulgar call, or take; 
for Numeration, and is that which teach - 
eth how to deſcribe 1 5 Number by the a- 
foreſaid Characters; Or, it teacheth how 
be * the Value thereof bein 80 lo deſcri- 
Nee is the manner of wor 


king, Ot 
Operating, with Numbers, or tis that by 
which, with certain given Numbers, we 
diſcover an unknown Number: It hath 4 
Species, or Parts, viz. Addition, Subtracti- 
on, Multiplication and Divifion, of W bich 
we ſhall hereafter treat. 

The true manner of Expreſſing, or no- 
ting Numbers Conſiſts in the knowFdge: - 
i; of two things, viz. The Order of Fase, 
And the Value of Each Place. 

Thhe places that any Number is ſaid to 
have, are only the Number of Figures, or 
Characters, chat repreſents it, as the Num- 
— repreſented by 235 conliſts of three 

Places. "NR 

The Order of Places is from the right * 
hand toward the left, as in the Number 
476, the Figure 6 is in the firſt Place, the 
Figure 7 in the Second place, and the Fig - 
gure 4 inthe Ts OF ERR Powe: 
7 2 | 


* ä — — gow 


(4) 


der gz ol che Cipher is in the Firſt place, Are. 
in the Second, 7 in the Third, and Fi in the Mil 
Fourth 57327! 218 NAS. £74) 9 ons 
The. Firſtꝰ place of à Number, which) is Won: 
the Figure next the night hand, as was hin- Mon 
red; is ccalledithe place of Unites; kor in 
this place y Figure fi ignifies only irs own' 1 

value, fon the Number 32), here 5 is in Mw; 

e Flrſt place, and en, only 0 many Ich 

Unites. Or Ones. sf ce 
The Second place in a Number is called ſa} 
the place of Tens, in which any kigure or 
_ ſignifies fo) many Tens. As it contains\ ſa 
VUrmtes as in the Number 32), che Figure 
is ia the: Second place, and ſi ignifies Wo 
Tens; or Twenty. 7. 

The Third place in a N N is e 
Hundreds, in which. any Figure ſignifies ſo 
many Hundreds as there are Unites in the 

aid Figure, as in the aforeſaid Number 
329 the Figure 3, is in the place of Hun- 
.dreds, and ſigniſtes 3 Hundred, ſo that if it 
bersquired to read or Expreſs this Number 
327 you muſt begin at the Left Hand, ac- 
coding to che preceding Directions, and 
prenounee it Three Hundred Twenty Se- ] 
ven; likewiſe this Number 307, is thus 
Read, Three Hundred and Seven; Under- 
ſtand*the like of others: The Fourth place 
1 if you” have more places than three in the 
er * is: Thouſands; the Fifch place! 
TOC . n * und 
dreds 


"ng 


6 


5 (ay 


dreds of Thouſands.” the Seventh place! 


Millions; the Eighth place Tens of Milli- 


ons; the Ninth place Hundreds of Milli- 
ons; the Tenth If week Milli- 


ons; and ſo on: 


* . AT V 1 $1 , 


nein ot | 

Now, fo ppoſe dbl Number 9876543210 
was given co have its Value Expreſſed, 
then from che fdtegoing Direktion I Pro- 
ceed- to Pronounce it thus, Nine Thou- 
ſand, Eight Hundred Seventy Six Milli- 
ons; Five Hundred Forty Three Thou- 
Gn! Two Hundred. and Ten. 

From what precedes, * tis very eaſy by 
theſe Characters, either to Denote any 
Summ you, hear Expreſſed in Words, or 
to Expreſs in Words what you find Dean: | 
ted by theſe Characters; in doing which, 
the OLE, 3 will much * you. 


* 7 * 
* = 
823 
. 
_ $46 * 4 x U 
. LS # I 
* K 2 
1 * nn * 4 
— $0 8 
4 = F -. 
, Lf * 2 
© a : 4 
— — F˙RW . 
N # 4 F e — . 
4 = . a 
* We * 
8 = 
"— 4 
* 1 
* 
— — 
4 * * 
4 f * * N 1 
* oY - 4 * .. 
4 * | 
2 - 
p » 
6 2 7 
* 
1 * a” 
BP P p = 
N , : 7 
| | N 
* gr ' 
A” 9 : a 4 
4 F / g 


Et 
4 
* 


98 Nich 1 

5 gt { Nine Hundred py Seven. 
"= 76 Nine Tbonſand Eig bt Hundred Seventy Pr 
938 765 Nipety: Eight Thouſand Hundred Sjxty Five.. 8 ” 
_ 987-654} Nin. Hund. Eighty: Seven Thouf. ſix Hind. Fifty four. = 
: 2 1 Nine 24311. Eight. Seventy ſix Thouf\, five Hund. forty: . 4 
2 1 Ninety Eight Mull. 7 Huy. Sixty five Thou. 4 Hand. Thirty Two. . 

Nin kd, Bight 7 * fix Hund. Fifty 4 Thou. 3 Hund. 2. 


Table. 
Fa 1. - 
V 
00 
4d 
de 
7 


. — 


(6) 


Notation, vulgerly ca! d Numeration 


2 2 
88 _ : 
3532 jo 4 £3 r. * Led 4 = | 
* 4 1 24 . 4 : | | 
+ * 0 k Pu, x — — 
Ke 4 2 4 . * . 1 . I 
: 4 * : I 4 
8 * . go 8 bu | 44 ] 
— —Y a | 
a - A: 
; |; 
— — lf — ; 
- Wy 2" 4 3 ö 
* * FLY 14 g 3 _ 7 
* 1 a 5 1 avid 
— * þ 8. „ | t 
PA, ; . *. 
# 8. 
5 > pe, 
2 » 1 % = | 
i. 
* — * | 
q 
Le 
: * ow 
oy * _ 0 
7 3 * 8 1 . « 
\ { ' p £ 2 3 5 
ty 4 ut na - 


le, 


Sd] 


(7) 1 


From oh nature of this Table 118 mani; 
feſt, that a Cipher on the left hand of any 
parcel of Figures doth not increaſe or de. 
creaſe its Value, For 05 4, is of the ſame va- 
lue with 54 : likewiſe from this Table may 

Number 


of places of Figures be 'Vatu- 
ed, Tho” I have gone no farther than nine 


laces, the laſt of which is Hundreds of 
Millicns, and if you west on, the next 
would be Thouſands of Millions, the next 
Tens of Thouſands of Millions, the next 
Hundreds of | Thouſands of Millions, the 
next Thouſands of Thouſands of Milli = 
or Millions. of Millions, the next Tens of | 
Millions of Millions, and ſo on; or by 
putting a 80 to every Sixth Figure from 
the Right hand you may by inſpection de- 


termine the Value of any parcel of Figures, 
For the firſt Six Fi 


gures next the Right 


Hand, denote Hundreds of Thouſands, the 


Second Six Figures Hundreds of Thou- 


lands of Milfions, the Third 6 Figures' | 
1 lg Thouſands ol "Millions of 


As op wn 4 theſe. 18 Figured rlacedand 
pointe 7432689 1765-44309 were given 
to be numbred or Valued; 1 DIONOUNCE the 


Number thus, Five Hundred, Seventy Four 


Thouſand, Three Hundred, Twenty Six 
Million of Millions, Eight Hundred, Nine- 


ty One Thouſand seven Hundred, Sixty” | 


Five Millions, rom Hundred, Twenty 
34 e 


, 


(8 i 
Three Thouſand, ee Hundred Ninety 


One: And after chis manner may you Ex- 


1 — the Value of any a Number of 
bl ms 189J 9451 27 d EITH 8 b ; 
—_. -£v. Smet 98230 er „ c 107% 216 23% 15902 
wh _ yer ds T aid mo; e ig > Au an 


- a 10 


457i 311 1 ae = | : | 

129. Ay ti 0 er 
FF Evcbith'y a0 be! het Le Collier My 
Gather —— ſeveral Suns into "one" 
Total, or bole Samm, which Toral'or whole 
_ Smipm, is alſo dulled the Agregare' © IP, 
" 38 158 Rule, Set the ſeveral Sums 6 if they Je: : 
. of one Denoinination) one under ano- 
ther, t thatcis Unites under Unites, Tens, . 
under Tens;:Hundreds under Hundreds, 
e, and underheath them draw a Line, 
then begin ti add With the: lO Welt Fig 
| next your RighriHand,) and Collect a TE, ! 
1 Figures in that rank quite to thę top Ain 
obne Sum; ſet down the odd Unftes abs 
1 bf, the: Tens, and for ſo many Tens as 5 8 | 
1 Aer garry many Unitest the next rank 
0 cf Figures, ꝓroceed thus With the reſt of 
10 the Ranks, that is, ſet down: the Unite 

and carry» the, Tens, only” Whatever the 
laſt row ar rank comes to, chat muſt . 

- wholly * daun to the former Fig Spres, , 

75 


r 
WG ot DIA 42 N > 80 4 200 11 


3 1261 4 


—— — 


— —— 


— 


or 


e * — — — _ — 
nb aan tes Wc 
ä — = — 
— 9 jam Eg — — = — — "oi 
— — — — — : 
— 


Dc 


Total, or ne, Sum. * 


ul” 93 WS 
Por Example, in the firſt | 

with 9, ſaying 9 and 4 is 13, 12 8 1 is 
21, and 5 is 26, and 6 is 32, "then I fer. 
down 2, and carry the 3 Tens to the bottom 
Figure of the newRow, ir makes 6 and the 
5 above is It, and 41s 15 and 2 is 17, 
«8d 3 is 20, which 20 1 {et down to the 
former 2, and it makes 2075 en the 


mr” 445 2210 ext: 244 | 
eg. br. K Integ, . 3 
833% IC i 3826 


' 5 - ” — < > % 32 
232 8 2 e — w_ — — 


: 6 . 3 2 Pugs — 
AOL... 169 2374 — 
NY 8 * 8 x 
89828ͤ Hat oi 9 5 Wund TO _— — ä 
> | 5 Po * 


3 . 3 * * 


. 


1 "de yay, ae = I" 


If the Quaniitic, ee to be added 
be of divers Denominarions, Fee Sbil- | 
lings, Pence; Pounds, Ounces, D Dr indo 0 
elle, then you muſt place thoſe of the the 3h 
Denomination, that is, of the ſame Name, 
under each other, wis. Pence under Pence, 
Shillings under Shillings;” and Pounds un- 
der Pounds, after which draw a Line un- 


der them, and begin your Addition firſt. 
with the leaſt Denomination,” Which is al- 
- ways: placed next Sous ri 50 8 255 mind 


* how many of lels, are C SE 


- 
4 ' 
5 
4 
4 
i 
F + 
» 
> 


9 


tained in the next greater Denomination; 
and ſo-many Times as you find, ſo many 
Ones, or Unites, carry to the next Deno- 
mination, as you did the Tens before, 
fey own the odd remainder if any 
rogeed _ with 1 reſt of 10 ugh 
nominations, till FOR ane t _ | 
them all, if there be never —— 
the Examples of Money following. | 


I. 1. 4. „ 2 6. hy 


* 7. 9 49 19.11 -27 1110+ 
2 9.11 36 8 10 36 19 1 
ci 10 24 19 IT 724 15 10 
16 xx 38 4 6 36 17 <2 
12 7 24 11 10 2973 o + 
— — — — 


— — LED ©... Met] 1 


a "ary 


TE 1 . 


75 ; 7 my» a5 s - 
» 6 as + MS. 
o + 7 $3 Ry « 3 C 0 12 9 


Note. OE To d. lands for Libs, Sale! 
dis, & Denarius, that is, a Pound, Shik 
ing and Penny, the Furthings are generally 
wit r that is, with two 
Numbers thus, as =, is one farthing, + D. 
is one Half- Penny, or two Farthings, 2. 
is Three Farthings; Obſerve alſo, that in 
Addition ſome ule the Method of Point- 
ing; as at every * ja the Pence, they 


make a point, and ſo 2 Many points as ate 
5 _— 


„ oo WW WF WP 


number of Pence is, under 126, ) proceed 
down the odd Pence, and 


carrytheTensto the 


69 


1 made in the whole Addition of Herber ; 
ſo many muſt be carried to the place * 
= Shillings, ſetting down the remains above 


12, under the place of Pence; fo likewiſe 


. at every 20, in the Shillings, make a ſpeck, 
= and ls may ſpecks as you find in the 
Addition of your Shillings , carry ſo ma+ 
ny to the Pounds, ſetting down the over- 


plus Shillings, and then go on to the Ad- 


dition of your Pounds, whether there be 


one, two, or more rows, 
But the Method 1 would commend 
to the practice of ſuch that are frequently 
concerned in the Collection, or adding up 
of large Summs is this, Add up thepence, and 
make a point at every 60, Which? is 5 Shik- 
lings, (as is Evident by the following Ta- 
le, and from which you may readily 
now how many Shillings and: Pence any 


thus, to the Top of the Pence row, ſet 


coy os the Shil- 
lings to the place of Shillings oy | 
only the place of Unites in the ling firſt, 
in which no ſtop need be made, E ſet 
down the odd Shillings above the Tens, and 
ceof Tens in theShil- 
lings, counting them but ag Oneg orVaites, 


that is, for ſo, many Angels, then for the 
Sum of Angels in the 


Second-ptage; take 
half of irfor the number of Pounds, becaule 
"wo Angels i is One Poung, ſetting down the | 


3 


— 


_ 
96?ỹZ̈—ẽWõ/ͥůt Lui 
n . 


— 


— — ↄ‚l. 4. 
— _ 
— Da99% 95 pa_—gs - 
* * £ 2 
N y £2. abi i) 


— —— 
— TT 


7 


2 
E 


- 
% 


Il 
| 


— fK7w.— 
BID - wy 


—— — 


odd Angel, if there be one, as ſuppoſe it 

came to 9 Angels, then the odd Angel muſt 
be ſet dow as one to the place of Unites in 
the Shillings, and the half is carried to 
the place of Pounds. By the uſe and practice 
of this way, you'l find your ſelf much rea- 
dier, and quicker in caſting. up large Sums, 


* * 3 Þ 3 .F 1 g * Ss 


38 77 1 g 5 "RI 1 , "+7 Lo 
#5, #2 7 4.1 * YES 4 ; 12415 2 5 WS: n 

5 44 281 C101 8 11 An ef dnt 1 2484 
, >. 3 ? ; * 


y - «! * 

» F 

" oa * CY was T4 11 ' + # E 

* 3 . * ee. 9 0 17 „ 4 14 7 115 
4 - : 1 1 + * 5 4 ; 13 4 OP 2 ' 


> : 
-© 4 4 ah 7 


* 
e 


EY 4. * | * 

7 — 

ö 4 
= 1 


3 


1 y O- 
, x 2 


B 2 30 ( 
5 40 1 5 
E 


4 SF 


100 is 


0 . 
1 0 Ne . * 
4 * * x : Ly 
5 & 4 * 4 4. . 
ws * 
* 1 8 
85 - 1 .: 
f — * » * bu * 
- * » bl 
. . * 
bs, ; y . g 
3 „ * 7 os. ©# % 3 4 7 * * ToODT ©) 7 * 17 [i 
mT ws # > % 8 * id Y i dw \.F 4 4*. P ” % 8 44 4 4 by * * 
Sa £ 


* 


1 
1 1 & * 7 1 # p , > 4 . * & — 
VV 2 tv! 
; © KJ *F 0 = g i N . A . . 


CARL SS „oel 


1 i. _ a... A tas AY 


Row ſo ſtru 
make the 


* 
z + FR 4 
* 
4 
* * X * 


430 


Tho 2 "of Addition. 


0 prove 3 ftrike olf the-u pper 

Number with a daſhof the Pen, — 
add up all the Sum again, except the up- 
per 1 - which is ſtruck out; 
done, Add the ſecond Sum to the upper 


This 


our If they both together 


rſt Total, the Work is right, 
other wiſe, not. See the dees FEES 


8 5 a 11. * 
7 24 10 9 
27 36 8 10 
36 271 19 11 
94 38 14 18 
38 26 1 
230 154 10 'F 
195 129 19 
230 154 180 3 


the ſureſt. 


7 3; 


Mr Record ſhows another way „ of pro- 
Addition, as may be ſeen in the 418. 
— of his . but I count this 


— 4 


[ 
+ 
1 
N 


ww 
— — — K In Ae. — — ye 
WC 
P 
TR. \ N . 


$7. 17s. 4d. 4 how muc 


(14) 
Some Examples in Addition. 
Suppaſe 1 received for 3 days rogether, 


w. 17 l. 12. 1 d. . 


Suppoſe I Received upon ſeveral days 


condly 81. 13 s. 1 s. 8 d. Fourth- 


by 41 17 5. 4 2 K Fillet. 64 | 


What is the Summ of all 1 have received. 
Anſw. 19 J. 195. 7 l. f. 
What Summ is that, from which if 1 


take 4). 10 3. 114 . there ſhall remain 


11 J. 155. gd. 4. Anſw. 16}, G5, 
84. 2. 


What Summ of Money is that, from 


which if I take away 197. 14s. 3 d. 2, 
there ſhall remain 1501. Anſw. 169 l. 
T4. 3 d. 2. 


is chat in all. 


the following Sums, viz. Firſt 2d. 4. Se- J 


. 


pe "* - . 
SUB 1 ö RAC 1 ION. 
0 i Y — 


| T you bow to take & leſſer Num- 
ber from 6 Exeter, and ſheweth you 
what remains : Or it ſhows-you how to find 
the Remainder, Exceſs, or Difference betwixt 
t Quantities. 1 35 
le, Kein Addition; fo i c e 
you muſt take care (whether the Summs gi- 
ven, be ot one or many Demominations) that 
they be ſer down in order, one under a- 
nother, As if they be of one Denomination, 
ſee that Unites ſtand under Unites, Tens 
under Tens, and Hundreds under Hun- 
dreds, &c. If they be of different Deno-—-ꝛ 
minations, as 2 Weight, Time, e. 
then ſee that each reſpective Denomination” 
be ſet under its like; that is Farthings un- 
der Farthings, Pence under Pence, &c. 
= This Deny Tone, begin at the firſt Fi- 
gure next the Right-hand, and operate 
= thus, 4 from 7 there remains 2, which 1 
ſet underneath the 4, 5 from 3 I can.. 


1 not, but 5 from 13 there remains 8, fr 


RES that 1 borrow d at's 1 is EY 3 Laa 5 there 


remains 2, then, 8 from 6 I cannot, but 


| altly, 1 that 1 
borrow, and We Baſt” 3 1 4, this I take 


from 8, there is left 4, dich I fet under 
Figure, as I have. done all the 


rxeſt. Sdis the whole remainder 48281,and 
5 the * ed. 5 


ee, 5 Eee 1 . 5 


28 OY io => 67543 


a LE 0 1283432 DI 


3 1 gs — * 


; ee N U 35267 441 1 I: 
9 — Ws # EN — — — — 
3 1431 n * * 8 5 . 


34 


r 214 0711 3 
In Suberaction e b l 
Meaſure, e. you muſt borrow. a whole. 
Integer of the next greater Denomina- 5 
11 don, as ſuppoſe 3 in Monc . was to rake 
=_ - - Shilling, 5 i. e. 1 W and as” to the 8 which 
makes 20, ſo that 1 take 10 from 20, and. 
ſet down ' the * remainder. ; . 


+ 7 8 . 
* 


X # 
* L 1 — - * 
SE . * : . 
: \ * %. I's of . k 105 x ” 


— * 


RT a0 £ „ 4 1 2. d. 5 * WEE 


CELLS EET EIT Mb 


Rom. 
= | * 
+ #8 * 4 1 : 94 1 1 

| - 


N 4 * A 5 * , g — 
+ 8 * SE * 2 1 py. 8 8 — : . 4 
Fat 4 : "M - 7 — 1 N — F * % =- — 7 - he | 
_ = £3 5#32# 5 * oy 4 4 f . 4 IJ +4 3 "4 22 IAG 8 a . : 
_ Ju " / 83 4 1 % « 4 * 
* 5 7 1 pas . * 4 * 
: * . L 
3 ey; +- PI AAS 3 0 
TA „„ 12 1 1 4 \ #4 Fa — 2 1 a vis 1 
* of = * 4 


4 


It is e that theReniaiaderAndSurhe | 
Subtracted, muſt make up che Sume ot 
of which the Subtract ion was made: Adt 


aw 


therefore the Remainder and Sume: ans: 
nuts "and if they both make the 8 | 
ent, nt, the Work: is right, orherwiſe" not 25 
auge F 1 
Satfss AE © - 
: PR IL K * . E 
e 625982 14 10 1002324 or DERRY 
Paid 235826 4 11 98234 14 8 TC 
— — —_— | = 


Y # 
RP £2 . — 2 — 
A . N wi 1 « K 
a 2 '4 
* 


Proof 625982 14 10 


616) 


More W | 


Lent 17 L. 12 or A. 2. Paid of this 
11], 145. og.d. What is left to pay. Anſw. 
TH 12:4-.04&4. 
, Lent 19 l 17. 0 d. 2 FY of which there 
is paid at one time o9 5. o8 4. at another 
2 4. 2, at at third 8 J. 13s. at a a fourth 41. 
175. 2d. . What doth yet remain. An- 
fwer, 5 Ni, 
What Sume of Money: Is chat, to which 
if 1 add 11 J. 15.5. 09.4. 4, the Sume ſhall 
52 16). 06 4. 08 4. 4. nfiver 40. 105. 


Wer Sume of Money, i is chat, to which: 

©] 7 19 704 03.4: T. it ſhall make 
I. 14.5. 03.4, F< Anſwer” 150 J. Uh he 

| 1 here note, That *twill be Bebe 

for the young Arithmetician to exerciſe 

himſelf boch in Adding and Subſtracting 

Sumes of Ws OTE ark &c. 


& 7 1 1 2. + q * 4 3 A 


3. 7 * d nne oni 44 An a 
1 „ ha i atk ain 


MO 781 [CATION 


11 9539 v7 


225 3 2 75 ms ih i Work, k 'of 4: 


9 4 TA an e 


bers, to find a. third, 5 5 TT 
contain either o * the 1 two " Fire 
Vimo, ſo, oft, as the, other. FAtajys x, "or 
nity. 2 
Ic 90 As 1 VE is to be galls 19 5 5. 
tion. FILE b | 
oo We 25 u Or or EI DK, re A © 0 
give you — ame as 1 you A Wan pi 
8 by 3, or 3 by 8, which is 24. 
One of the two given Numbers is cal- 
led the * 5" 84 and is The Number to 
be Molciphcd. 


© wi" 
«54s + 


by which: we Multiply. ThE 4 

And the Number ariſing from the Mul. 

tiplication is called the Product or Fact. 
Hence it matters not Which of the two 
giver 1 antities you make the Multi pli- 
cand, of Which the Multiplyor, for 8 mul- 
ti plied by 3, is the ſame with 3 multiplied 
by 8; tho' for convenience ſake, we ge- 
N 3 nerally. 


— ry — 2 — 
. CTY * 3 we 0 6h <2. -*I® wot 2 — — — — — — = = 
— — * * — 
— — — — 
— PP — 

— 2 — — . an SIE IE: re IRA IRA 6 12-22 A, AYP" hon, 

„ - a n * — — — 

K we * 
3 


i 
9. — 2 Ln — o _— — — > = = = 
ae & * — = 4 N : * — >, 
— DE. > —— Y 2 K 
. P! ˙-» . — , . — 4 


— — 52 4 
* ea ae ———— — 
2 d 


te 
TD 2 *I oY 3 — 


—— — 2 


n 


n= ot A „„ 
* 2 N * 
8 


the. 

| The reaſon alſo of that common Notion 
in Multiplication is hence manifeſt, that 
the Multiplicand is to be put fo often to it 
% there are Units * the Multi- 
lior. 

From whence it : follows, that all 8 
tities multiplied by a Fraction are decrea- 
fed, rbat 3s, the Product of two Quanti- 
ties, of which one is a FraQtion, is always 


: 1 than either of thoſe Quantities; for the 


Produtt will” be only part of the Muttipi- 
cand, becauſe the * is but part of 


my. 
8 ow. for © taps diring the Practice of 


this Rule, it is. bſolurely neceſlary to get 
ba by heart. 


F N . 
R i 101 F 739 5 111 — 1 


551 : ; 3 "p 4. 75 As 7 4 1 7 de 
V 


. 1 2 224 8 A . Af 5 
Sat, i 577 © E {© I * + 91 ll Z + * . 


M; eee 


(21) 


4 
” 
12 
_— * 
1 F 
& W ig 


. — 


— — 
2 — 


—— ä | 6. 


22 Rs ” — x —— re 
mg > — —— — * 4th 
— P 


mn > ANY EY: ben fie 448 — I B-- - 
- — 2 ˙ „„ 


\ 


— 


by heart, Br eed to the A oe of Ope- 
ratir * he Numbers to be multi- 


plix "ut þ Act one under the other, it 
- ap wn herher the greater be upper 
of love Hhete 19 place Unites 
al 3s c. tho for 1 hods ſake 
we commonly ſet the bigg 77 a- 
d. ther unde . placing U 
ites, Tend under Tens, Nc. 


ut bo being thus placed, as in 
49% Examples appear, I begin 
0 times 9 is 


36, I et down 6 and ſry Y rd times 


nd carry 
Es a 18 8 111 18 1 1 that is 
then 4 times 6 is 24 and 1 

wn 5 and garry 2 3 next 4 
ES 5 is 20, and 2 is 22, that is 2 and 


rr, 2, then 4 times 3 8 12 21475 is 14, 
h I fre "Hwa. it mak Produk 
92116; L Is the Gelee n | finiſh d. 


31, ſer 


4 2 «ring, 236891 
| * 2 


£58 


In a * 2, 1150 . 
ee ure next the right 
Jang is 10 Pic dae Fe gon r was in the 

mul 


D 


_ cu r 


C), 
multiplication of one figure, the product 
of the ſecond figure mult be {ſer down un. 
der the former a figure ſhort, that is; the 
firſt figure:in this produ& muſt be ſer un- 
der the ſecond. figure in the kt product; 
and ſo if their be 3, 4, Or more places in 
the Mwiphor, you mult (er the firſt Figure 
of the third product a figure ſhort of the 
ſecond, and the firſt figure of the fourth a 
figure ſhort of the third, and ſo a figure 
ſhort every line, that is, Unites in the later 
product maſt ſtand under Tens in the for- 
mer, obſerving alſo to 7 the Figures 
directly under one another. Having thus 
gone throꝭ all the figures of the Multiplyor, 
and plac'd them as before ditected, caſt 


Ly 
8 
* 
2 


4 * 17 7 : 1 — 
F T x . , 7 „ , 7 4 „ 
23 1yY 2: ef ; 
— 4 x — * — P a” i + ” * by 
3846 Eo 
4 ö ow” #1 ” . y 1 * 1 * 
7  ® - — , 4 * * _- 
6 z4 4 
7 6.6 # . 6 „ 6 * — 34 — 
4 4 £ ; + 2s 1 * 

1 a U f 2. 

4 CF . : ; Pr * 


* * 

» % 
- 
* 


r = As 
£1.51 Fit 
3 04 S# $4 $32" 4 && 


r N m— 
22054 


42 
wa 


«KJ 
* : — FO * * 


* 
k 


5 6 
Pi; I. A £17 


a y ene in kiakiphear 


* And here obferve, that if the Murih f 
* gand, or 12 or, or both, have a Cypher 


— —— = 


75 
2 
1 


EOS — r n 
of ood * a —— 8 ba g id 


i MO in the laſt lace, you need on- 
[> Wd nods by the 12 ſetting the 
| Auer of .Cyphers that are both in Multi- 
Wi licand and Mu rip) yor, on the right hand of 
il ; ti product of che Figures, and it will 
| Bie the Product oe the propoſed Qgan- 


b 


- I Hence tis evident, That t to \ Multiply 2+ 
ny partct of Figures by 10, 100, 1000, &c. 
zs only to put one, two or three Cyphers 
at the end, or right hand or Pe for af 

will make che Product. 


186900 1000600 


* G . L was . " 2 7 * * 
. **. * , . 4 — 
* % 1 2 r 4 4 4 a — - 


3 = * 72 
econ 
ö 5 * * 1 
9 . * > 2 * 
* . \ 


C 
Slͤecondliy, If you would multiply any 
Quantity by 3, Add a Cypher at the end of 

it, and then take half the Number, and it 

ſhall be the Product required. Sce the fol. 


8 lowing Example. 
| 36792 0 e | ae 
_-_ g67920- 


e . 
Thirdly, The preceding Table being 
perfectly learnt, tis eaſy to multiply by 
10, 11, Or 12, and make but one Line; as 
ſuppoſe 432 to be multiplied by 12, then 
inſtead 3 multiplying by 2 and 2, Multiply - 
by 12, ſaying, 12 times 2 is 24, ſet down 
4 and carry 2; then 12 times 3 is 36 and 
2 1 carried is 38, that is 8 and carry 3; 
Laſtly 12 times 4 is 48 and 3 is 51, which 
31 I fer down entirely to the 84 it makes 
$5184, the Product of 432 multiply'd 
A „ 


Wag - 


5184 


 Fearthly, If there happen a Cipher in the 
middle of your Multipher you need do no 
pore buy put a Cipher under the fecond 


2 
"HEN 


\ 


EO Rs... 
% . 
\ 
1 


(26 ) 1 
Figure of the preceding Product tp fill up its 
room, and ſet down the firſt figure of the 
next Product on the left hand of the Ci- 
pher in the ſame Line J as is evident by the 


Cre 
che 
fol 


— — tan} > 
* 26> ways 
& * 2 


following Example. 
2 O4. 


* „ ts: 1 were 


2172 
| e 


. — — — — a, 3 — OE = = 


Z 


7 — — 
— 


; 5 8 71 
e eee 


9 


4 A «ih £ 
2 9 
* 


. x 
2 7 48 3 : CLE + 
+ 1 * F . 2 > * * : 
"Er. * 3 P oa * 
{7% . CE 
6 7 * 
% "4 * 2 vs i -$ * 1 ” * 
\ E $ 4 L : 4 1 
RO "= —. "> $ d 4 1 
ON 6 
- 
” OO" h 19 
” 3 ! . E 75 2 M 
WY = - *. XK wa * , OP 1 g 
£ * * * 


3 — 
4 —— * * 


* 


j . % 
a 0 \ 
: { -3 > ? 
4 , a 
2 : 6 * { 
i io r a + Sx f N . \ 
* 2 ; * . b « 
7 4 | a % 4 * . E „ * * * 77 * # * 
PF — " 


£10743 VC 
The trueſt way to prove Multiplication is 

by Diviſion, but that being not yet learn'd 
cannot be uſed, and therefore I ſhall ſhow 

. x common way by the Croſs, which is 

12 Ns, 5 21 4 be 0 a agrees B-'y 93306 | 

1 Make aCrofs, then caſt away 9 ſo off, as 

you can out of the Mwltiplicand, and what 
remains-fet on one ſide of the Croſs, do the 

like by the Maltiplior, and ſer the remainder 

. on the oppoſite ſide of the Croſs, multiply 
theſe two Numbers together, and from the 
Product caſt away all the 9's you can, the 
remainder ſet on the top of the Croſs; Laſt- 
Jy, caſt away the 9's from the ER, 


= "0 
- = _ _ 1 
—— - — — > =p f _— « l , l 
- a a RW 1 — 2 83 0 1 = 
ad a * = . - — N * ©” - - * * 
— * - . — 
— < +: doom * , * _ * 
a - a — a 
> 1 a 
— — — — — « P 
8 - - py . 5 
. * - 
. 


ol 


what remains ſet under che Grofs, 1 


A 


—_ — = — 4 - 

eat ro em— gh Eg 
Cot _ 
1 > - r= þ x : 
5 __ RAE ENERGY - 
* 
5 

* = 


* 
— 8 — — > — 


— 


be 
of 


the Figure at the top and bottom | of 
TY 22015 Kroß 


7 © s . 
#4 K - 
* 
Set 


— nn, - | 


A 
Croſs are the ſame, the Work is right, elſe 
there is an Errour. See the Proof of che 
following Example. 


e 
1101 
; ; . p 

33948; | 


Ie Bae, 


0 NI 


1 a Traveller goes 29 Miles in one Day 


how many Miles will he 8⁰ in 17 Days? T 


Anſwer, 493 Miles. 
f 1 gave 35 l. a piece to 796 Men, bow 
much was the whole given away. Anſwer, | 


28860 l. 


A certain Summe of Money is divided 
betwirt 98 Men, their Shares came to 14 l. 


each, how much Money was Diſtributed 
in all? Anſwer, 1372 1. 


The Share of che Cargo ta a Ship is e 
qually divided betwixt 178 Men, each 
Man having to his Share 37 J. What Was 
the whole ee in the Sp Worth! A Ax 


en UL} L. 


. 
„ 


"el DIVISION 
; F Long 2 2 +3 3 


— 


A . 


: 
; 

& 
= * 
11 
4 

* 

* 

* : 
\ : 
14 : 
_ 

17 
4 : 
. « 
? 

x 
vi 
7 
[ 

— * 

i 

, 

1 

i 

5 : 
= 18 

= 

g / 
1 

. 

Ly 

4 
l 8 
| 19 
El 
bl 1 5 
19 

, : 

4 4 4 
+290 , 
+. | 

* 
1 
19 
1 | 
+, 4F 
n 
* : 
w" * 0 
i 1 

$ ; 
a 21 

341 

11 
1174 
1 

I 

1 

1 . 

tif 

| 
. 
= 

or 

1 

. 

i! 

= 

"73 

+ X 


— — 


= — — 
— — 
— — — 


r 
— re = 


— — 


Number to be divide 


T undoes Nultiplication, and performs in 
ſhort the Work of many Subſtractions, and 


Feacheth to find how often one Number cen- 
rains, or is contain ly another; or it ſhow- 


4b bow to divide a Number into any equal 
| * : : F 


* 


* 


by 3, that , tis required to find how ma- 
ny z's there Are in 0 5 Here 12 is the 
7 


As ſuppoſe 12 was given to be divided 


8 to be divided, apd is therefore 
called the Dividend; The Number 3 is that 
2 which we divide, and therefore is cal- 


ed, the. Dior : Laſtly, the number of 


Ames that 1 2. Contains. 3 (which 18 4 N is 


Called the Quore, from Quorres, becauſe it 
ſhows. how, oft the Dividend contains the 


Diviſor; and if any thing remain after the 
Diviſion is ended, then is uch Number cal- 


led the Remginder. r. 
Hence it follows, that fo oft as the Di- 


vidend contains the Diviſor, ſo oft doth the 


Quore contain 1 or Unity. 


* * 
4 2 5 25 « 


4 
» 

F \ 

— 


2 


„ * 
— 


„%%% „* 


thod is as follows. 1 
Plüace the Dividend between two crook- 


1 7 as 


* 8 


or (from the Principles of Multiplice- 


tien) that the Dividend contains the Quote, 
ſo oft as the Diviſor contains Unity. _ 
From whence tis evident, that if the 


Diviſor be leſs than Unity, the Quote will 


be greater than the Dividen. 


As alſo, that if you divide any product 


by the Multiplior, the Quote will be the 


the Multiplicand, which is the ſureſt Proof 
of Mulriplication. s. 


| Rule. The manner of operating in this 


Rule, is differently ſer down by ſeveral Au- 
thors ; I ſhall not therefore enlarge upon 
the Rules and Directions of each particular, 
but ſhall proceed to ſhe w you the plaineſt, 


and that which is moſt uſually practized in 


the beſt Schools, and by thoſe who are 
converſant in ſuch Operations, which Me- 


ed Lines, and the Diviſor on the left hand 


of the Dividend, as in the following Ex- 
ample; this done, obſerve that in work- 


ing Diviſion Three things muſt be particu- 


larly heeded, wiz. Firſt, to Seek ; Secondly, 


to Multiply; And Thirdly, to Subſtra : 
This noted proceed, by Asking how oft 7 
is in 8 (the firſt Figure in the Dividend 
the Anſwer. is 1, this I fer in the other 


crooked Line; on the right hand of the Di- 
vidend; then 1 7 by-1- gives 7, 


which I ſet under 8, and Subtract chere. 


(30) 
from; the Remainder. 1 J ſet underneath, 
and to it bring down 4, the next figure in 
the Dividend; then I ſeek again how, oft 
7 is in 14, I find 2, which I ſet in the Quote 
on the right hand of the former figure 1, 
multiplying 7 thereby which gives 14, 
this Subtract cherefrom leaves nothing; 
then I bring down 6, the third Figure in 
the e and becauſe I cannot take 


7 out of 6, I {et down o in the Quote, and 
Prin down 2 the laſt ſigure in the Divi- 
dend to 6, and ſeek. how oft 7 is in 62, 
which I find to be 8, this 8 J ſet in the 


duct 56 1 ſubſcribe under 62, and taking 
it therefrom. leaves 6 remaining, and gives 
1208 for the Quote; all Which plainly ap- 
pears by the firit of the following Examples. 

And here note, that if the Remainder is 
more than the Diviſor, the work is not 
rightly perform'd: But this Errour is eaſi- 
ly. reQtibed, by taking either the laſt, or 


v 
. 


ſome other figure in the Quote 1,2 013 more. 


eee eee 
FF 1 8 | 


J i 7 2 — 
1 by Ju þ 0 A x 
PE + 34+ 44 55 $4. 4% 01 
/ | 4 7 21 
I * > 1 ö 
eee i 
s 2 p . 
* N 17 * 1 * 


A 14 A * * 
: Py * k * 7 
# EL STINET > (IL Qi 
. a 4 Ss S J 7 *; þ 
75: 12 39] 4.- Hf13: , * A Sd 
THY 


. | S&T 

nan it 23 0 5100 

* 24 * . 72 * 7 75 8 ＋ 

niyiqnium ;: busbiv 

1 1 ' k 1 * by 

ln 6 obnigfet ide 
* FA 


36 7 whel 
> SR tos 
48 FRI 7 66 34 * Zh 


. © SY | 
| | 2 In 
n Na 
. OP: 4 14 ; 
= * 4 T4 


im Dividing 


> 
— 


gures there is more difficulty, the reaſon 
of which I conceive is this; there is no cer- 


rain Rule can be preſcribed to know what' 


Number of times upon each Demand the 


Diviſor is contained in the Dividend, till 


you have made a tryal, by taking the firſt; 
figure a certain number of times, and then 


trying whether you can take the product 


of that figure (thus found) into all the o-. 


ther figures of the Diviſor, out of thoſe 
f idend, which ſtand over | 


figures in the Div 

theſe figures inthe Diviſor. 
The manner of operating, when we di- 

vide by ſeveral figures, is thus, Suppoſe I 


would divide 3278 by 19 ; having placd 


the Dividend and Diviſor, as in the laſt, I 


ask how oft the firft figure 1 is in 3, which 
is but once, for there is but once 19 in 32, 
tho there is three times 1 in 3 ; Dy this x 
Pro uct un- 
der 32 the firſt part of the Dividend, I ſub- 
ſtract as before, bringing down to the re- 


I multiply 19, and ſetting the 


mainder 13% tke next figure in the Divi- 
dend which is 7, juſt as I did by dividing 


13. 1 find but'7 times, for if Trake's timeg 


in one figure; then I ask how off 1 meg 
tlie remainder 37 will not be faffitient rs 


rake 8 times 9 Hut of (for this isthe grea- 


wal bear it) This'7 1 ſet in the Quote, ani 


Fd 


- 


by two, three ot four Pi 


I 


reſt difficulty, vis roknow When you take” 
he firſt figpre. Wherher the cond figure; 


4 
\'Y 


multiplying thereby, ſetting 133 the Pro- 
duct under the former Dividend, which 
done I ſubſtract it therefrom, and bring 
down 8 to the 4 remaining; ſo then it 
will be the Ones in 4, or the 19's in 48, 
which is 2, this I ſet in the Quote by the 
former 7, and multiplying 19 thereby, the 
Product 38 J ſer under , and Subſiract 
it therefrom, ſo is the remainder 10, and 
the Quote 172, as appears by the laſt of 
che following Examples. . 


38) 4896 (s 15) 3278 (171 
6.T r! oe IE. 
9 „ 137 
76 e 
. e 
| 335 048 


* 


. 
1 
> 2 

* 


gfe 01 l D iN Eh Bet 18121 
5 Abreviations in Diviſion. Parra 
F the Diviſor has one, or more Ciphers 


1 in the laſt place, that is, on the right 
hand, then for ſo many Cyphers as there 
are, cut ſo many places 7000 the Dividend 
toward . band, whether they Be 
Cyphers, or Figures, and divide the re. 


- 
- 
of * 
* 
* 
I 


© +4 


| maining Figures in the Dividend, by the 
* remaining Figures in the Diviſor, and it 
ch vill give you the Quote of the propoſed + 
'S Gan las: | 


Example. ö 


+ ä po) 85H C 


as * * * 
bs 
* ; 46d 5 
1 N * 4 ” + Z + 
a an l — 7 | 1 

* . : x : 8 

# % s 4 * ” : i 3 as 
i : 1 { j MY 

" * 
* * 1 
: 7 4 "4 
1 * 


f e 


14 ADS 
AS}: > 
R 


—— nas 


— 


But here obſerve that whatever Figures 


were cut off in the Dividend muſt be 
brought down at laſt to the remaining Fi- 


» BB gures in the Diviſor; to compleat the 
: whole remainder, ſee the preceding Ram- 


ple. 


as of "WE 


' parcel of Figures by 10. 100. loco, Cc. 
is only to cut ſo many Figures from the 


BY right hand as there are Cyphers in ſuch Di- 
f | Viſor, fo will the remaining Figures be the 


{ 


. Quote, 


Hence tis evident, that to divide any 


- , as * 3 
f 3 ef 
1 S we. 


— 
— 


* * — N 


CES R 9 =P = nr q 
nnn bo ond; > AR 
3 * 


1 * 3 4 2 — yr? * Re nn * — 2 * . a 
=>. p BY x RE - FR. - 2 1 3 
* . " ; 5 . 1 , i 
3 — ae d 7 2 » — * 
1 e * 0 3 N 2 
X ; : * : 3 4 o 2 N - 8 
1 p * 1 - - b ” * n= #7 f 1 * CT . £ 5 * 
W 5 1 wi 7 =, 
. : : — * * 
* "$2 po 25 1 i n 4 
2 % * 4 . 
pt * 4 ” 4 N 7 
= * * ? 4 
= — — 
* : 4 | Xt 
** 1 . 
. 4 
| 


? * ] 


-» 
”— 2 "a „ __ o Py l 
I "A% ENG SIE,” * How road GE, Hons 
8 _ — 
- l * * * * 
% 


: 
4 
"i 
; 
* 


W 
(34) 

Tn. | 
1]000)68921136(6892// 


8 To dividing by 2, 3, 47 57 6, 7, 


3, 9, 10, 11, 12 there is a ſhort. practical 
vay (now frequently uſed by great Clerks) 
by which the multiplicity of Figures is a- 


voted, and only what's abſolutely neceſſary 
ſet down, the manner of it is thus. 
Example, Divide 756469 by 7, having 


ſet the Dividend with the Diviſor in a 
crooked Line, on the. left fide thereof 


draw a Line underneath, then enquire how 
oft 7 in 7, once and chere remains o, next 


| hes 7 in 5, no times, next the 7 in 56, 8 
times, then the 7 in 4z no times, next the 
+. 46, 6 times, there remains 4, then the 


in 49, 7 times, there remains nothing; 
all theſe Figures of the Quotient I place un- 
- derneath the Line, as in the following | Ex- 
ample" more ry wall appear. 


1756469 5 8584320 
108067 | Y N 31666 2 rem. 


aftly, Before I proceed to the proof of 
Divil „I shall inſert a Specimen of work- 


Ing one Sum in Diviſion nine different 


N 5 


| : | : : L | * 


+] * | N 


£" + 9 
„ 3 
3 1 * 


e 
3244 
298507 


26666 26666 © 
222 >, oO. 


2 
2 


2 — FL 


- "I0N7- -.., T 
2603557501371. 260 35679(1 372 bi 
| 785 _ ; 


r 2 
1 4 4 
s | ? 5 % * 


% * 


the two following are the alias ways of 7 
working Diviſion one of which they cal! 
the long the other the ſhort way, —_ 


49356750374 . 20356701374, . 


22ͤͤ Pines 188 


| $6" HAIG — IB 
| n ©, 
5 A» 2 


=. 
l * E | 9 p 9 4 ha 
« & d lth j 3-4 | A . 4 4 | | 
© . 1 4 : — "_ 


F | * 


N = n 
0 m eee on ge nee eo eo re eee 
* 1 * * K * en * " y e 
: * = . = . 9 N 
* 
5 
F * 5 
x 


F by 


CIOS: 
287” 
| e 
28807 | 2985077 
chere, eli: 


The Proof of Diviſion. Toe 


Ne Proof of Diviſion is by Multipli- 
cation, and that's Infalible, for ſince 


the Quote ſhews how oft the Diviſor is 


contained in the Dividend; therefore if the 
Quote of any Diviſion be multiplied by the 
Diviſor, the Product muſt be equal to the 
Dividend, only if there be a remainder, that 


"muſt be added i in when you multiply. 


There is alſo another certain way of pro- 
ving Diviſion, and that's by Addition; for 


*ris evident that the ſeveral Products of each 


particular Figure of the Quote, multiplied 


into the Diviſor With che remainder added 


togetker 


NO mY 


7 „ 9 


* ; 
N 
by os 
\ ( J J 


together, as they ſtand in operation, will 


make up the Dividend; all which is evi- 
dent by the following Example, where I 


| have noted the ſeveral Products which are 


to be added by the Letter a. / 
A third Proof of Diviſion is by the Croſs 


(thus) we: caſt the 9's out of the Divi- 


ſor, and ſet the remainder down in one fide 


of the Croſs; next I caſt the g's from the 
Quote, and ſet that remainder in that 


part of the Croſs oppoſite to the for- 


mer, theſe two I mulyply together, and + 
having caſt the 9's out of the Product, I_ 


add the overplus to the remainder of the 
Diviſion, the Sum if under 9, elſe the ex- 


ceſs above 9, ſet down in the upper part ef 


the Croſs, then caſt all the.9's out of the Di- 
vidend and if there remain the like Figure 


there did in the Quote, the Work is right, 


% 


3 


„ (360 


ee the in We ple e 2 iche 
oe GANT | 


and ty 


4 9 


4 8 
NP * # ' 1 * * k i 
& 3 4 k . ads 1 * "ip N ; 
1 * - % 
9 * * 
8 Þ * * * 3 4 9 of 
7 4 * : ” 4 9 "ip 6 a 
+ =y — j * ö 
” : * \ 4 


ö 
2 5 LY 


EEE C 


'e ee N 286766 i 
@ 156 61458 


0 7 


f 

* 

4 | — — 
: — ty Fl T 


<4 5 N 


* * 
» 
»*, #5 9 3 | . x 8 5 
f 1 $921 f 312 
3 8. 1 1 . 


= 


"Als Examples 


If 3 in 17 Days I Travel 49 3 Miles, how 
5 Miles is that in one Dy ? ye, 
5 Mikes. F a 

278601. be given. away to 2 certain 
- wrmber of Men, cach Man 35 J. how ma- 
5 __ will it ſuffice 2 Anſwer, 796. 8 


7 vir „7 ' BL „ , "Ori f 5 
In 


ee 


ww 0 


; a" 
Pg wt 
F 


1 
In 7656 $hillings, how many French. 


Crowns, each Six Shillings ? Anſwer, 12.76, 


The Cargo of a Ship is valued at 6586 l. 
this is ro be diſtributed equally N 176 
Men, what ſhall each Man have for his wars 
Anſwer, 37 J. 

The ſhare of the Cargo of a Ship is worth. 


65861. and having counted it among them 


ſelves finds it comes to 371. per Man, the 


Queſtion is how, many Nan there was in 


the wth ſaver; ag 


Kela, on. 


EduRion'i: not 8 any real Rule ho” 
Arichmetick, bat rather an Applicatien 
of Multiplication and Diviſion, by which 3s 


pen how to reduce or change any number of | 
pieces of Eopne, Weight, Meaſure, &c. from 


one Denomination to another; which thing is of 
great uſe amongſt Tradeſmen i in common Buſineſs, 
and ſometimes this is from aleſſer Name to 4 


greater, and [ometimes from a greater to 4 leſ- 75 
ſer, for the performance of which obſerve. 


Firſt, That all great Names are brought 


into leſſer hy Multiplication. 


Secondly, That all fmall Names are 
brou But into greater; by Diviſion. ; 


ev | 
*X Fd 
, * 
\ 
WIEN. £ 7 1 
ZE 7 : ; = K 3 =. 
* 


1 


640 
Thirdly, That the Dividend and Diviſor 
muſt aan he of one Name, that is, borh ec 
Shillings, both Pence, both Ounces, both Quart:, 
Ge. and that the remainder is of the 
fame Name with either of them, to clear b 
all J ſhall give an Example that will con- 
tain both Gaſes, with wont and Notes t 
upon the ſame. : pn: e 0 


4 V3 neat 130 ack — ar 
1 8 1 20 (17.64. arr. 


. 10 


—_ | 340472 Piſtoles a at Uo 
Wo "175 64. — Dantip. 
+ "> T3 
be ente, Sassen lese | 


. 


» — — 1 * 

2-Þ* — n 1.8 — 0" 
N 0 er m ” _ — = — 

- — = > — — rr drr 

— — ——— — —— 3 - * — — 

— —— — ä H— n — — — — — — 

12 | * we 7 4 2 3 K. 1 hc * 5 * 
5 — 0 g 

. 1 * 1 
5 — 


— „ * 2 * 
— 2 by = Fu: Wa * * — Ce” 

— Gag — — 
2 —— 09h —— — — 
8 —— ex EIA — — — 

* £ et . $ ON * ” * 
* 4 8 
7 2 
* 4 . — 


* 


. „n 
Firſt, Reduce the whole Sum of Money 

to Farthings, by reaſon one of the Deno- 

minations required have odd Farthings in 
them, and this is done by Multiplication, 
becauſe tis a greater Name to a leſſer. 
Secondly, Bring each particular Piece to 
the lowyeſt Denomination tis mentioned to 
contain. TS. TSR 
Thirdly, By the number of Shillings,Pence, 
or Farthings contained in any one Piece; 
divide the number of the fame Denomina- 
tion contained in the whole Sum of Money 
propos d, the Quote is the number of Pieces 
contained in the ſaid propoſed Sum. 

But to be a little plainer ( becauſe I ſhall 
not give more Examples of this kind) Ifirſt 
multiply 3547. by 20, the number of Shil- 
lings in a Pound, taking in the 13 Shillin | 
this brings them into Shillings, which Shik 
lings I multiply by 12, becauſe 12 Pence is 
one Shilling, adding in the odd 2 Pence, this 
brings the Shillings into Pence, which Penee 
1 multiply by 4 tobring them into Farthings. 

' This done I take out 340472, the Far- 
things in 354 J. 135. 2 d. and divide them 
by 840, the Farthings in a Piſtole, it gives 
405, the number of Piſtoles in 3541. 13 5.24. 

or ſo oft as 840 is contained in 340472 ſo 

| many Piſtoles is contained in 354 J. 13 5. 2 d. 

ö Again I take out 340472; the Farthings - 

mn the aforemention d Sum, and divide by - 
5, the Quote gives 68094, the number ß 
antiprats Contained in the ſaid Sum. BD „ 


32 7 


= AS 


een 
B 
* WAN 2 80 N 3 
2 COR IND or WT" 
CCC 
„ TXT rt Cp a = n 
7 2 n 3 ö Y IMS 
54 n of Ie 1 7 1 TS, 1 
n x9. 4 ern 8 : 0-4 
JC SE ON en EE To Ges 
l N . 


f 1 i W 3 ghd. + A * =, 
4 2 y | 2 , . 

_ . * 4 8 > . 

| 4 kJ j Ms. * . , % 


"Tad *- 
- But Note, that if I had divided 85 118, 
BE. the Pence in 354 l. 13 5.-2.4. by 210, the 
Pence in a Piſtole, the ſame Quote Would 
have come out as in the preceding. In like 
manner, Mutatis Mutamdis, may you re- 
duce Weight, Meaſure, Time, Sc. Hoo: _w 
— to another. 


X | 3 The- Proof of bit Rule. aid ; 


1 ads no. e e of This 
| Rule, but to take care that your Multiplica- 
; un and Divik ions are truly W 3 


— 

— ><. 22 K 1 ey \ 
I ES ERES = — FE ee RS — | D > 13 
— . * — — ny > — —_— — 1 * — 222 — —— = — a * ” 2 * 

— — Eten ̃ es ——— ß —.— —̃ — — 8 — nos edn —— — —  — x > 
© deem IR ALS CA R—w2 10 Gaag 4 14 — 2 \ w S r e ' 23 3 — * = Dal 8 
L * n E oy PE * 3 * n KY OT SIS BY - * * * * * 4 7 

A R * | 1 mne en 
; ** 0 3% 6 
a % 1 * : a 2 +> 9 * 
4 s 4 
F 1 = 1 4 7 . * 
0 * - 4 
* y - 
* : * 
1 - 
* 1 
% 


"Mord Examples. 


bl | "Dn 2374. 105 34 bow many Piftoles 
—_.-*. at 17 4. 6 d. and Rix Dollars at 25 wap” 
1 | 2251 271 Piltoles nt 7 nn 

| '$ 1142 Rix Dollars. 

In 598 Piſtoles, each 17 . 64 10 ma- 
ny Pounds Sterling, and Guineas at 22 5, | 


Anſwer 2 ne, 


— — * 
> = r 
— Ak de ac 

a IEEE 

© Fa 
1 


Guincas. 
In 683 1 of Eight, each 74. ly 
how many Ducats N. 4. 1 d. and Are r 
Sterling? ; 
1 Ae le r 
= Note, In theſe Queſtions x is 8 
= thing commonly 3 _ ee 
N Pee Mr” 7 


% 


e 
e 


2 — wn. 


a 3 * a 


T Je cal, Por or Rule of 


Tyre. 


Bl, * called laue it teaoberh bow * 1 
| three given Numbers to find a fourth, = 
greateſt difficulty in this Rule is how I 
to Fon Queſtion. To do which -obferve 9 
that the firſt and third Number be of one na- 4 4 
ture, that is, if the firſt is Money, che third . "= 
muſt be Money. If rhe firſt be Weight, the 
. third müde V Weight. If the firſt be Tus; = 
'F che third muſt be Time, Ge. _ == 
| The ſecond Number muſt be of the ſame | f 
Nature with that requir'd, which is the 
fourth; and therefore you cannot wellniiſs 


* Y 'P 
„ 


& 


placing the ſecond Term aright ; the third 

Term or Number is always known by its Y 
being immediately placed after bow much, 
what  coft, what will, and ſuch ne Word — 
that ask the Queſtion. 5+ - _ 
The Queſtion: being Stated, the firtand BR 
third: Number muſt be brought into one 7 ' 

Name, and the middle Number muſt be re. 
duced to the loweſt Name mention d. This 1 
done multiply ſecond and (third Ter, 
ber when ſo reduced; the Produft divids 


K the fe, rhe Wore gives "ths; Aufwer, | 


= 


* 


(44) 
fo the Queſtion, „ in the ſame Denomination 
as in . you — of d it zt the 


Fr ri. 
18 F oſe 35 U 165. 4d. * 3 Ells of 


Cloth, what will 3 Ells coſt at the lame | 


Race : 5 | 

In this Queſtion the ſecond term muſt be 
Money, becauſe that requir'd is fo, the 

| rear term muſt be 3 Ells, becauſe that inime- 

diately follaws he Words What will, that 

ask the Queſtion, and by Conſequence the 
firſt term muſt be 86 lle it being the ſame 


with the third, and therefore T ſtate i ir thus, | 


If 86 Ell——37 15 x6 Fo 443 Ell. 


The Queſtion being thus stated, L reduce 
che middle Number into Pence, the loweſt 


Name mentioned, by multiplying by 20, | 


and then by 5 This done multiply this 


laſt Product by 3. The Product which is 


27228, 1 divide by 86, the firſt term; the 
Quote 316 is the Number of Pence. {the 
Name I left the ſecond Number in before 


I multiplyed by the third) that Anſwers the 


Queſtion, which may by Reduction be 


dDrought into Shillings and pound which 


18 done! in the 3 operanion. of 9 


i 
ir 86 Ells coſt 37 4 16. 44 whar con 3 Els, 
e 


| 16027228031 756 : 
— q 12 LES 
. 
Soom ' Au, ⁊ 165 a 
568 2 e 4 * - Gail 
; Sn — ! 


BF... 27228 


Over and above the 1 45 44. there 8 
is a ſmall remainder, 2 is * Fracti- 


onal part of a Pen. 
The Value of which is found by multi- 
| wh the remainder 52 by 4 and dividing 


y 86, ſo will the Quote be 2 N 
W . FraRtional pa beſides. > FIR 


337 
— & *-4 » 


_ The Pro f f this Rule. 0 


. 


_ Proof of this Rule is alma "RR 
Hol the reaſon of the Anſwer ; for if at 
the rate of 86 Ells for 37 I. 165. * three 
Ells will coſt 1 J. 65. 4 4. then, at the ſame 
rate, When 3 Ells ct il. 65. 4d. $6 Ells 


Will coſt 37 J. 16s. 4d. Wees tis but 
back ſtating the Queſtion, and ſaying, If 


3 Ells coſt 1 J. 65. 4 d. what will 96 Ells 
colt ; here working as before directed you 
thall _ 37k 165, 44. the given Nice. 


| 


\ 


—_— 
— . 


r 
n 


<1 4 


#4 9 


1 (460 
8 of the aforeſaid 86 Ells, a6 you TOM the 
= following Operation, which is a ſure Proof 


_ of the Queſtion. 
if; Ells col 11 6544 2 wh ted a: . A 
: 2 5 3168 ä | | 1 


„ 776 TE, | 


% : | Rs - 36 : REESE — T 
3 3 ig 2 _ AG 


C 
316 | — — — — i 
1 e 1 

4,29 Hi ORE RS. : 52. 1 ca 9 3 | 7 
27228, ck Ty ; ( 
"hes: Jets Note that in the. preceding 4 

=_ ion there remains 52 after you divided 
| >. oe product of the ſecond and third by the | 
5 füirſt, which 52 muſt now in the Proof be 8 
added to the product of the ſecond. and 
third before you 5 by the firſt, 8 
By obſerving Hirections may all 
Queſtions in OY Rule be ſolved, only in 
ſome there is required the Addition or Sub. 
traction of two Sums of Money, ſometimes 
before the Queſtion is ſtated, and ſometime 


moi till ander che eee 1s n ; 
| , * 
6 129 > ” 
* I 
8 5 
2 —— = % 
\ 
— * ; — 
* — 
= . a 1 


n 


fer, 1524 425. 


7 
1 — 


e 1 and Fe. Beavers coſt 1 19 f 
4d. be muſt I] fell one Beaver ta gain 
1 J. 10 s. $4. by the ſale of the whole? 

Before I ſtate this Queſtion. I muſt add the 
Money I am to gain, which is 15 J. 10s. 84, 
N Tp 5. 4d. the Money the Beavers - 
coſt. 

Again in this Queſtion , Bou 1498 
Pound of Tabacce which coſt 53 phe 17 1 d. 
and fome damage —— to it, I loſt 
13 J. 15s. 2 d. by the ſale of the whole, the 
Queſtion is what one Pound was ſold for? 

Here 1 muſt ſubtract the leſs from the 
prime coſt of the Tabacco, and then ftate 


the Queſtion with the r by fay- 


3 


and ſuch like Queſtions are ſuch as require 


ing, it 1498 Pound coſt. the remainin 
Money, what will one Pound coſt? Th 


ſome ſmall Operation before you ſtate the 
nei in onder for irs Solution, N 


More Examples. 


aL 3 oo 
=» 4 


If 1 ſpend 55 3 d. in one, Day bor 
much is e in one Year? 20 Se 


951. 16s. 3 


If an 8 "of Silver coſt. 44. 8d: T. 
how much will 3587. 2 2 24. buy? An- 


"+ 


— 92 F *. 
* * 7 e . 


„ hy 5 N 
- ST « : * 


%. 


6 


. 


1 
LT 


95 Ty * — 99 ** R 8 * . 
k, * . 4 wy ö 
iS. 9 * 1 * * 
1 | wp TIT 
k * ; 
a Fed 
— * 
* 7 7 
. W 3 a 
1 1 
* 48 


Ĩ 397 Ellsof Cloth colt 86 14 24 


What colt one Ell? Anſ. 4s. 4d. 1 1. 
If 97 Dozen of Beavers coſt 679 l. 19. 
44. how muſt I ſell one Beaver for to 
gain 15 J. 185. 4 d. by the ſale of the whole: . 
Anſwer, 11 5. 11 d. 383% © E 
' Bought 1498 Pound of Tabacco which 
coſt 537. 175. 84. and ſome damage hap- 
pening to it I loſt 13 J. rs. 2 d. by the ſale 
of the whole, the Queſtion i is age nd one 
Pound! was fold for? Arſe 6d. + $3S% 
A Gentleman's daily . Is 135. 
5 d. æ, above which ke lays up 150 Nobles 
_ Yearly, the Queſtion is what his Eſtate is 
worth per Annum ? Anſ. 298 J. 5 5. 6 d. . 


If buy a piece of Cloth for 37 J. 18 5. 2d. 


and 1 ſell one Ell Exgliſh for 18 5. 3 d. I 
demand how many bor gy were in the fie 2 
N 519. 3 4 575 

Beſides theſe there are other Queſtions, 
_ ſome of which require two, others three or 
more Operations of the Single. Rule of 


5 *.. Three, which ſome Authors put under the 


Title of the Double Rule of Three Direct. But 
: becauſe their Solutions depends only upon 
the Single Rule of Three, I therefore thought 
Ir molt proper to place them money 5 they are 


„ 2 followeth. 


A Gentleman's Living is Wel 4361 
14. Cd. per Annum; how much mult he 
ſpend Daily to lay up — 50 af 45 1 
_ Anſwer, 19 5. 8 d. 25%. 


Fe ments, to 1 om 
. 


r 


weight of Tobacco in the Ra to be Cur 
and Dry'd, and when it came home it hold 

out but 6178 Pound, I demand what is loſt 

in the Pound, and ſuppoſing it 40 inme 
Roll 10 d. „ and the cutting 1 „ What 2 


the Pound, and ep reſt in Wine at 141. 12. 2. 


Goods muſt he receive for r. Satisfach 


and C to have the fourth part; what muſt 22 


. e 2 


Direct: In which the greater the chird 
- Number is, ſo much the 


1 


12 5 7 n 
A. PEE delivered RE Pound . 


it now ſtandeth him in? aer 3 Oz. . 


. and 389 J. 10 5. 3 d. 


K Merefant ſent Goods to Spain. ro the _ 7 
value of 76 3 J. 105. to have Returns. from 
thence, the q in Spaniſh Tobacco at 74. 9 


the Tunn; how much of each of heſe 
ion? be”. 


Anfwer, 656 J. 35 2. 34 Ton. 454, 
There 1s 1807 6 g. to be Givided . mo 

tween three Children, A is to have the 7 2 

half of the Money, B is to have the third, 


each Child have for his Portion? By” 
831. 4s. £3434. 551, 95 24444. 4 1 
4 046 Ze, 


* 799; & 


The Rule of Three: 


Erg fo called ne it e Wa 
or Contrary Proportion to the Rule of Three 


greater will the 5 5 
ſourth be; bur 8 the * the 3 


+ 
I 


— 

. 1 * - e ; # . . * 8 N 
_—_— wo Mb” 2 - NT 4 , 
£6 2 : 4 k* Fd wy a = : - 4 3 WT ; G 1 1 * 
1 x a. 5 * * 8 * 

. 7 * * . ; "oi 

. 

4188 


| i) 
* iz io much the lefſer wil the Gurth 


© The Method of Operating in tui Fale i 
3 cite contrary to that of the Direct; for ha. 
UMing ſtated the ueſtion according to 'the. Pre- 


2 5. 


—_ Sept given in the preceding Rule, work thus 
=_ Multiply the frft Term by the ſecond, aud 2 
= - vide the Product by the 71 ird, the Quote is the 
= "Anſwer to be Queſtion, in the Jane term Jo 
A Left the middle Number in. 
But before I proceed to the Stating a nd 
=  *Obetating a Queſtion, I ſhall ſhew how 


by theDireR or indirect Rule. 
3 If the Nature of the Queſtion be ſo chat 
ore require more, or leſs Teſs, the Anſwer. is 
2 1 dy the Direct Rül e 

| Wy But if »ore require leſs,” or leſs oY the 


. 


I l CE 5g 1 — = LN MET ELEEY "TT + heap —_—— 
— a - * — + thine \ — 5 — 5 LC 
————— — Ferre >- g : 
— oe 1d norms ere gene eo — he — — gt 
— SOLON - - -— — — — 2 2 
— — i na pe Sn» = — 7 
— pay ry ne — ̃ — r — 
Ae Lorne he 2 " — 1 3 = — — RT — 29 = 
= 2 i — — — 5 9 — — 
rn * 34.7 * ö a _ 


Anſwer is found by the Indirect Rule, and 
the - third Term is the 'Diviſor. For Ar. 


| © 3 
of hee volt * Alddeth ident i 
1 Tull N22 * 3 Sheep $1 


> 
— 
TITS 
Og 
— , 
* 
FE; * 


= 
— — wm J ewe 
fg — r — 
* 3 So ILL —— 
de wont os — Loon 5 
ſe 2 r 
hs — TS 0a we ten — PIO 
— 0 As. - 
cy ** , 4 "7 182 


than 


Days, then will 12 Men do the ſaid piece in 
RJ IP 5 Days, and 3 Men will require 20 Days, 
= - that is demos Men the leſs time, and the 
les Men che more time. This being pie- 
—_— -miſed, I ſhall DEE to 22855 48 In Fran- 
. 65 19% n — 5 ; ay {ERS 
R 1 


: it * EI 10 know when a Queſtion'is to be Anſwered 


5 J. That in the more . the more Mo- 


32 . e if 8 Men do. a piece of Work in 8 


* 
Fn 


WEE 


1 
I 5 cbs 298 Men Hniſhen joe 
Work; 2 how many Dat s will 276 


nil rhe [nid piece Sn ee PO Di: oi 
Mey FTE tr Men, r 


29 —— * — bis It 


# 


a 


* : , g 7 > 
* » 4 
! . 
— ay — 
* 
E fit. * Ss A 
7 © erb 7160 10 eie nien 
_ C 87 ; 
* ma #84 4 e 
* Ae Z 159 92 * * 4 ; 1 is © } . . 
. "1 \ 12-0 2 r j 4 57 T Re" is * % 11 : . 
n FP heb bikes 47 Bay: {hk 4 ALFLITY 
* p * * 1 * 
4 Ft: 5 N je 
SM p 
wp" 
Se 1 
ob LOSS $ *. 
n $4 +) 1 — > 1 1 
$580 +4 0 1:0 4h Wer 2 eee 
4 : Ko I e 2 0 * RF 1 . : * N 0 
291190 3 — Wat „ 
fi 2 


* . 1 © 2 174 0 14971 * C3 7 : 1 4 
1 4 18 328 { 14 1 Ne 1 


5 1117 WE > 778 


45550 The Proof of ibis Ru : off Mu 


he Proof of this Rule 15 to * * 
manner with the former, wiz. by a back 
tartng, fay ing, IF 356 Men do à piece of 


Work in 630 Days, ein What time will 298 


Men do the ſaid Work in? Here operati 
s in the preceding Caſe, %. by multiply+ _ 


ing the ürſt by the ſecond, taking in the 


remainder,” and then dividing by rhe third, 
you will find 796 come out for the Anſwer, 
which 18 manifeſtly from what IE . a 
{ure — „ TE "Here 

: ere 


a 


1 


"_ 


— 4 —— - 
vl * N 
by - 


8 


HNlere alſo, as in the preceding Rule, infl it 
ſome Queſtions there is required the Additi. Tra 
on and Subſtraction of Numbers, and ina 

this Rule tis commonly after the Operation ſaid 

S's, 1s ended. . So — 00S BN... e r lo 


For Example. . Me 


-* A A certain piece of Land will Graze 25 
Horſes for 137 Days, how many mor: 
1 Horſes muſt I take in to eat up the ſaid Px. 
ſtuxe in 38 Days. Having ſtated an 
wrought this Queſtion by the foregoin 
Rule there will come out 915, the whol: 
number of Horſes the Land will Graz: 
for 38 Days. If now from 915 you tak: 

£54, the remainder is 661, the Horſes tha 
muſt be put into thoſe already there to ext 
up thePaſture.—— Theſe, with others d 
the like Nature, does many times occur. 


Os — 5” _ 
* 
= 


215: a0; 1.1; Dore Examples)” 
5 * how much mufl the Penny White Lo. 
weigh, when Wheat is ſold for8 5. 2 d. Bu 

F when it weigheth 18 pt. I the Bu. i 
ſiold for 66. 44. 1 Anſwer, 14 t. 422. 
1 . Tf when the Buſhel of Wheat is ſold for 
© 76, 9d. 2, the pemy White Loaf weight _ 
Iz #-wt. What muſt the Buſhel of Wheat be 
_ . fold for when the Penny White Loaf weigtu 
17 P. ur. 40 Anſwer, 5 l. 11 d. 4 . * 


— —— 
Lr 


* 
? 
1 
4 
ot 


'X 53 * 
lr when nh Days are 13 oo ae 2 
dit Traveller performs his Journey in 35 Days 2, 
d iin how many Days will he perform the. 
lor ſaid Journey, when the Days are 11 hours, 
+ long? Anſwer, 43 Days . 

A Captain is 3 321 1 8 
Men „ for which he has only proviſion 
for 237 Days, how many of theſe Men 
muſt he disband to make the ſaid Provi-, 
ſion laſt 2 Years and $2, Anſwer, 1e 6 
Men $$$. © 

Suppoſe 358 pieces, at 144. 7d. Z each 
was exchanged for 4 436 Pieces, at What race 
was that Piece valued. at? Anſwer, BI 

How much Shalloon of I a Yard wide, 
will Lino a Coat, that has 2 Yards + of Clob 


FE e y. 3: LEY - 


«+ 


1 % . * 4 1 5 


2 8 
2 = 4 © . ” . 


©; 508 —_——___ 


| "The Dottrine of FE i 
4  Fraftions. 7 8 we 


Whit a Pulling ts and 15. , 
A | Unite. or Tnteper © is one whole: thing,” 
as one Pound, one Dare, one ue? one 
Hour, n Ys 
A Fraction, or 3 Number, is. 4 * or 


parts of a a and is n y tw 
E3 5 


* 


A 88 FR one Ba, with a Line Bt fo 
= berween them thus” 5 2 e, the is pen 
ws under steten the Namwaror, the are f 
= * the Denominator, qhey are read or pro- 
mounced thus, one alf, 7 tuo thir, s, 4 47 
Y -- fourths, and ſo of: any "other; paming Y 
Jumerator fitſt; and the Denominator 
att rhe Denominator ſhewing' the parts in. 
18 ch the Unite is broke, and The Nu. 
=—_ . - 5 the part (or parts) of the Deno: 
1 minator that is to beraken or uleg. 


= 4 | 216 ſeveral Hie of Tin,” 1 
1 Of FraQions, of bre dei Nyrmbersithere 
. be fo kinds, viz. Py, 


1 | * ere 6 Ni; xt, 
=o Ge Compound, LEE TUEITI LETTERS 
*z A Proper — that whoſe Nutt6ra- 
dor is leſs than che Denman, as 2, 3, 
= „ „„ 3 
—_—. - n proper Fraftiom has its Numerator 
—_— greater than ( of a kaſt-equalro N the De⸗ 
nJx0minator, as +, +, f, +, Cc. 
aa, are whole Numbers and Fractions 
iet together thus, 24, 35 74; CG. 
Factions are known by haviog 
the word IF] berwixt them, and are Writ- 
=_  tcnthus, of 5, alſo of 5 of 4, [they axe 
=_. _ likewiſe called Frafiens of Fraftibns. 
_  - Now before we can paſs to the” Rated, of |. 
= Addition, SubſtraFion.., „ Maltiplication, and 

8 8 Tp e Ld FR F e e 4 

. 8 e | 


* 


— 


. T 55 'Y e 

ine fit for ſuch Operation, 8 e 5 
the Wis performed by Hon, "of which chere 1 
the ar five kinds, 28 follows. . e | e 


70. * p ann . 2 f | - 
* 17 $ 0 eu, the Pup.) 5 been, 2 


N -Eacherh to 3 a whale or mixt 1 
n. 1 Number into à Fraction, which Era. 2 
u. gion ſhall be equal in value to the faid 
o- hole or mia Number; and contrath,. 1 
teacheth to turn a Fraction i lee Va. 5 
ent whole or mitt Number. ee” 
i 12q blo n "= 

e If it be whole Number chan; | _— 5 
e multiply ic by the aſſign d Denomina og | 

„and ſet the- Product thereof for a Numera- - 

tor over the ſaid Drnominatör; ſo fal 
„mis Fraction be equal to the gives whole 1 
5 Number. as - 
| Example, Reduce 7 to a Fradtion;-whoſe RE. 
Denomibator Hall beams 2h i, - oa 
| 7. whole Number. 5 1, 


e en be 


25 
- VE 
* \ | 8 $ 

** . * 0 ww : 4 a : 
K 0 ; 

py 

x 
* 


A K 7 — | 
j by 1 2 wen 5 airs TY 
1 3 . 


75 _ 


'S 


— 


982% 


a 2 at 
* 4 #< G 


rey, as 7 898 
28 Founhs, . if rs 


. ) 104 Fraktion 5 xi" 32) 
Reduce 38 © wholeDeno-<6 . 43 
0 minator is 7 6 433 


s s n 7 18 ; 0 5 7 
l * | * for * * IC 
\ 

"4 * 1 

4 « 
4 1 

"oy . $ 4 \ % Were ** g 

4 2 


Rule 2d. 11 a mixt eee is £0 — © 
be reduced, then multip y the whole Num- 
ber by the Denominator of the Fraction, 

adding thereto the Numerator, the Summ 
hall be a new Numerator, which if ſer over 
the old Denominator will give a Fraction of 

the fame value ths" the is gp mixt 


NO [#343796 


romp, Reduor 2 247 to . bone, 
„ new w Numeratarſothar 2 #5 BY 
5 More Examples . 
4 0 3 
1 22 
_— A LO Fo 
- Rule 1 If an i Fraftion i is to be 
reduced into its equivalent whole or mixt 
7 Number; then divide the Numerator by 
£1 7 og ſs wikhe Quote give a 


* ow * equi. to the Faction gi. 


pen. : e Example 
\ 4 ; e f : ; 
a | 
# : 
1 
bo 1 


9 2 * ” 13 
- »- 3 1 
n . b 
14 * 5 * t 
* o 
n \ . 
RE” 
* * * 
bo . 7 * . 
* 0 1 x 


=o ; . 5 + c 
: | 4 | 
9 * 
* * * „ 
op þ ns 1 . * 
: g 4 7 - 


Exam TY 1. Reduce 22 1 
whote AT, N in 0 ts equivalent . 


5 "VEG ſo that 7 ische whole Na aber. 
1 en, * * 


More Examples Y 0 5 
2 ) to its Equiva- 5 


[> 


. Reduce 


* 2s 


lent whole 
Number. 


E 
EN 


C17 
If act Dividing any thing remain fer it 


for a Numerator over the Fractions" = 
-  minator, and Jin” the faid Fractio 


ee a : 2 et | * 


F h * 's 
$ ? f 1 
* 1 
ew 


Example 2 2. ns 4; into its ; Bqu ö „ 
mixt Wander. EX 45 : 2 
„ 5 fe The proof of any of theſe dis 55 5 
ae by a contrary OperatonGk 8 


- This Roduian is Feb Mn y ys bor 
res no working with whole. Numbers 


and Fractions. till the whole eg wack are” 
E 4 7 . * Gr Y 


DE | Redalthon the ae, 


my Null all the 8 one 
into anpther continually, and fer the Produèt 
fox à Henominator. Then multiply all the _ 
Numerators one into another, and ſet the 
Product for a Numerator over the former 

engminator, the Fraction thus formed is 
cgquivalent tO the given ay Fracti- 
on. 


: 4 % | d 3 „ 
+68 $13 1 l 


Example, Reduce 4 os = 2 to 2 0 nde 
: Fraction. | 
3 Numer. 171. 55 ee TY 
3 Numer. 24. 9 Denom. 24d. 


1 : 8 g * - 4 8 "a 3 2 0 . 
N n p L IL PE * 3 
„ , ; 
1 * 


FW Numer. 34. 12 Denom. 3. 
Sei 3 2 x bu 2 TEN” 3 75 * oo | 3 
7 s Num. fought 921 om. oug 
| GH : LEH Ty, a 
„ 
5 ha 2 _ of x = + * 
9 a 2 PW 13.5 8499 wilt 
— | ; 5 
t 2 FI P 2 PF F 
| 5 ' 
: | 
** 
| ; PLCs % | 
s LN * 
| - | XA i 
9 w—_ 


Ihe ay of us 3 is thus. 
Muliply the Numerator of the ſimple 
Fraction into all the Denominators of the 
Compound: Then the Denominator of the 
Simple into all the Numerators of the Co. 


ound. If the two o*Produtts are "qual the, 


pins Ce g 
ork is 1 ele t. mim 
; ? . 
. 
* 1 
* 
1 3 
91 
"" 
1 
1 
* 
1 s | ! 
Pg * i 
N. 8 833 N 
CSS : „ 1 — Fo 4 . 2 e 
- % N : : * 
— * - 
4 1 
% £ | ; 0 | - %, 
s . 5 4 
| GER, 4 4 „ f 2 
: LEFT 8 12. 2 2 f 0 81 F | . * 5 * 4 , 
— ; . 1 f 2. Bs 1 +I 
1 XY Mort * 64. } 3 
F 6 * * * R * 
N 5 ? a 4 5 


2 £2 5 


to a fimpl ple 70 45 


n 
Re ace 23 . 
: wn of Fol Fraction. 


* 


This ReMiBlin 3 18 HER abtoo pe. "87 94 ; 


1 for there is no Working with Com. 
Us Fractions and others, il the 1 
ompound Fractions, are reduced to Sim. 


FS. | ; 


* 


— £ 
þ 
* 
-» % RY m Xe , 
# 
} — — — 
5 7 
— - # ' 
1 
* * 
4 "4 
* 
, % 
% 
* 3 7 o” 
F 
5 - LP \ 
7 
1 
4 FAY 
* a * 0 * 


5 4 1 p 
g = a * : v1 # p 7% 0 15 34 * 
- ies Sx) . + 4 KW; Fa FS 
. 8 : 
* - + . 4 7 5 ” * F 7 1 
( ' ' { 
LO A It 
* f 288 
* ? / ) T..+% 
© LY 
* £ IE 7 f 
* 4 * o 
1 py ; : x 
* 


{ 


G — 


# 


\ 
*- 


# * "0 


by &) ws, 27 625 17 
R neduion the 7 15. 


4 I Mg Bacherh ro Abreviate a een that 


js to reduce it to its e * 
FM keeping the ſame value. 


= . Divide; 
=_ - notninator (if the 


5 both even) by 2, 4,6, 


even, and the other odd, or both odd, try 
ſome odd Number, as 3, 5, 7, 9, &c. 5 
peat this Diviſion as often- as you can, ſo 
854 the laſt Quotient of the Numerator bn 


"FR Denominator a new Denominator. 


—_ Eau. Redr ace 3541 into its loweſt Terms 


* 1 


12 at lai [+ H | Fl; gar 244 = * 


% 
Y 


* 


= 1 means a Fraction is brought to its loweſt 
Terms at the fitſt Operation : For FRRONG © oF. 
=. which the Rule 3: WE | | 


hot * 
we” 


EE . —— CEOS OE, 22 = ge nn * 
—— — 8 = FASL | 2 | RS OG 


EET 
— 3 
DSI 
* r 
A 4 * * . AT 
hy 


— gee 
9 
— 


hr" 


Numerator and De- 


= <8, . If * e. and Denom. be one 


E - ne Numerator, and the laſt Quote of the. 


3 '% But che general way of reducing. a Fra- 
con to its loweſt Terms is to find a cm. 
D Q 2 Mea ſurer, that is, the greateſt Number 
= ” Ds divide both Numerator and De- 
nominator without a remainder, by which 


p— 
ak 


* * 
8 - v is *. 
, I | | 
t 
# * Ry E 3 
„ f 
f 
” ; * % 7 1 * 


_ þ „ 
. . * . þ * 7 + > ö * 4 
. . 2 * "aſe 54 
* A N \ * * * [3 


n 
+ 


WES +”: _ 
Rule 2. unte the Denomioator bay as F | 
888 if any thing remain, by it di- 
vide the former Diviſor, and if 1e this ' 
Diviſion wh thing remain, divide the laſt. 
 Divifor by it; Proceed thus till nothing "Fo 
remain, 5 wal the laſt Diviſor be the 
greateſt common Meaſurer, and is à Number 1 
we HH divide both Numerator and Deno- 
minator without a remainder, and fo re. 
duce a Fraction to its loweſt Terms at the 
firſt Operation; but if after all the Diviſi -- 1 
ons are ended there remains 1, then is 2 „ 
25 «pag in its loweſt Terms already. 


” Exam. Reduce tt roirs loweſt Terms: 4 
b 1 Kh: oo 

OG eee 

STS | 936 J 312 


312) 53603 71 : ET 


- ator and Denominator without a Rea . 
L der, See the work. „„ 
ee wh 1 4956 13 + 


J 
4 1 


13104 2 


1 A 93 > > 
#4 F 255 
. * 
uM 
* 


— 


. * 3 \ d 
Ts + - , F . 

” & * 

= . 
4. ** i * N 

4 - 
* 0 x | 
5 5 * 52 
Fo 7 
#*'% 8 - 
7 25 4 \ 
* * t 
* 


3 


* * — 
; a 
TM 
27 ; 
3 8 * 
f 
& 2 


. Wi the n of le given dared it 
it the 80 r are AE Toh the Work is 


28 r 5 * 7 "= 


* 


1 | 
5 90 matopy d Y 
9 maſs 4 uy et 2 
"—- I 948 qual. 4 
"4 : bi \ BY 44 
a 1040. N n 
N Wha Ale ee 5 2 7 
. me Fit to We l 
2 2 1 elk Terms 


8H Relacrich 18 alſs vary uleful, - for oy 1 
it Fractions that are expfeſs'd by . 
Numbers, are made to be Expreſs' d by =o 8 


| ler, by which their true n is 81 more 


Aacheth 1 to being Frations 57 5 
divers Denominations into Fractions | 
of one Denomination, R till rer | 
-the fame value. 1 


. Rule Mikigly all = D con- 5 
i Miaually ons into another, and ſet the Pro. | 


pe 277 216 Fas *. , . - aa 
2 Wis. 


duct thereof ira new Gee then 
multiply the Numerator of che firſt Fraction 
into all the Denominators except its own, 
the Product is the Numerator of the firſt 
Fraction, and muſt be ſet over the N 


minator before found; o likewiſe For the 


ſecond Fraftion you muſt multiply its Nu- 
merator into all the Denominators, ex 
its own, the Product is the N'amerator. of 

the ſecond Fraftiob. proceed thus With . 
the reſt of the Numerators, chat is, maſtiply 


each Numeracor by all- 0 Denomipators 5 


except its own, ſetting the ſevetal Produts 
for new Numerators over the 24 7 
Denominator firſt found, ſo hall theſe new 
. Fractions be of one 1 ane 2 
e 0 the former. 1 5 W tore: 

| nomination. by EE 


* 
8 x, : 
. 
r ' 1 

} 


if 
* 
; 


445 Denom. 15. Fee 4 Numer, „ | ta of 2 


By Demom. 24. 13 


8 
A 


6 Denom. 34. 0 * 1 2 3s 


3 


26, Common "Ry W New Numer 421 


: wes „ 
42 


14. 


e e 


nee 


Ky 


—— FSR "IE : | 5 
W os 2 by 8 | tems 50 | 
af Don, * I Bauen 7 5 
* „ — . a ty” 5 
3 ö bf | 1 75 
| a 5 4 Ee 2 | | + 28 


. : 1 


| = Te 64 
\ # 6 Denors. 7% | Ani uf. 
C 2 . 7 New Numer, ut. 105 New Numer. 24 


5 *% 
HE | 1 ' 2 BY 


K ee: = tt and $ = tend i= 
| I he proof of this Reduction i is 45 in the 


Io ut, that is, yon muſt multiply the Nume- 
- * © rutor of the Fraftion given, by the Deno- | 


-minator of that tis reduc'd to; ſo alſo the 


the Numerator of the aforeſaid Fraction, 
then if the two Products are equal the Work 


15 right, E, not. The 0 eration 76 as ol- 
be. N f fo 


KP. d by 3 is + equate 01 126 Ry" 
\ F454 = VV 


: " "Mews eu. e 


. 11 TS to one A . 44, 
„ 77 der, ; Denom. 745 71, IS 


| N 112. 
Notes, 1. If mixt Numbers are given, 


"0 thus tobe Rides reduce W ne Frafti- | 
nal Parts. 

24. If Compound Fractions are to 99 re- 

duced to one Denominator they muſt firſt be 

doubt to PS * WH 8 


"This 


* , - 9 


: 0 54 ; „ ig 
. 1d Þ 


the Denominator of rhe Fraction given by 


By the laſt 1 1 and thitefire 4 | 


«> a 
FL os! fn 


This Rediffion'1 18 alſo abſolutely t ne p : 's 25 
for before Flackions are brought to | 
fame Denomination, . n neither „ 


» 
* — & of a 
2 3 5 S * 3 
5 3 n 
a - 87 
- 1 
MS, 
5 5 
© p 45 4 * 1 s K* 2 ö 
q * wo , 2 e %”. 
. - ＋ « 7 4 * 3 
2 lf pag P: % . : * 7 J 2 I FCA 3. 4 * E 7 
Xs % " : 5 5 * >. a " 6x. 4 
xls $5 % 3 ERS. © 


7 SG, into a2: 
' norher equal in I 1 ſhall have A 


$ 8 1. 


1 * _ x N ” 4732 4 
2 an * * 
4 a It * 
5 n « 


p * 9 
ere S . 
+ # 


$4 


Rule. Multi vly- the 3 f che g S Bi- 5 
ven Fraction by the aſſign d Denominaror;. 
and the 'Produt divide by the old Be-. 


* 


* 


nominator, the Quote is the Numerator t Ee. 
the aſſign'd Denominator. 5 5 


ways N 4 


» 2 4 + : — * — 1 \ : 
— % WES. # 13 2 n n * 


» as. Reduce 


4 X 
* 
- - 
oy . g 
. E E 4 0 
Ky „ 3 Nc ; 
: 4 * % * & + {> 1 
„ CESS 1 
3 1 17 # %. . 
** 1 . * 2 "4 1 
* 


Denominator 271 


by 
* 


6 l r as 0 #41. 
1 7 


— * * * 


6 my . 
71 | 218 Oe. BA New Nauen en. LOGON 
g Ts 


— 


1 » * 
* TI MAY 5 


54 1 * iin 255 5 
1 TH 155. Wai 
3 — ? * 


5 e 
* FIR. * 
* * 


" that i is, you, alt multiply. 
ol the given Fraction 75 | 


of chat its 3. reduc d to ; 


* od bis by | 15 : 2 T4 


* * 1 ; 
* — % = 
. « 4 7 4 
he * I 3 
3 4 po 5 = 5 * - 
þ a 0 
8 24 7 "; fc 3 ER 1 
5 8 1 3 br, 4 
* * . 2 1 4 * — 1 2 ＋ E 42 * 
— 2 j ＋ of - - 8 
2 2 25 4 Pd 1 4 * 4 N & 4 of us 8 
* 2 F A - wa - 
% 4 — * ye f 4 „ 
ad + FL : - & as) $0 1 
- "= * ; we * 8 
* 
— I. a 4 7 y f Yo: 2 - 
* 81 2 2 * 
- A 5 x | 
h 4 > 2 a 
4 = POW. PY — 2 4 2 . 
1 6 
! Li 
. 


+ 3 i" 4 5 


t e * 


* kts 
. N 1 * * & * 


7 This Rediftion i 18 t 13 
-thers, for by it the value of any Fraction is 


n FN rer — 5 S Je. * 
R 9 r r _ _ — 
© © he EE LO Ss 7 7 2 . 3 = 1 
6 4 "+ * 7 * 7 L 1 - WY. TR 5 4 
8 « 1 2 2 * 7 as 9 
4 * > a 4 


r * N * — — 
pe AI 8 9 * - 3 > 1 
* 8 n rr 
N N n ; N Nero ö 
7 7 "eu q - 4% — = * , * N 


Nu, Str. aud contrary, that is, it teacheth 
| 1 io tun an part of Cyyn, Weight, Time,” 8c. 
into a Fration; Which becauſe it is one 


"Ra farther upon it. . 
23 3 in order tc be as clear as Pen in this 
Mlatter, 1 muſt again tell you chat this Re- 
duction teaches o change a Fraction to 
another that ſhall have any aſſign'd Deno- 
minator, yer ſtill keeping the ſame value; 


: Ok — 22 N 
OOO IE ft rere 
n N 9 3 2 od \ — 
* LE 4 * F A 94 
- l * 
WE I 
* > » . — . 
_*” . 1 IP * 7 ” g 
2 n LR AL NG ; NN 
3 „ SE EI rs Wu * , 
: ls,” 4 +» * 
- 2 n * 
My * . 
2 2 
4 
— 0 N - * * * 
z 6 0 | - 3 
N 5 * * 9 9 — 1 · 
* * * * - 
I 1 N 
> A l | 
* 6 . 
I x #<Y 
o 2. Fa 1 
>» 
a 


and ſuppoſe the-> ro be + of -a'Pound Ster- 


buy many 7 


e e one Shilling is 
"A FTIR the EX, 


* 
* 
* 


2 FO 8 . . 1 N 7 
us. e e n e 


. i a n Fraftion Who : 
| 1 e Turn it to a Simple, by Reda i- 
ne 2, and then work e as the ending Rule + 


'moſt uſeful of: all s. 1 
"=p in the known Parts of « 09th, Weight, . 


of the chickeſt things in Fractions, 1 Mall en. 


ſo that if it were tequired to reduce 10 
another whoſe” Denominator ſhall be 20, 


ling; here then "tis evident; "that if Tknow 
hs 2 is, I know how 


IS 


3 Was requ equircd, if they 4; nge 
- | his Fration to another, that ſhall have #2 _ 0 9 
for it Denominator, tis evident I ſhall know | 5 2 1 
5 how many Pence tis, becauſe one Penny eme 


the 12th of a Shilling. The like 4 


underſtood of Weight, Tire, &c. 


therefore to find the value oFanp Fraftion . 


| inthe known parts of Coyn, 3 Time, LIM 


Ke. take che following Direction + o 


— 


* 


_ . Multiply: che Numerator by the paits of. : 
1 the; next 2 Denomination, that are r 2 
gaqual to an Uuite that che ie ban, gives 
— 1 the partg of. The Product divide by the De- 
nominator, the Quote gives the value in the 
= Fe .mukciply'd by ; ; if after this Di. 
bos ang thing remain, muliply ir by che. © 
nent in eriour Denomination, be 
Product b 98 


o 


1 


* 


8 2 5 
% 7 7 85 
R * 7 = * 
4 x 8 
0 ; 
-,”*. 8 
* 8 . . 


W ESTES 
- 7 — 
* * 


2 


, 
by 
"& 


g n 05 55 Fart bing: 44 * Au. * 5 th if) | 
5.0 Rn ou ror 1 1940 


— 


El 
Lap | 


4 80 chat the 3 


= 


. 


0 8 


3%. * 15 8 133% b. gh n . $972 P2354 1 ** 


% 


+ 2 


# Fs, 
” "a 5 1 : ; 4 
- L „ CET EOS 
4 # 2 : £5. 10 1 5 * 1 6 Ac WEL. ';" ARE as 1 TRE | 
| Ren 5 - We hy. vg g 13 
E. CO . 4 Ts 13 w 
A 3 


wt $A + 
8 * 


. 1 


ECM 2 6} © . 10 1 rg Þ 
2 Bo 13 . 7 N "I 6. ; 


- I pe { * x 4 
*. 1 * * 3 * * 4 0 0 wh 4 * 
ws N a WF W I ; gy es K þ $55 # 8 ö * g 


» 


0 7 8 
ee What's the F of 45 
* Weight? W n $9 


: R * * 3 * 1 - N 
þ + ah . N. BY 2 * 1 4 2 
. 1 9 5 „ v% © 981 „% 
' : ny . ; 
A — 
* - * 1 * 3 E 


8 
63 A Nor 


— — 


. — 


. * 9080 ces 77 Ly 
* * 1 I 1 1 8 - 45 1 * a 1 N : os 3 ft, . 
© : by 6 * 1 5 * bY * 3 : q — fox Ps. of Tr. * „ 0 s : ; * | 1 vs Fg fl D $73 | BY A T 4 4 } N 1 
4 


Wo 7-0 ATP : +738 * 6. 2 . , TT | 
oh. 3 | Wa yo FOIA ag ge,” / RO, A 
R #5 * 5 ** 1 e + A206 * „ n F „„ * 
wy ; *% s l 5 5 0 2 * — 
” + x 5 — * as * oy ” "3 : jo 


#: 


* SIP + a 1 
1 - 2 * * P 1 
/ + „ 4 - \ = 
8 1 f wir Fi Reminder DO: n 
b 11 * r | = 7 : a d DR 4 4 1 N | a = 2 4 * _ Ky 44 : * 


. at is ES {Þ, 2 Pap * vs Res N * 5 


1 git 67) A Be 175 „„ 
3 ac in on av, T 
Y * 


„ . 14 Dram: 


3 1 ty 
1 
A : * * 

* . 5 » — 

» by : 4 — + 

4 4 I; * 1 * 

7 o 

N 


So chat 5 of a Pound Hawerdupoize is 8 
7 Ounces: T4 Draws 7 FY N 8 9 PO” Lhe 5 


N p # * 

4 * ih 
r N — 2 
2 F 2 5 of * x 4 — 


| - akier chis Method. may che Value 2 40% | 
4  Frattion be found, whether it 75 C 
; Weight, Time,. Liquor \Meaſure, Aas . 

ſure, &c. and giyen in known, and km niliax * - 
Terms, as in thie Second Example; Where 
the value off of a: Pound Sterling was re- 
; guir d: | anſwer, that it's 17 Shillings and 
10 Pence half Penny, and of a Farthi 

So likewiſe in the Third Exam le, the 5 
* of a Pound Haverdupoize is found. to. 


"a 


5 _ Uunces,. 14 Prams, and of a Dram. 1 | 5 £ 1 1 
I you wouldcum-any part of Gor, Time WES 


Veight, &. into a Fraction, tis but the con, Ee 2 
verſe of the formet Rule, and therefore maß 
dein „ 


1 f 7 
£ ” g 
cedes; For if 3 ou do bu . 
2 7 * 
Ve c 2 bh * £2 
2 1 
| u 2 4 
i } ; ; Ba. 'Þ * a R wb ws Fr — Y 
— 1 . Fe 4 4 5 : \ 4 4 
— 7 1 


- * . x CES YE; 
. 4 85 * 4 v 3 EN n £4 l % 
4 x 12 Wy 3 1720 4 > 1 - * 5 5 
5 7 ? . 
— >> of x - F 
* * . : S < 0 % ” * o 
* 7 A ann * i 
$ 7 
%, . 
7 , 
oo 
4 
* 
A 


* 3 4+ of a Pound; as alſo a Farthing 
e the of g of 2 bf 2 Pound, 


| ! „ the Vulgar to know them by. The Univ. 


5 7 2 Shilling 9 d. is, Anſwer. Th Or when 


i 
i 
"8 
* 
| aA N N a, 
n+ 8 F 
: : i +; 3-7 * S * 8989 1 7 „ Me | 
by * a . i ** ö * : 
l 1 35 2 n 1 : 2 - 5 * 4 
* 7 1 * 2 % "- 1 > g 8 by i : — 1 7 v T - 
* : * - OE 4 4 . SS. $ by, 3 } 8 3 
E 4 1 * F 7 8 der * , L : 1 £ 


. 
— 8 i 9 
7 2 3. 
* n * 9 2 * 
* * 
x 2 


or 


that Orr > bert * 2 pound — 1 
and a penny the 7 of a Shilling, or the 7; 0 | 
the ; £ 


tze Names of a Shilling,” A Penny, and a * 
thing, being only Denominatiòps given for 5 


Way of expreſſing them being to call 'a Shil-{ “ 
| ling the x3 of a Pound, 'and's Penny” *the 
n Of a Shilling, alſo a Farthing the 5 of 2 
Penny y, and this way of expreſſing "them 
| ( ſuppoſing the value of the Pound Ken) x 
___ would be Intelligible to all Nations that 
. © have the knowledge of Numbers. So that 
f it were required to know hat part of 


abreyiared . In like manner if it is requir d 


15 to knaw what part of a Pound a Penny is, 


here Imuſt conſider that one Penny is the | 
d of 3 of a Pound Sterling, and Rae 
Tots by Reduction 2d. is -;: of a Pound. 
Laſtly if ir be required to know what part 
of a pound 2. 9 is, 1 confider it thus, 


1 X 25. 94. is 2. fl. N "when. reduced to 


an improper Fraction 2 of a 1 ſo 
the Queſtion will be, what's the 14 of "IN 
of a Pound Sterling, (the 4+ being only 


12 ES; 7 ” parts of a Shilling) working therefore by 


Reduction 2d. you ſhall find "hue" 25. 94. 


Sh 1 0 
£0 ly 1 __ Nb W 
2 * 1 1 7 4 i 1 


7 N 1 *H 
5 nee 
* 0 
"So : 
"it ; ? 
G — Ay * - 


E 


SE 
2 
1 


7 — . . \ * 2 ” . 
* 3 * 2 — 
4 : n 
* 7 1 % * 3 % 4 [4 n 
Rei } 5 n 
= 7 7 4 x * 
N - 3 
k L : . 
5 Es "4 * 8 


nh. = muſt all be reduc d te 
me tame, then add the Numerarors toge 
i ther, and ſet the Sum for a new Numera- 
tor over the common Denominator, It „ 


BS St Sum FrOuinngs "2 

TS © 

15 

3 

4 

3 

| 

» | 

8 ene k n nne Me the 

: * thoſe tw]. given, hap n to be an i in 5 
. Per Fraction; then by © Reductian 1 ff. Rule 
90 Is reduce it into its equivalent, hole ur 

5 B Number, as in the lat Example. 
rt TheProat of Addition is beſt done bya 

, careful Red ion, and 


5 FI . you are to add 1 mixt ho. 
bers, add only the Fractional parts being | firſt 


| reduced to the ſame Denomination. 


= 5 1 If you are to add Compound practi- 


ons, reduce them firſt to Simple, and * 
9 3 Common Denominator. 

3. If the Fractions to be added are not 
E of the ſame, whole (though of the. 

me kind) as thus, the ſum of of a 
Shilling, and 3 of a bound Sterling is re- 
8 z here they are not only of diffe- 
rent Denominations, but parts of different 
. wholes, and therefore more E word. 
ed thus. | 

What's the Semen of = * ef 
Pound l ? BRIE: * 38. ; 


3 


Fe RA AN tur Mes AUT 10 
Wm Fractions fic for 3 
ate in all Reſpects and Caſes to be obſervd 
in Subſtraction, fo that whether they are 
Simple, Miet or Compound, they muſt be re- 
duc d to a common Dengminato © 
Then take the Numerator of the Sa- 
- "Sor, or Fraction to be ſubſtracted from the 
- Numerator of the Subffrabend or Eraction, 
from which we are to ſubſtract, and ſet 
the ET over the common Denomi- 


f * 
has : « 7 : 
x * y | T Nator 
= E 7 , 4 + 
: # 1 "4 85 . Ly . 
: * * | * 


3 . F: * ESD, $4. 
5 9 ; 


* 


5 ie 5 * — E 35 5 F q 
: wy * 7 2 3 h 3 0 p _ 
1 1 ; „ 7 - 1 * 
EN 7 0 . KW X / # N : 


„ e ES. | a 
vr 785 oy | > 9 Subſtract 


* 


1 a or Ge ſo — OE N 2 


% 


N | oh] * * . pt E: x: * g >, 20 #7 4 3 * . %® -4 © i 
* | 4 


93 ſtand ee en 
3 i 


he proof of this! Io; 


' - onal ion, viz. By adding the Re: 
mainder to the. quantity taken away, the / ; 
| Sum is che quantity firſt pr 8 


: 
of d 
* 3 1 * 
” 
. - i Ke 
F 4 4 7 
1 1 1 8 1 
1 ? . 
* ww * 
; 85 n 753 
Fg * a) £ 7 x 2 5 1 
7 : 2 w ! * bo 
* > 


5 * From © take 3 Ku 7; & 


* . p * > 1 2. 
: 4 2 . * 4 2 * * 4 7 
bo f 
Py + 


or 1280 ubſtr 


* 
4 
1 
1 
- # 4 
7 2 
* * 
: l XY 
; x 
= > : = 
4 4 4 
15 t ; 3 
= = 
: 5 2 
4 o, 
, - 


A" 1 
5 chen ae r two | Wok. e 
 rators together for a Numerator, and te 
two Denominators: for 2 Denominator, the 1 


1 | 2 
N | Fration form'd by theſe: two . "4: 
. the Product r | uir* 5 0 ; z 155 Wm *%g | : vi 
r 7 5 7 p - . 5 8 F b . : . ** 63s * LEY ** 8 2 e 8 IH 


- * Y 
— 7 j 
* 3 _ 
bl 6 * 
I 1 
* — 
4 - 
. " — * 
: F * * * * - 9 
* — ＋ 1 * — — 
* 
» i — 
* * L 
© L - 
- . A $ 


P 
—— — 


r 


5 5 5 7 
= if > 
* * ws * : 
». 
8 115 4 — * * 
** yy b 
wy } >= » 3, 
| i ' 
1 . 
' * 2 1 
_— - , Y. 


„ 


is the Produ@ required.” 


2 2225 e 2 


= 
8 
e 
* 
44 : 
\ 4 
* 


R 1 


4 =» - 
| - $ 
4 of 
[| * .. 9 7 


miau 4 5 


3 5 : Par... * wr 7 7 . R f 
3 Ne 1, mixt 3 are to be mul- TY. 
1 reduce them into impro - 
| 2 = Reduction i ſt. Rule 2d, 
WE" Alt Dn * om 


b 8 
Mort rt une rs rt 


£ * 


} 


minator of the Diviſor, and ſer 5 Produt 


amber an improper r Faden by paning hy 


Ir che" Dividend und Deng be 1 
Simple Fractions, then Mulriply ne 3 
Numerator of the Dividend by the Ben- 


for a Numerator. Multiply: alſo the Deng» © + 
minator of the Dividend by the Numera- : : 5 

tor of rhe Diviſor, and take the Product or N 
2 Denominator, the” Fraction thus forged | 


"36-4 Ky 5 a 


I me? ONT eee 
7 AF 2 » 7 F | q FR J 2 "85: oa * * 2 
8 F * \ F 
. \ LING „r * es 423 <- E FS 1 ; > 4 7 — * 4 
—— : 4 * Ss : 15 . . 7 -# 
8 . * { * | ta * + ge 0 * . of 


1 bY 8 
* Wes 
* 4 2 $4 v. Tn 


Here (as in whole Numbers) che prof of - 7 om 8 «15 
Diriſion 4 is by Multiplication, as well as = = 
_ of Mulciplication by Diviſion ;; and there A 
fre, Firſt; To prove Multiplication "tis - — Jl 
but dividing, the Product of two Fracti 2 
y one of them, and the Quote will be x ER 
other. For Example, The Product of + 4 BY. 

is 34-10 that divide 22 + by 3 the Quote 1 
abreviated is DE 


_ . 
"1 


- c 


2% 


"oi Diviſion; eh 1 ote of an 1 
. Fradt ions by the . and the 
bote will be the Dividend, for che Quote 

* by + is ; Mulciply thereforo £2 by 
4 {ak Pon Is ISS, OS. abreviated 
en ile Dividend. 1 


. „ rr i IE . 
5 | Me Sen. . 
45 


* *: 3 * 3 3 
. . * 3 5 n . 
2 K* 1 5 . * N * 7 45 + * yo of Fa x 9 "i * 15 7 Fo. a 5 7 


y —< 41 
bat "ſo f by ; . * 
7 2 8 G a8 


N 5 72 £ Les - 15 5 | 


2 Note r. 1 e 1 3 Divifor,” or 
* whole of mixt Numbers, Reduce 
chem to improper Fractigns by Reduction iſt, 
"Bk 1 or 2, and. then divide gs 0 
he preceding! Rule. 
2. If they be Compound Fans r re 
duce them to Oe ones by Reduction x9.” 1 


n een . 


R Rule of 'T; 10 2 Hen = in 


"Ap x: 7 +4 oy. 
ny 8 
woke Fractions,” W 


Ws ; * : 4 
5 ho . . 


* 


HE 8 N given fol gag — 
Lb rs 2 Queſtion in the Ruſe of 
1 in whole Numbers, holds alſo in 
tis of Fraftions : So that having ſtared the 
— Queſtion as * there directed, tis but Mul- 


E; 


. 

7 wn Ir MN ft WR 
8 l 5 
A 
e 


\ 


* 


* 


5 77 5 PI 
_ thei /Fiattions' in "Ry Fe? ” 
Third Place together, and dividing the Fra- 
quct by the Firſt, according to the 


— * 


ding of 1 the Nechlent is che 
ues to the Queſtion wo, N N 


8 7 38 3 


38. 
3 


pony 


Exomple, If of « Yard echo 1 
Nate 3 


, e os n £ 5 it QC: 4 wh 4 Yam} * r N n 
. q 42S. "F 5 | 7 CY 1 

Li's — N 
x 


BT * ofa Pain, for Anſar 


* „ * * 


3 proof of. this. Rule is. by 2 ack | — 0 : : 


Carcing the — laying, 


w "4 7 LE 2 4 . 7 n 


IP +, | 
0 « 2 ** 5 * IO. £ OW 1 > 68 
. | 3 ; 
ARSE, Dares 680, or x. 0 2 
1 A STh2 l 3 Aa 4 7 + 


3 


e Tt boner 
ſee the Anſwer is 4 „vhich is right,” ah 
Lure prog of the Queſtion, | 


— 
31 


oo ed 5 bs 


3 * % * 3 1 4 * | . { £ 
„ k, 3 „„ 
L fp 64*7 Its 42 Wire e * U 4 4281 . 


78 773 1 


S 5 f rt $4 4 * . 2 1 4 Ir ud N 
If g of a Pound Troy colt + ; ofw'Gi "WE. 


at 22 5. What ſhall ++ of a Poundcolt Af. 
thor 1 ISAS . — 


f* 0 e e eee, If 1 
win Fe of an Noble buy? 4. „ 


* 


Wo or I 1557 Noble, 


. 2 
7 g A 0 : = 
2 * * 8 a : £ 
* ; 2 
e * * Ll 
| . * 

p a x »= 
ow ” a : * 

: 

* * -4 
* 
: 
* 

| Pg 
— a - 

— i Se — "4" 

* Sx 
: — 

* 8 

" : 
N * 

Rig 
1 LS 


ing Rules given for Multiplying OM. 5 2 


of a Pound, What colt 3of 2 Yard at that * ; : 1 


er 87 L ug 5 
Note, 1. If there be mixt. Numb 
. e. mio improper Fractions 
2. If any ofthe given Fractions be Com- 5 


I 


pound, th mul Be redue'd*ro Simple Fra- 
Son ! 


18 
. ERE alſo; asin chat of whole Num- 
ts ly-che ſecond 1 
= the firſt, divide the Product by 


» 
: 


Nn many = will build 


42 Aufier 1 922 | 
£- Lent AT Or '2 Pound for _ 
How much gught to be Lent me = 


2 Years, that I may not loſe n 
CR 3 
If when the Buſbel 


the more ate abt 
"the Sa 


* 1 R 4 © 
”—_ 


ob 
Ws 
ent 


What part of a Pound Serling is ; 
22 A Merchant, je > of Z ot a Coal Mine, 
„„ weten tao f che whole ? Anſ: 


* = —D -M \ : \ : ar _ ©, n $- 5X 4 

x SEEN * . 12 I 1383 ; "=: fools F * 
: 725 ( : a; F * 1 6 oe 3 a . # 5 0 : 
er ae 5 M 1 


- + 4 * 
: &.. i £ 5 eb” 5 , 83 LS W 


riots Ar Anſw. 11 5.4 WE 
1 561 Pole, a 45. 2 J. Anſwer. 


TY . 


, AE of , f 3 


8 9 we . 1 l x 5 N . : , . 
. 1 - \ 8 N 3 , 
* * % F x a T ; . T; 4 ; % WP * ; . * 
"4 I ' * id N 
[1 


i 
4 
b 


£1 


5 Te 


er 2 4 . 2 ö * 8 * 5 
> | . a | 
| 1 8 x 2 . 
; $5 CE a % 2 $ Vw 
4 4 I 
N oy 
X _ 
| 5 | ; 2 8 2 £5, : $i Ys 2 th | 
of x4 ae 3. 
* 3 
82 ak | pwer Fg. .- 
Y PA 1 5 py Fs þ 


r3. 
re of 


What: 83 30 15 Dar 3 Hours 3 2 Aar 75 
11 4 16h, 20m. Tt OTE Torts, We 


> AT 1 Tee: EE as Seal 3 
+. R %.,4 14 # 7 F + a g 4 * 1 1 IN g * bx 5 0 > . 1 . 2 
3 j Bb BED ks, * 


„ » Reduthio F 5 Fourth; dend Addi * 3 
Wut Quantity is bij roots ich if ** Fe 1 5 

cake £370 5 e walt be 33) Ws Auer, LE E | 

| CT ee 0 + Rat 55 51 ET. 1 e 


£5” by . rer f * FIN a 4 


a ud 


* 
; , K — 
: 5 . 72 * 
A - Is . 3 
2 2 es G 
4 " — "4. 2 
75 8 n RE iS 
3 N . FRI ly r 
- * - _ - — 4 TC. 
b a 
— LEST. <4 AVE * bod = 
4 g "0 he 


= 
5 
. — — N , 246 #636 = „„ 
TT NS a> <A D Drops; 1 <TD OA Den 6 
arp 38 <e —— tied wy a * 
7 n 7 & 4 Ra = 
8 24 22 * ry 
E = 


8 Ni 
n 


* 


2 — 1 


2 


e 


* 4 
"_ "I" 


: oh 
r 
Es 5 . 


Po, Aft 


4&4 


„ Wi e isthat ro Ser 4 add, 5 2 = 


* . By — s ccond, Fourth and ade, *; + = [ 
What Quantity 3 is that PM which | + 
1 1465 of 5 the remainder ſhall be 1 off > 
| Apr, : Ca Le 
| A Merchant. has x and; 2 of £ "of a Ship. 3 1 
What part is that of the whole! FP Aunſiner. ä 
Or rf. OM 20 a 
| IE Another perſqn has? 5 of ; y FE 2 of 12 3 2 1. "A ys 3X 
Ide ſhare in the Cargo of 2 Ship, bi, 1 
” 18 Pay of 73 whole 5 , . 3 e + 1 0 = 


J * 2 
menen 


1 hs. 4 ve". 


[4 
4 x 4 * 
UAE" ERA 
* 2 9 
— > LE — —— n — 
Ly Sz ww l oy * — 


* 

4 
£6 
As # 


oF 2 * 5 
2 3.6 SMC > A oy 3 LE 
75 4 „ De „ 2A 


Reli, as Ska Parth and Subfratfie = bo "= 
| e eee 2 Z 
88 5 1 
+. That vantity is chat to which if I 4 „ 
i 30 #4 the ſum will ber 2” Asus. 1 1 . 3 1 
VVV 
another 2 A 4 os, Quettion is whe. = of =. 


92351 = 


* 


_ af their Parts were N and Ir bor, 
1 which had the 3 of the two? "fo. Ty 


I 5 FE T * Redutio Sd, Fun, Alu and 


3 a 


we 


=. gs 3 is; of 1 = : of 4 of 2 LY 
$0800 9 Anſ x4. 3 5:34.42 555 

EF.  _ How much is 3 of ; and 7 of £2 of © 2” 
—_ N 8 Auer, 
13 Ces 8. * 6. © n 20g PRs tf ” W 25 1 . pf 


4 A * Nazi the Fourth, dire and 80. 


F 7 4 25 4 P 
& 5.8 W ; 8 f 
1 A 2 5 y 
= : oy 2 2 4 14 1 3 R * * * 1 23 1 5 2 N ' 
65 * * F : 9 * 7 xt 2 7 . | wa * q F y 
| 2 5 | P 5 « 4 
X * 7 ; Fn 
* 11 FEES 7 _ 
4 * » * 1 - 
- 2 + 


| | 4 Y X $ Y [3 * L 
We P \ * 7 bk g } L 5 
E - . S. 3 4 4 4 '$ * 


5 . . a, 5 


75 25 . 3 ä 
oy 5 0 5 r 


that's the produit 8, 4 35 
here you are. to Conider that 6 d. is 
= part. of a Shilling, and 5 N the 8 -; 
"Queſtion. more rightly, Nope is, What's | +4 
L - 7 Dee of 3 ; by. 352 „ * t 
12 — * 7 1 14 | its 5 
| 9 pin Wigs the” coc 'of 41, 
"ES 11 4.chere { as be — 74 
a > — Pug bl 19 + 11,0. is 228 | 
L we 7 ine, and fo the Qu 
| 37 9:1, Heb 


. 


5 * 
„ 


4 4 


. Eur MO" 7 eee = 
| * * e £ 


5 28 the Namerator Fraction to its, Denami- 
Wen the: zof 40f the fare of 2 Ships 


Portion, of which he ſpent 3, Of the reſt 
ne ſpent: „ and then he bad 2521, leſt, hat 


| 40f + tothe ſimple Frattion of 3, this; 1 2 = 


| was f of z of his elder! Brothers N f 1 7 8 4 


f. 
tated is, What's the proddck % 1 2 
3 Anſ. 15 U. Le. ee P> S bo * | of += 
A cerwmin: Perſon: bödng 80 'A fac 2a . | 
Mine ſells 3 of his ſhare or 17s J. Whats. . 
the whole: Mine worth Anſ. 380 bx. fn 
' Reduce; of.4; to a imple Fraction, then 


nator, ſo is 271 to the Anſwer. The fol- 


2 N is done frer the. 
manner. ame 


9&2 £ 


worth «471: 73s: 4 dichowmuch. is e 
whole worth ? r 


A Father dying left his Son a 22 


john hy did: the Father give him 5 ior, 
71. it een a SI60H i 
From Unieß take 2 : there remains 5 next — _ 
rom f it leaves , then fag ag 3.10 $ 95 1 we Y 
252 tO the Anſwer re quired: ; 1 e = 
A younger Brother Ren 2181 which « * I 

] 


now -3.5 times his elder Brothers Portion 
Wa 1 " Lime his Fathers Eſtate, I e 
the Fathers Eſtate. * Anſe 22651; :. 1 4 i 

Reduce ; of 2 to a ſimple Fraction, then . Cs. i # 
as the Numerator of the Fraction to its = 
Denominator, ſo is 210. to the elder Bro- 2 
chers * Is this 1 by 43 E "+> 4M 


* "A 7 
gives | _—_ 
. : y : 
__ 7 2 8 
AR: 54 b ** 4 2 > 7 « i = 
, - FR nf Woot ; 
z'% - N . „„ R— 
15 Bhs * * , 6 3 * 
Sx : i 4 . on — —— — — 1 1 
5 1 y 2 f * 4 
g hy 2 1 1 . 7 * nm os Tot 8: 3 
8 * 7. . 1 
— — 1 9 OY . 4 
2, *. # ? : i - 5 * { 
' - 
-— 7 3 
43; $ : > 2 2 
2 + . : 
: 1 4 8 if 4 


8 e 
, Sies 1 105 1 ot the Fathers Eine; fa 
= - therefore as 41003, is 3; the elder 1885 
1 has Potion to tho achers ee A 1 
6 Þ „ 
e perſon 05 his Will gave to one 
=: 105 Child 3 of ; of his Eſtate, and to another 
= £o0f'; of his Eſtate, and when they counted 
1 _ their Portions the one had 5434. 1-5. 9d. 
mmote then the other. I demand. what was 
the Fathers Eſtate. Anſwer, The firtt hod - 
6371. 105. gli rhe Second 1180 J. 12 . 6 d. 
aud the Fathers e's is Rk, 3 . 6 1 


_— 4. A vatper f FROM to one of his Children P 
=. of z of his Eftare,/ and of the remainder he 
. 1 1 Saane: another of 3; and When they told 
=: their Money; the one had 173 l. 126. 4d. 
= more than the other, how much had each, 
_ 2a what was their Fathers Eſtate? Anſw. 
een bad gu I. 134. 7d , tbe Second 
_— 243 L 44 34 & and their * N 
1 e 1388“. 48 4% * 6 317 


ag * 
, < 
TILT Wh 4 Ie ; 

= 4 * n n 9 


1 FD © ol he method of beg bete two . 
= 22 3 5 {0889s not much unlike that of the Mer- 
. chant f done by Reduction cen Fourth | 
- "a Suben V h 


W 


REES 


ge” © N *' 8 
* - A N 
4 « 9 1 "> * 
* « * . 
5 . 7 : ; 
l 1 k b * oe 1 
K ͤ 2 A F * 4 
= Wo ;F — . * 1 
! "454 * . 
- 1 . Ny 
4 
© 


8 | 


* 


HA 1. a FraQtion 3 is, 25 2 . „ 
| I have already declared in the Do | 
Arine of Vulgar Fractions, and therefore 
ſhall here only ſhew the different way of 
noting theſe from that of Vulgar, with 5 = 
their great Ule in the Solution of ſereral _ 
8 Arithmetick Queſtions. + + . 
A Decimal Fractien is that whiich hath 1 
for its Denominator an Unite; with a 
certain Number of Cyphers as, 10, 100 
7 1000, 10000; Fc. are all Denominators | 

of Decimal Fractions. NE” eds 
Hence tis evident, that we e hes. 


Unite into 10, zo, 1000, 10080, Ge. 
. equal Parts, for dividing it firſt into 1b — 3 m_ 
„ | ayal Parts, and then each of thoſe again 
into 10 other equal Parts, will divide the - 

*- Vnite into 100 equal Parts, and if 'again' 


we divide each other of thoſe Hundred 
equal Parts to Ten other equal Parts, the 
Unite or Integer will be divided into 1 . 
equal Parts; and ſo by Decimating the 
Firſt, and Subdecimating the Second, we. 
Proceed ad Been, | 2 >... th 


- { | 


„ r A + x 
* 


* 2 Cy 


* "II "y eng 2 5 the Lt s J 
| 28 e 2 
SE * 3 4 £ q 
> a x ; 4 
: 0 . 
2 


— 


Nw a he SA TP of Diet. - 
3 Fractions differ only in the Number 


. 7 PRE, * "3% ® * * 
* 8 10 
” * 2 0 * 0 5 8 


15 5 of places, and not in che Figures, they being 


- always an Unite with Cyphers, they may 
be expreſo d without their Denominators 
with a point before them, as gr is thus ex- 
preſs d 80 and "+45; thus, . 054 alſo 12 45 
thus. 027 and Here obſerve, that this point 


| «Mingus them from whole Numbers. 
Hence the Denominator of a Decimal 


Fraktion is eaſily known by the places of 


the Numerator, the Denominator being al- 
Wes one place more, as 6 hath ro for 
_ && Denominator, and -054 hathf 10, and 


dz hath 1000 fox its Denominator; un- 


©  derftand the like of any other. 


The order of places in Deeimals 3 


Left to Right, and therefore contrary to 


the Order of places in a Whole Number, 
which is. from Right to Left, as in this 


Decimal, f 48, here's is in the firſt place 


next the Lal Hand, * fignifies ſo many 


Tenth Parts of an Unze, and is therefore 
Called Primes; the 4 in the Second place, 
S ſignifies fo many Hundred Parts of an U- 
0 wp and is called Seconds; the 8 in the 


ird place, denotes ſo. many Thouſand 


Parts of an Unite or Integer, and is called 
1 ok.” ne to on as” in” "_ OS 


” A r 2 > * 
Pp - — © dh A; * F 4 2 y w . * 7 ; 5 . a 0 - ? ** t 5 . EY 
2 * . - N : wo n „ . "FR I „ wells >» p "oo x 
: ** "o . 1 1 : + eons of NF 
5 1 - —_ { b . : 
. 8 2 3 5 
* th LOD EPS : 
* 4 $4.8 34A 
- | CEE Kh 
n A * RY 
* 2 , 
. 5 CANE . 
wo . h : 
be 4. 
© * L 
A — 
b © 
75 
Fg <= 
« 1 i 
. 2 5 : | 
* af off 44 
3 * — f 
* '> bee 
ins, 


* 
ki 1 
l = 4 a7 
”_— =” SOOUP__T Ss. erorrnmonf 9. oa— 
© N 
of IR , " 9 


9 


q - 
"1 to b «x - 


2 


E 5 4 gur pumnou / 


5 v * > — 
* . 0 3 hy Ys 


. = C * 


» _ 


OG | Sed padpunh-” 


$A 4 _ 9 
4 25 a 

. 1. * 8 N * 5 
oy it ” . 

N ; 5 Kath 


, 9. 1 ＋ we i 
; 1 : n ” F * 
4 * q : 4 
— © * 1 * 2 wr. 4% * pn 
4. 2 Fig q, 
k - — 2 | IP 4 » ' +» + x A 
N 0 oY Lan 18 5s 2 


li —— — 
5 * 2 . So 


7 * 9 Y * 
5 as) NE * 5 i 
* . 4 0 , 
Se 2 P 

. a + Wy = 9 . * 

2 » : VS 4 . a big? - 
= 89 * . w * % W 
wat 3 RN > * 
— pa N 5 oe 0 
7 +. os > 

k U 


| ; . s ' 
8 5 * & 
* * * 
N 8 6 * a - 
- 8 * * 4 4 
* 8 
5 


3 8 81 Sh pings the Notation. of theſe Numbers, 


. # 5; 
% - * 4s 


hg 3 


" : p 1 r 2 P a 4 os * <A ; 
* = EY A a S 3 1 2 : 
* N 8 £ 
© — - # 
. 


— 
* 


* „ 3 * . 15 a , pe N ay 
* > > — 1 p VS : » 8 7 
2 2 a . * > } 1 * * 
a ” - 
48. et PTE EE TIC Env ., * N ; 
* 2 18 F REY : : N 
a a 1 * £ : | * — 1 
z " > © * . 
3 3 " - þ : . ; ' 
* . X . 4 1 " 
Oo 


This Table conſiſts only of a Decimal _ 
PFraction againſt Which, above is ſet the 


Value of each place, and below its Name. 
From a little Conſideration of what has 
been aid tis evident, that Cyphers prefixt 


on the Right hand of the Numreator of a 


Dccimal Fraction, doth | neither increaſe 
nor leſſen its value, for 2 is Of the ſame 
value with . 20 or 200, &. and therefore 

tis very eaſie reducing Decimal Fractions 
to a common Denominator, for tis but 

ſetting Cyphers on the Right-hand' of the 

Numerator. As ſuppoſe .3 and. 84, and 

476, and 2356 were Decimal Fractions, 

Aud it was requir'd to reduce them to one 

Dienominator; here I conſider that the De- 
" Fihe greateſt Decimal given - 

is 1000, 1 therefore add fo many Cyphers 

to each of the Numerators. that will make 
+. each of their Denominators to conſiſt of 

z places, ſo that the above propoſed De- 

eimal When reduced ſtand chus 3000, and 

38400 and . 4760, and 2356. 
Im have been as clear as poſſible in ek, 

cauſe of the. great falicity” they bring 

| . 4 >. | F = 2 5 

with their practice in ſeveral Operations, 


not only in Arithmetick, but in moſt other 


parts of the Mathematicks. For had the 
Diviſion of our 5 Meaſure, &c. 
been decimally, we had never been trou- 


8 | F 4 255 8 I . 5 l a . | E>. ; . | ; 25 ; 


b , 4 . „ ' F {.Þ 
COR 8 % . * 3 * „ +v 
£ , ; 

2h . 


| 
| 
4, 
' 
| 


as bee a > ny 
* 82 8 <> 
N 7 1 2 IN; 25 8 7 ps FI ** 7 3 


3 


® 


; 833 vb 


_ = 


ſuch W in . Open and 1 


indeed the Art of Arithmetick would be 
Taught with much more caſe and expe · 


dition than now it is, in caſe ſuch 4 
Reformation Oe ever be cue 8 


7 Is 6 NR 4 3 
ö " 8 7 WA . 1 * * a * 4 ” 5 7 
8 ; N 5 3 3 [ © * 8 p » 3% : 
ö . - : 8 — SY 2 , 7 N * "oF 4% * 3 2 7 1 * , J * 
8 1 — 8 5 
5 * f : 1 . 1 — 4 * ah 
4 — 


Pl 1 
. 
—— — cc. 12 11 — ** 2 . 
— — — 25 * p F J 
* PX £4 IE Tt» 
0 # 


Addition of Dicks”: 2 5 1 — 29Y J 


s to the manner of Mine,” "is; the 1 
8 ſame as in common Addition, the 
- buſt neſs being only to ſee if they are-righr- _ 

ly placed, according to the manner of their 
Notation, which thing is eaſily effected by. 

ſetting the point prefixt to them under 
each other, for then the reſt of the place: 
will fall right whether they be whole Num- 
bers and Decimals, or all Dee Lee the $9] 


Hane Examples, gs 8 


parts. 5 In. parts. ti Parts) | | 


155 4 29 2. 43 a 8 2 


theſe to- 3583 5. 6 615. 369 


— ·˙· RS = ; 


Sun 1 46056 oft 48. 645. tas... - 


: 
e \ 
. 


"Shiv you Rage in 1 11 chefe Caſes. this" bu. 
my ag under 7 FO under Ser N 


P : 5 : 5 * 0 
; . 9 5 xt , *. & el wy; 
* d 
AN 5 E - 
PD 
Y - 5 
*. 
' , * * 7 * 
- 
* * 
- 
= ” 
$ = 


— N 4 OTE 2 2 
c 3 
r 


3 4 5 f 
4 * p EW. ty, : — 
== — n 7 


- * * * / 
5 0 5 
7 8 5 LR” 
4 
— 
8 : Fr ” — 9 5 
* 2 r Ne * 
_ 2 E 
* M7 * * - 90 
1 
4 


FIR &. and whe Integers are join d with. 
a Decimals, there Unite, r under Unites, 

and Ten under Tens, &c. in which Exam- 
8 ples. tis very plain, that the Method of ad- 
.-. ding is juſt as it was in whole —— 
only you are to make the Summ conſiſt of 
(92g ſomanp. Decimal places as is in the greateſt 


s ol it: So in the ſirſt Example the Summ 


1 1 of ſix places, or Figures, and the 
greateſt part of the Summ But of Five, 1 
Therefore cut off Five Figures in the Summ 
towards the Right-hand for che Decimal 
Parts, the remainder on the Left are In- 
n | 


* 


Note, at in chis, and che following - 


- +” Rule, che Decimals given to be added, or 
5 Lubſtratted, muſt be parts of 725 ine e whole, 


EM 4 . More Kang. 5 1015 : 


- What's 3 Summ of 25 and eo 


F: and 94. and 89.76. Anſw. 122. In, 707 


mr 1 
What's. wie Summ of 3.87 and 486 nd 


5 : 4 and .025.. Anſw. 490 In. 295 . * 


What's the Summ of 59 4 and 187 


and 7 6 and c N $49 in 935 


| Parts, 1 
Note, That 1s. over the e and 


8 Sy TOP for $46; Ak and. | 


1 ky 3 bp 4 
"4 
fs, - 3 
3 
. * 5 N — 
e — 
. 95 * 
* = & * 7 
— ; gs 
s * ; . Pi Eo 8 
* * 8 2 8 
8 * * 2 ; * Fa 
8 3 * 1 $ i 
+ — 


52 Fs * * * 
5 5 + TREE 
* * - 


* 
5 * 
x: * . 
&. * F 
\ 4 % : | A * . 


. . 2 2 
g >, | 5 
% 4-4 6 | 2 > 


HE Operation here is in all ref; 
like to that in Vulgar Subſtrattion, 
F the main thing (as in the laſt) being on- 


ly to ſee that they are rightly placed,” 7 5 


which is done by the Direction given in 


the foregoing Rule of Addition. See 7 
Following N i 


, . „ doy Ppoe7 
8 8 7 Ss a * one 5 ö > fs. 12 | 4 
| by 4 + 

£ = 


2 
N 
1 
n 
22 
'» 
Guy 
\N 
1 
wh 
D 
» 
Ly 
Q 
@ 


- Here you ſee we $ubſtraR as in common | | Y 


ubltraction, only obſerve” that where the 


| Decimals have not an equal Number 4 
I Places, the vacancies are ſupplied with Cy, 


- | pliers, or underſtood ſc to be, eſpecially 3 
in che upper Number. R N 

1 . OE Fr More Examples 8 x WD WW” 
From 15 SubſtraR 5. 8. Av. „ 5 


From 1 Subſtract. 9872 Anſw.” 55 28. 
1 * 6 Subſtrae 


k 755 
8 * * * 5 « * 
—_ Y . EEE - * Pg * 
p \*. 4 N x l 
0 9 * » & _ 4 : . * * S» ] 1 # 2 * 
2 5 * : 3 5 
I k - _ 4 , * 1 #7 


2 


P 


4 — 


r 


— 


8 


3.98625. Anſon: 2 +, 


* . S- — 
N * 8 a4", 1 2 2 
<_ 
7,905 a+ * 


Ky 
— * 
LY $A — — 
„ 83 ” * 
a J , 
* . n _ 
* Jae: 
C6, . 8 


: N * R V R 


134 


N. n of elek. both the 
manner of placing and multiplying i is 
in all Reſpects and Cales the ſame with that 
of placing and multiplying whole Num- 
+ bers, the buſineſs here being only to find 
the Whole value of the Product after the 
Operation is ended, which to 9, Rake this 
MICA TY 

8 K UL E, 

| See Peu, ny Decimal places es. are. in 
the Multiphcand and Multiply Hor, and from. "the 
Product tewards the Right-band, cut off \ Jo 
many as are in both 7 5 ſo ſhall the Figures 
en the Rig ber- band of the paint be Decimal pla- 
ces, and thoſe. on the pres . ay 
The . e F 


| : — 5 2 5 i 
2 MS f 3 AL 1 5 N 
n oo By 
4 "We 5 46 > uy 6723 5 
LY 4 BY 2 „14 f "IF Se#4; 7 . . 03,7 . 
F FRA 14 4 * N 5 * > : fel ES M 


8 . 5 e p 26501.- 20169 
„„ WY 40338 | 


: — 75 . TR — 

br. 7644. 5 49 mY 8 2 3549 38 
8 Eh —— : . 

Ws a> DE As, . 2, 9 l * w - 4 P 


— 


C 
But if when the Maltiplicaion is ended? © 
_ ariſe not ſo many Figures in be 
Product as ought to be cut off, then 1ꝛk 
ſuch defect to be ſupplied: by annexing as” p- 1.42.8 
many Cyphers on the Leſt hand thereof a2 
there wants places, with a+ point before 1 
them, and you have the true value of U 
Product. See the W e 2 


- 


2 1.5% 
8 N 3 2 * 0 4 2 . 2 Y SEN 2 1 6 , 4 V - 7 © hb . 3 5 
* » 1 6 4 — * * \ 7 . ; +. 0: 8 
þ 5 k * C * . DD 9 7 L - 3 : f . $55 * + 
1 3 3 r 4 : - : * Ws 3 : 4 | „ 
* a A = * . 4 . 1 ; * 2 b 
a | 4 : * * = 
| - 
„ { - — 8 
— 


. ; . „„ E 5 
LS . . = * 4 - i , 3 — 1 1 „ 
F r 5 1 I : k 1 * F. 3 ; ” . 2 % X 53 * ” 1 
a [ g 4s F * 0 ' "3s + ws Se rot 4 Y . iy 


. s * 5 c 
- $ * ” c : — 
by 2 N T4 o : 2 SB» et Ek +44 op AR 
3 \ * . \ q N "> i , * 
W 5 6 0 2 7 & > , FOE BP; 5 25 CE 7 . 
f . , f 5 , 5 - — 95 ry % l : F289 ; 
” * «4-3 > þ a * =” 7 5 * i * 4 : 


| — R — ST LIN TER. 
5, math 3 * - : | . . Wn K #- | 8 
a : | | l e K * f 1 * 5 


rale, 2755 0 n 


be FE 
4 | | . 
— r + , f - . * 3 * 
14 1 x „ ; IF #7: 1 72 Le 
2 3 oe _ PS. , MN 
a 4 » * 1 i 2 5 2 
ws. Hy N 5 . "8 ; * 8 3 * * 7 = | 2 
nant * # K* + 45 6 «7 « f * 5 "Os. » 13 19 *. e 
I * 


5 : "43% 


value of the Quote 1 in DIG. WD ins 


2 . 12 8 FP - DE 
2 LD, 2 T Wt kx of FA þ 3 * Ws * : * r 7 * N 5 7 1 Ty pts 
= * . * be £ - M # > / - 57S 4 — * * 
a fi 1 * * * > i * " . * * 2 * * 4 . * 4 bo ; a * fy N ; 


| | 2 — W 1 8 1 78; 
„„ 5 More Examples Woh 303 e 


d * — 4 4 I * 8 * 8 1 
9 . * : 7 
1 2 *. 7 5 2 2 8 8 i 3 
o =, £ q * * 


be 3 onde . to vou, in a Gti the true EM 


5 i 5 5 > Rt * 4 * 7 * L 1 6 * — 4 7 
A 8 2 * n 5 45 "WP TI; "> : ? 2 I 2 N I N 3 
* 0 0 » a 4 5 . %» *# - , ns F * wt* * Le 


> ES J NN : 3 p A . a | 8-4 " 
* j : 
»  # 
& 


Mult. 4.0, 72715 bosse 232 e 


; vv 4 2 
5 ——— ——— | | — — 8 


eee 101.616 + 8 


? 


487 


8 
2 
© 
© 
O 
ee 


3 


. 
* 


„N . rn es | 


There i is in this kind of · Multiplicatĩ on a * 5 3 4 
certain way of Contraction, by which youñ 4c 


1 


may get the Product to as few or Tony 8 "2 


9 Pp 
F, ” : 34 2 — * 0 
' . 3 Th ; 8 R IF 


* 
* 1 
? * 
: & 
1 0 ir = 
* 4 . 
” p . 
= : * 4 
8 * 
Fl - * * 
Pp 1 : 
* , 
* 7. * * 
vers, Þ 3 
1 3 
A % » 2 ; * : 

„ 

pe — > EE ” 

N 3 * * 

4 
Yelp 4 (Ss 3: 9 
4 2 — 


Raw 4 
” Om 4 : 
= 7 8 
5 wk 1 * 
2 *. hn _ 5 » > 


— 18258 * 2 
5 | ; 
, £1 : 3 . 1 : it 


2M N 705755 
4 . . * a = 2 * * CL > , 
N b 1 8 BEE . : 
3 * 8 * 3 jy 4 4% + -* - ” * — 
* + 
* £ 3 g . r 
5 8 3 So 
" Fog 28 * 2 ; 
* , 4 & * 3 4% Ky * 
r 2 „ - . 
. 


A 8 ie * . ; * 


„ * ore k & FE TTY n a . 2 N e * ? 7 4 
A l BY, WET = 9 * TTY . on, A SY N e 6 5 - 
n * EY _ 855 P — 3 < 3 7” ; . 3 118 : * . . n * 5 x 7 N ry 
4 by * * „ 9 . n r 7 3 1 x N 
ö N 2 5 | 2 3 „ * s * 
2 * r * S 8 : s 29.2 1 * — 
C : 5 * 7 1 4 
« - a5 * . - "Re K 
1 he * ** \ 
r 9 * 1 
. 


| 0 Ex] 
p oi alt: Ha without the 8 
Multiplication of the whole: The Me- 
thod of Which is as follows. oh. 
As ſuppoſe 9.58 was to be Multi plied by: 
8 79, here tis evident the Decimal will con- 
liſt of four Places, and Lal two vould be he 
 Cufficient. OTE | 
Set down tlie bier of: the two Gann, 
 rities for the Multiplicand, and then fer the 


place of Unites in the Multiplior, under 5 


chat place of Parts in the Multiplicand you 
9014 have the Product; this gone, invert 
che order of all the other places i in the Mul. 
1 that is, fer the place of Tens where 
Primes ſhould be, and the place of Primes 
where Tens ſhould be, and ſo on with the 

- Snvercion-of the reſt; then let each Figure 
of: the Maltiplior multiply chat of the Mul. 
1 Which is juſt over, remembring to 

add what would have been brought thither 
from the following places, which done, add 
oor, together, and from the Sum cut off 


*two- Figures (in this Example) next the 


- Right a you have your deſire; all 


| hichby the following Examples, .compa- 
ire — 2 N * 4 1 


common way. 1 2 
9868 Muſtipicand 
8.70 Multiplior 


3 2 


* 


* nn * 4 . Lf A - — 
4 wm „ 
. « 13 We. 2 
3 ” „ 
4 5% 
0 * 
x 2 
* 1 
1 » A F 
K 4 
FR bee £ #7 
„ 1 ; 
5 « # 15 n 
7 2 oh 4 
* ” 7. © . 1 * *. ot 2 
* + . +% 
4 > — N k ok 
* * 
»- — 
4 e 
. . 4 i 
4 
= © - 
be F . ” 
P * 4 C 
- * 
32 "I 
4 . A ” * * % * 
: 7 7 8 * 7 1 
* „ , 
* » » > a 
% * 8 — > * 
7 + 
* * 4 
7 R > k 
5 my 4 * EMS I * 
8 . © * a q „ 
8 - 7 ; 
. * 8 * 
—— — ” ' 
4 


By the common way. 4 


2 4 a+ . 5 0 4 > : "t\ 


85 


— 1 ri 
6 _ a, . ., : 
ew by 


os 
F*% 


» 


- 25 
I an 

- 

"5 7 
* 
— a, . 
* * 
+ 
in 
" k 
. 


8 bg. 7 


: ads + Y 
raed al 4 : 1 
Lk 9 * F 4 * 


$4 N 


| Erroras cauſcd 75 che want of dhe carriage : 
- from the next row, and therefore if you 


would have it exactiy to three places, eſpe- 


# cially 1 m a 1 75 fog OP.” to N Ir o Rr 


A" W 1 y 
* — * 
ths. - - x * 
. ox ls "hs * 
— i : : LA, * , 
2 —— . 118 22 
hy r — N FI" 
. o * \ „ 3 — 
1 r . I 


Due on of Doane, 


viſion is in every thing like to that of 


Common Diviſion, and therefore no regard 


a to their Place and Nature is here to be 


| had, any more than what was in Diviſion of 


whole Numbers, the Miſtery of this lying 


. In their Preparation When need re- 
quires. Secondly, In finding the true value 


of the Quote a ter the Divition is ended. 


EN Er#, Therefore when it hap 1 = 
"the Diviſor hath more places 3 5 Divi 
| dend. you muſt put to the right Hand of 
8 I he Dividend, (whether it be a whole Num- 
8 mixt or Decimal Fraction) a certain 

number of Cyphers at pleaſure, by which ä 
it is made fir for Operation. x, 

5 Ass ſuppoſe 14 Was to be divided by 361, 
2660 evident here is an abſolixe-neceſfity of 


2 Cyphers to 14 the Dividend, be- 


_ HE. . working Wa Di- 5 


ory * can divide by 361 the Bulle. = 


— 


notice > thers muſt bo as.many Decimal 1 

in the Diviſor and Quotient as are in the 
Dividend, for the Dividend is in effect hs -. 3d 
Product, and the Diviſor and Quotient te 
MNultiplicand and Multiplior, and therefore 
for the finding the Value of the | orient | „ 
5 this 1 18 the | | | - 3 : 85 4 
i 


Look FORE: many Decimal places are in 
the Dividend more than-in the Diviſor, for 
ſo many Decimal places will there be in | 
the Quote. 

And therefore when it happens the — TW” 
dend hath not ſo many decimal places as the $4 5 
Diviſor, then muſt ſuch defect be ſupply'd * 

buy annexing e to the Right Hand of 
"= he 3 5 
839.380 


5 8 | 
| args As ee. 


- Having om 2 Gee to SIR * | 
= Dividends, the firſt Dividend being an 
24 f eger, conſiſts only of the 4 Decimals . 
N but the later being a Decimal, is -Y 5 
* made to conſiſt of 6 Decimals. They be- 
ing chus prepared, and the work of Divi- 
; ſion over, you ſee the Quote conſiſts of 4 
ik - o places; now conſidering how many Deci- 
ic mal places there is in each of ra 5 Divi- 
dends, more than in their proper Diviſors, 
and you ſhall find, that in the, firſt Quote 
there gught to be two places of Decimals, 


*. + 


5 We. and in the ſecond fix of the like places, „. 
wich becauſe there i e four L prefix rwo JF 
©, Cypbers on the left Hand thereof, ir rs 3 
4 3 . true Y. 5 : 

8 . game Examples. | 3 Lo. | 


: 


* 234 2 „ prepared 3.0000 prep. 1.50000 prep. 004000 2 t. ooo 
1 | | | y * * "Wo . ” > 5 ; 
WW > ' true Quote aero true 7 true Q.. — Q.1.53 


. 1 % . N * a een 


3 20550 508: 9). . 5 — |: 


— 
a 7 


1 . 1 pee to theſe ws es fer aul de —_ 

= Dividends prepared with their Quotients _ 

' ney valued, the conſideration of which, 
with che preceding direction, 1 bo will - ". 
de a ſufficient light i in all other L at 
SE * 5 2 4 


; E 
: * 
- o 93563 * * 5 5» Ss 
\ — ; * 
4 * 
: 1 


* 5 
- 14 - * 
1 Sg 7” 
* * * 
— 


* 
8 


hs a Moses 


- Reduttio of Delia.” 


how-to reduce 4 V. Algar Fraction 4% 4 


J Decimal, and contrary, which is no wote by 
than what in effect was done in Redaon 


the Fifth of Valgar, Frattions ; only here 1 


ſhall perticularly 2pl 1 it to 125 bukneſs of I 


Decimals. 


5 


4 


7. 0. reduce a 7. 1 hadi 70 4 


AAU A - Decimal. 


I ; . 8 
| Rule, Multiply the Nama of Ne. 


alga Fraction by 10, 108, 1000, Se. 


Fil 


according to the number of places IP 
would have the Decimal to conſiſt, the Pro- 


duct divide by the Denominator ir Lata 
| the Decimal "Oo. | | 


-_ 


© AAS rp og > 


85 Example L Reduce to a Decimal radio 


44 


4 Numer. Vu Fra. 


100 Deu Decimal: 8 


—— 


— 


4 * ka . 4 4 P Ss 4 ' 7 7 0 
n — — > i 
. f 5 n 
3 » —_ | Fi 
> , ; 
4 1 Y 1 5 
F 8 a : 
N + ” 4 
” — Fl - þ 7 . 
— 4 \ " , 
: * 
FRY. 0 
— 5 ; ” 
. 
* 


'H A T I 55 ge is ro ſow you 


* 9 7 


> 


>» 
—_— 
** 
- 


"Ef 80 that 75 is the Decimal equivalent 
VVVVVTVVVVCCCCCC gar va . 


„ 


, 


: * | S BY 
Norte. From the preceding Rule tis evi- 
—_ dent, That if to the Numerator of any Vulgar 
= ©  Frattion, you annex ſo many Eyphers as yow | 
would have your Decimal to conſiſt of places, |: 
and divide by the Denominator, the 1 

13 gives the Decimal requirec. 


© Example II. Reduce 3j to a Decimal of |» 
+ five places. EE © 


— {> 2 


1 


* 
4 * 


I᷑o0o r5 the Numerator of the given Vul- © 
gar Fraction, I annex 5 Cyphers, it makes 7 
© x$500000, this I divide by 19 the Denomi- 
nator, the Quote is the Decimal required. 

Cee the following Operation. , 


# 


. 
| 


a 


ho ü th comm. 


be segggg O6, 


— % — 


8 


RY. . ©, 08 
$0 that the Decimal equal to the given © 


Vulgar Fraction is .78947, which becauſe S 
of rhe remainder is not exactiy true, har © 
yet ſo near that it wants not rae, part of a 

Unite of the Truth, and if you proceed __.. 


7 + farther to make the Decimal conſiſt of NG 
plwaces it will be 789473, and then it will - 
not. want 5 part of an Unite of che 
Truth; for if the Decimal be made 789474 4. 
tit will exceed the true value. 5 

And thus by increaſing the number of "HY 
places in the Decimal, you may at laſt come 
06: of, near, tho' never to the Truth it 
| ; e | | S * ih" pb 


| "Rams Ill: Reduce B to a Decimal of - 
hve Saas | e a N 9 4 2 


F TH ns 


* 


1 5 i 


- ; 49 Parts 8 \ at 4 
| CE ENT» | N 
ꝓ— IJ. e . 1 
e +; © 2 ai 
> 1 160 „ 32353 
Bo ors | — 7; * „ 
3 * N e 3 : 4, a | yy 115. 1 
9 5 "Ha < — * Decimal 16 8 
tc five places) Ladd five Cyphers to x the 2 
Numerator of the given Fraction, and then 
divide by 32 the Denominator, the due 


* 8 be the COS, * z 755 ip 2 J 
12 * 


| 


(1020 5 


S note, That becauſe I annex fre 
rs to 1 the given Numerator, and 


Were ariſes but four Figures in the Quote, I 


ure in the Quote as there wants places, as 
nm the prectiling Example, where the Quote 
Ku >= ty Ye bur of four places; here I annex 


= &Typher on the left Hand of 3 the firſt 
| vote, and then it becomes 


Figure in the 
Th 125 che tru 


| — 2 


Fe 


N ae le 3 parts of ens | 


Weight, Time, Sc. 10 4 Decimal. 


cc. may be turn'd into a Decimal) of rhe 
fame value, or infinitely near it; for if in 


5 2 Money a Pound Sterling be an Integer, what- 


ſoever is leſs than a Pound is either a part 


br parts of the ſame; and when you know 
w "What part or parts thereof it is, you may ea- 
ll reduce it to a Decimal of the ſame value 


from what was E in che laſt. 


Ms, Whar' 8 the Decimal of + 


That is reduce 3 to a: Deeimal c whit ; 


1 WS of. two * n 


* 
* We: ES 
* * . 
3 


_ miſt ſupply ſuch defect | by prefixing as ma- 
— 2 on the left Hand of the firſt Fi 


5 From what precedes tis evident how 
„ the known parts of Money, Weight, Time, 


been before directed, 1 find the Decimal of . 8 NE 


3 8 » 
es. . N L * 
— $ a —ͤ— 
3 E F 
% 3 ro OY / . 
' 8 $2 
- : * *, — * . 
1 5 ; 4 
— " 4 * 4 — - 4 
5 1 - 
1 0) 


wt 25 
2 — 
1 * 100 4 


# — 
* d 


Here welking brd 4 to what bach 


95. to be. 45. 58 
50 ff 1 Would know the Decimal of 74 1 
conſider that 9 d. is of x 25 of a pound, or 2 


wok therefore according to the preced- .- 
ing Rule, and you! hind the equivalent De- _ 7 
eimal .0375. „5 

Again, if 1 would hd Be chad of >... 1 

Farthings 1 conſider chat 3 Far- 
Things is 2 or 5 25 of a Pound, andi 
| therefore: working as beine I find the De⸗ 1 
eimal! to be .0031 near. "A 

© Laſtly, If it were required to find the Des _— 
cimal of 7, 84.4, that is 371 Fantlogy, - 2 
or 5, here repeating the like Operation, 1! 
find the equivalent Decimal to be. 386433 
the like is to be underſtood in redueing to 04 4 — 
Decimals the known parts of Weight, Times,” 9 
© nw”. ion. 9 — „„ 


3 * 


oc . 


| 
= "wa 


5 + 
5 
LY 5 _ 
A A . — 
R ; 
2 . 
"4 ; 
$I 1 
— W - 
by j , a= 
” k 
* 5 — 
%. 


— e a N L 
Wo 
Y 9 


* * 1 
LS * 
„ 2 


* 
e 


= 
. E _— 5 * 
— - 
4 ** 4 A 
I e e Fr * * 
„ . 0 W 
n re 0 <A 9 
* r 5 an 
oy 5 „NN * em - 
ane * 2 1 * 
8 — 


| ed” + 
8:4 | 
* 
. 
$ 4 


K. 
"a * 2 : 
* | =, . 
* Y 
ER - Ne. 
4 3. 7 N d 
8 Þ 
.25 5 8 
13 
„ 
12 
„„ 


id 


| a and may be reduced as | 
' by the [ame Rule, and after the ' ſame manner 


1885 + * . 2 | ? BY; | 5 
Zo find the valu- of a Decimal Fraction in 


the known parts of Money, Weight, 
Time, Meaſure, Motion, OO. 


\ 


This ! is but the . bo the former, | 
and therefore the Rule for finding the true 
value of a Decimal is grounded upon the 


fame reaſon as that of turning any part of 


Corn. Sc. to a Decimal. 155 
For *twil hold as the Decimal Denomi- 
| vator is to its Numerator, ſo is the parts 

_ __ ofthe next inferior Denominator to the 

Numerator or Number of ſuch ane con- 


tain' d in the Decimal. 


. * . I And hence comes this Rule. AAalriph 


the given Decimal by the parts tbe next in- 


" feriour Denomination that A equal to tbe Inte- 


ger the Decimal gives the part , and from the 


ProdutÞ cut off ſo many Fi igures toward the 
© | right. Hand as there are places in the given 
' Decimal, the remaining Figures on the left 
fide are the value of the ſaid Decimal in aucb 


Denominatian; if any thing remain, it is the 
Decimal of an Integer in be D 


as you pleaſe 


nation laſt 


as it was in Reduction the 18 7 K 1 


| | | 
# 0 5 Fradtions. ö . TIN 
* 5 : I — A 5 + 4 4 b ; 
: N | 5, Bs | . 
* : 2 | : b 65 N 4 743 4 0 


£2 57 — * 
3 


room thereof give you a Practical Rule für 


che true value of this Decimal” 3765 of a 


Pound e as ſoon As = Tow here ir 55 . 


Exam et How nh is 
"Pile Serling 2 1 fay 


as 10800 to 3745 ſo i 20074 64 SY 
. $I 20 ER IP Is. „ op AA HT IAN 


> 3 3 
; 5 My 1 : s? > 4 tÞv 1 ; N 
8 * : 3 * * * %, 
| oo 72 e e 
£8 ; * N * 4 1 * 
* 44 124 6 4/1 a i 593 
0 & A e F f a ' 8 & 4 __— ? 


3765 7 a 


- 


— k 3 5 * 1 


T2... 1 © 
N : = . { 4 ac 


” 
- > - 
« q — $ 
1 . by - . 
* 
„„ 2, 4400 | | 
% 5 * . ; . 15 
; : ; 4 N k d } 
* - " * 
1 
4 ” 


* chat from the preceding Work 1 find © 


Pound Sterling to be 75. 64. 5 .44.; after © 
a like proceſs. may the value * De- 
cimal of Weight, Time, Megfure, Ge. be i 
found. * | 

More Examples of this kind will be OF 
leſs, I ſhall therefore forbear, and in the 


finding the value of any Decimal of $7 Tos 


d. ; FS 


8 The F ure in Fat 12 WR or Place | oy on F 23 
Primes, being doubled gives you the . 
(of Rings, and f ihe Een in he te. 


* 
R 
FLY ” 
« TTY - * 
N . 2 
' * E 1 
— iz 
* + ; 
— Af * 2 n * 1 
q „ * 1 an . g 
* 
e * 
5 oy x >. T. £ L 
of N * 2 
5 * 2 - 6 
by” z 4 
8 
* * 


=_— == place . x abies it, tak t ; Shilling for - 
., Fad ad 4 to the former Number found by . 
=, + doubling ; Then for that which remains above 
I, with the Figure in the Third place, count 
. fo many Farthings leſs by r, that thoſe ro Fi- 
by gures make, being ſet in a numeral order, or if 
. Fignve in the Second place be under 5, then 
>» , xeckon ſo many Farthings wanting 1 as that 
4 "and the Fi ure in the Third place of the De- 
= _.  cimal make in Number. An ny or wo. | 
_*: will make 3 it 48 5 f 


1 1. "TM * > (5 : 
- 5 N 1 4 4 ! — 
* 7 { * 7 # 


. I F 1 What's the 375 - «Pound 
© ok leg . 4 


lere 1 * Which! "TY in Shi 
of Primes, — that gives 64. Then be- 
Fauſe the next Figure 7 is above 5 I add 1 

Shilling to the 6 before found, and it makes 
7. then the 2 left og the 7 wich the gin 
the place of thirds makes 25, which being 
leſſen d by 1 is 24 Dae P _ the 


e 375 17 6 4. 


4 * Exam. Il What's 7 of a Pound 
Sterling "Ip 


tere the firſt Figu 7 doubled "Hs I 
_ number of 8 Shillings as before, an 


18 


7 


the other 19 ner remains] account A 0 


F 


10g Farthings, Which is 4d. ſo thas the vas. 4 
ue of che Decimal 719 $$ 44h „ 


More Examples might 1— given, ! 
but I'think theſe are ſufficient. to Illaſtrate 


this Practical way of finding the 3 
| of a Pound | mg. 4x" 19 "1 "lh g x? 1 : be. 
| - +1 flall therefore conclude 0 


pe incertion of a Decimal Ta 


dhe value of any Decimal part of a Pou I 
| Sterling, omitting thoſe of Weight, - Meaſure; _ 


me, &c. becauſe of their being fo ſeldom 
uſed, and if required, fo ally. Galculated 
| from the aforemention'd gy 5 


\ 


* , l 1 
= 1 % - F 
iſe for le in 1 
4 5 5 222 * * 
6 N * E 6 
this Nature. - . ö * - £ 4 * * 7 0 : 
* 1 v x * 
* $ * ” * " * * & 4 x * « P 4 2 ; s * £ 
# 1 a : : g a 2 1 5 8 * Fe 2 k 8 2 
fy s = " - % : * + * n * + * ; 
. k \ 8 4 * * * g # \ * * 4 
> ö 4 Dd i 4 "= - we 27 4 x + 
* * 7 ; N * % * LR E os 
LR & * * 1 * * * 7 k | * 
* * * 
13 F 9 — 8 * , - 
A OS 
a” 7 ag, 
1 * ! - . * % * — 
” * 4 £ : 2 
: 4 — * — ag © 8 * 
4 &- * , 
F 7 bs » ad. — 2 
* + — Ar *" 1 # © 
7 4 — * . 4% * 
7 - $- - 
= * Fs 4 of” 
L * 2 ; 5 : N 
« 
* * ; . c 
« \ 77 = 4 
— 1 
. * 
; 85 SY "> 2 4 " 
v. . 133 1 
& 2 
* * - 
P : 
* 4 - v 4 4 
1 9 
* . * 1 . : 
* 4 
. 4 * 4 * - 3 2 * 45 2 
2 ” Ot * Y * A FH 
© F 0 
— . 4 # * 4 - 4 * 
2 $ 1 4 
o 1 , b 1 * 
. * ” Fl * = + > 2 9 
» * * =. 5 A g (5 * 
F 4 985 * 
— K 8 : : 5 
* my * FT 3 * g £ > 
„ ＋ 1 1 7 
#4 4 
, „ Wk 
7 * 1 vw 4 
* Lo 1 " > - © 
* . 6 ag — : "i F 1 5 * * 
J 7 * 4 J 4 - 1 
% 6 * > . a . 7 + 
* 8 ; 
- . ; — 
% . 1 
- * is 
> % 
4 " 
— 
= # , 
, # 1 
: & 2 — 
* * 
1 
r 
* 
* 3 oy . 
> # 2 * 
Led * * 4 
& 4 ; 
% 
* 
* 
8 | : 
* Y 4 ry * 
Cy e 
1 * *% 
* Mo 
77 -I 4 £ * 
* SY, K 
* 2 * 9 
. —— =- 
* D 4 


. 


7 


* * 


CEE Ines —— rw a oa 
4 2 


* 
4 7 : 
\ 
--of ; 
con- 
0 
g 


— 
* 


* 
* 


4 


4 
cima 


2 


* 


* 


the De 


2 


* 


4 Sterl 


ewing 


- 
* 
*e » 


a Poun 


[1 


* ; v8 


ge Roam a 


At 


"4 TABLE, þ6 


1 
* 


an) part of 


— 


2 n Fm F 
a WT 5 „ . 
1 —— 


— — 1 r 


- nth - br 4 a N 


. 1 1 1 175 5 - | ' ; 
— c „ © 0-7 FE ak 
t ö | | 5 2 55 5 ; 223 
. . he U of the al EY * 


” 6 4 « 
— $ 78 01 * 


"Fe: "The Wb making this Table 1 8. | me J 
B dent from what precedes, and its uſe a. 


— 


moſt apparent. For let the Decimal f 15 
135. 754. 3 be required, ſeek in the Table 
"= firſt fot the Decimal of 13 5. which is 6g, + © 
next for the Decimal of 74 Which ? 
02917, and” laſtiy for the Decimal of 3, ke 9 
- which is ,00208, I ſet theſe Decimals in N 
1 . order following, and add them toge· 
„r 9 TY * — | 


Lo gy 5 | I3 4. 65 . l „ 7 2 
P 0 91% r 9 9 


ER * ; o v4 <a 
95 2 q OO 8 te 
- . 1 : . & = a, 
* 5 5 | i * ; A 2 L 2 1 1 
: 3 - — þ : : „ 


5 
Z - C 2 7 - * 2 
x ' 9 . o bl 2] * 
* —_— — * » ov 
r ” . 5 
1 - * N 3 7” * 8 
” 7 a » 


bn 12 13 5. 741 34. | 99 => bit 8 


n mn Fe 
a— 
— « V4 -, 
— % 
1 » 1 
” 


% * 


/ 
% 


5 By which you ſee the Decimal of 13 5 1 

: is .6$125. In like manner may 3 = 
3 of any other Sum be found, 2 1 
alſo the Sum belonging to any given O. 


N ® - . * Fe : 4 4 - - * . & 2 „ A * * 3 * 
i , , + 3 % * 25 a ? ; + ” 9 9 ; * 
* * 0 Y 1 * F - - . jp 4 4 -— 


p ; 
1 x - * : 1 . p K > __ 2 A 
F Ll 4 < > * A je F. 1 
* w . 7 * 


6 . p n 2 x $2 3 3 
= | „. DN of Decimals. | © 2 1; 447 4 —_—_—_ 


o ner the uſe of theſe Numbereinall 6M 
Solutions where they might be An i 
 _  expediting an Operation would be endieſs, © 


# 2 8 


1 


b 
e 


* * : , # 


_ I 


__- f r= heloxet on ruſe in moſt parts of che © | 
=_ nen but principally in Gauging, 
BY -  Survoing, Meaſuring, Calculating Tables of In- 


tereft, Rats of Logarithens,as may be ſeen in, 
'- . moſt Books that have writ of theſe Sub- 
Jess; I ſhall therefore omit giving Ex- 
$ 2 . 1 uſing them in any of theſe paris, 
except 1 had treated diſtinctly of each of 
them; and ſhall cloſe this Paragraph with 


mie Collection of a few-cafie.. Queſtions, 
Id = are 55 obo d ok the Nun | 


* p 'S: 


11 Multiplication. | » | 


_— os -6 Piſtoles ar 18 45 each, ow maar: 
Pounds Sterling? Anſwer, 6801. 8 5. 


In 439 Guinea s, at 22 5 6 d each, how 


many Pounds wy 4 after, 493 J. 
17. 64. 
5 ſpend 4 6d. per Day, how much 
s that for one Year ?- Anſwer, 841. 25, 64d. 
"If a Tard of Cloath is worth 6 5. 9 d 
ehr comes 59 Yards. to at ar nd An. 


fuer, 19 18 34. 


chere Was- 138 


. Men 


1 If a Piece of Pavement 8 4 Bon 5 | 
1 18 8 2 Inches long, and 24 Foot 9 Inches broad, 
= - what's the Comet in fare mr? | 

VB " IE a "Man's flare in the Cargo a 
h 25 comes on 14. What was the 


* 


"* 


* , my 
wt hn TY 
1 
. 


35 2 £ 
„ 9 * 
** 

* 


_ 9 * SE 
* * > A 
yy” * * 1 
PT. YN "- 
9 I 
— 4 
* 


I ii the tees autor 
If the Intereſt of 500. for one Day is 


24. 3 d. what's that for a 58. ? Anſwer, © 
41. 1 3% „ 


/ 


4 + © , Wada 2 — p 


+ _ 4 N 


85 295 By Diviſn. f „ 


* 


In 6801. 8s. how!: many Piſtoles at 18 25 
each? | Anſwer 756. 


In 493 l. 17 Ga. . how many Guinc 3 
at 22 . 6d, each? \Anſwer 439.) 
If 1 ſpend 82 J. 2. 6 d. in one Year, 
what is thar for one Day * * * Anſwer 9 * | 


If 59 Yards of Cloath colt wh is. 


3 d. what coſt 1 Yard? Anſwer6s. 9 d. | 


If the Content. of a Piece of Paving be 
863 Foot. 875, and the length 34 Foot 6 


Inches, what's the true breadth ? Anſwer. 
2.4. Foot 9 Inches. F 


.*; the. whole Cargo of Ship wy 61 161 A 
12 5. and there be 158 Men in che Ship, 
what comes each Man's ſhare ide e 


384. „„ N 


If the Intereſt of bee. food a Years is aſt” 


17. 210 What is chat korn ou N 
"a Pr 


3 -$ 
< 14 4 * 
51 4s ' 2 * « 4 
* 2 1 
U- . 
2 


5 conceive 7 pe to: a 


a Rule of Three, being in all kinds and 
reſpects 


e ſhall therefore leave the: gk 


£ 
. % 
- 
” 
- 4 
a 
{ : 15 . 
* . 5 
: : Ra a OW, 4 1 * 
£ . 
3 


in, 70 


with 5 


9 


perform'd like that in Vulgat Fra- 2 | 


CLE, 


r Qutions of this ne 10 the logeni- 7 


Sh the 
Ung and Pound are, for by this you may 
mentally Multi 


N 


Rocker is a \ Rule 1 which PIE wala of 7 
any part or parts of a Pond, Ell, Yard, 


&c. or any number of Pound:, Ella, Tard, 
c. may be briefly found or caſt up, when 


__ Price of One or Unity is given, and 
this is done by conſidering what part or 


parts of a Penny, Shilling or Found the price 
| of One or Unity is. 


| tis neceſſary to learn 
Aliquot parts 100 a penny, Shil- 


In order to bh this 


ply and Divide, that u, put- 
king down only the Products without the 
Multiplyors and ONT, they wa al- 
Ways mall. 

te Method 1 mall proſecute in this will > 
be ſomewhar different from ſeveral Au- 
© org. For Example, 1 952 i nl 
At x Farthing per Day; h . wi 

" king a Farthing, the 5g; Ser, a Pound, I take 
'Kas the-zof a Penny, and ſo practically di- 
vide 4952 by 4 it gives 1238 Pence, 'for 
ſo many. Fours as are in 4952, fo - 
3 On _ TY amount 9 theſe. 
Pence 


of ta- Jas 


1 413 39 Wi UE SE, 
' Pence: 158 05 y divide by 12 to redude_ 
chem to Shillings, andi ahe eee 15 


t turn them 1 into Pounds. 


A 4% 4 5 * 


Again ſuppoſe 2864 ls at a Half. pen 1 
an an ff, here Zaſtead 3 5 A 
penny as 733 Of, g Pound, Aue As the My „ 
half of a Penny, and 05 divide 2864 by 1 1 
2 it gives 1432 Pence, becauſe 2 
= gives a penny, and there ſo many ass : 
s are in it fo Many e the y Mbit .. 
599 mount to; after which Tdwide das Pence .. 
by 12 co reduck heft ro Shillings, anc _ -* 7 
by 20ʃto Wee chem e nn Sth, the. * 
3 LARRY 422 : Yan oy Frag 
10 My Raalte W d Opertitipi; hacia © 
I count tworior} threes! imal Beem 
94 more practical and ſooner petrſorm u thin "= 
one large Diviſon. Firſt, Becauſe ads ©: 
ſtake is ſooner made in athtre Divitiog " 
than in a ſmalſ one, and Secondly chere is 25 7 
many times à large remainder whicheret 4 _ 
quires ſome tr nm to reduce (RIES ws 
— _ W 2, % TOYS SI ER 8 \ A a 
5 * 3 Torment; ni 1 
* E But bethre proceed any 3 ir 4. 2 
abſolutely neceſſary the FR ebe * 
Kae Table by e oe” 


2 


—. 


* 8 * 
$32) . e e 4304 
K N - : N a 2 : : 5 4 
* L 4 5 WW 7 e « - y * N 5 3 4 * . 42 
5 8 % . 4 £44 "4 8 7 * . 13 " » X * „ WN 2 IJ 
0 A * hy : 7 * 1 1 me as 4 , + 5 8 5 . os 44. * | 9 * 1 : : , NES, * e + 
6, 4 ae W 3 8 3 1 1 * * 3 9 $ we f 4 * tab 2 # 3 3 7 FY * 1 N "4 * * ; 
X } « : 1 I p 4 - 6 - a, $ : k 4 
C ons: i „„ 
Id 2 2 , * ; , 8 N 8  Z' x „ * 3 bn : y - N +» CS 
E 2 ES ap 7 4% 1 3 af tw „* 7. WV < e L ; * « ; 1 1 
: * 1 * o 2 8 F 5 6 : 5 * - — g 


2 F N Ch # ++ . , * * © ; s 15 . 
Vs Wh 7 ct © TIES dS 10950 Fun ee; „ 
e ee e e e 
* . p WEL : . „ ; 4 1 hb 


£ 
* dy 4 
—S De ? | 


all * Aliquor parts of a Shil- 
a 4 Jos uſe is to Aud ih the value of 
of things, when the price of 
” thoſe things is one of theſe Aliquot 
As fuppole 852 Ounces at 1 d. an 
Daune, here tis evident 12 Ounces will 
__:: come to juſt 1. If therefore 1 divide 852 
* dy 1 the Quote will give 71, the number 
_ of Shillings thoſe Ounces amonnt to, which 


I V eaſily rurn'dinto Pounds by dividing.by 


— 568 Drams; at 1 d. 
8 Drams will amount to 
re ſo many Eights as are 
| in 568, fc ; mary Sbillings ae moſs Drams 
3 410 "amount to. 


20. Again, 


2 . 


Phe like is to be underdbod 11 ah * ; 


be 24. 34. 44. or 6 d. per Ounce,Dram, &c. 
7 For then if your divide. the number of Oun- 
1 . ces, Drams, &c. by 6 it will give you their 


1 IM ; price iy Shillings at 2 4 each; if by 4 at 


y 2 4 = 8 * - WE, So a ef - Fr x 2 TE 
— 8 * ws. * > l x - . 
= : 1 7 wn 7 N 7 — * ti * 

* 1 : F 4 "* * 

* ed 9 * N * 
F - 7 * 
* L : 
- * = 


ry 2 
2 34. esch; if by 3 at 44 each ; if by 
bp > 6 dl. cach; for ſix two pences G 8 
* Shilling, and four three pences make one 
ba Shilling ;* ſo alſo doth three Groats, | .and 
. Iik<wile two N r 
But if the price of the Integet be 
chan one Shilling, tis beſt done by the Ali- 
5 quot parts of a: Pound (except in ſome 
* KF Cafes which ſhall hereafter be ſhown ) the 
Fable of Which! is as followeth, 


* 
e 5 "Ea. Fo 
* n C OS 26-4 47.7 


* 7 


\ 4 < * W * 
* 4 4 * 
, e #7 . ad ©. * ; 
EEA e a * | 
1 CY - b = 
, = 
* * 1 LS O+ 18; w 
1 1 * . * 
* Jo * 3 2 |... 
EI > 
* I „ 
1 x . 2 4 N 5 . 
- \ * * 


1 
18 
1 

wok 

wt 

«IA, 

* 

LEY 
A g 1 
a FR: 
wa * 

* 

* 

* 

STI 


= " ww Www ww or 
4 
» * 
# 
* 
4s 


© 5% 12 28 84 , 
18 1 4 1 * bs *.4 
> uy L Ws 
x 4 pa * E 4 14 © Oo 18 : - a 
* N >... 0 * } 2 "5 
+ 0 F de 
* nf * +, - 6 ? 18 4 * PO 5 
4 * . "EF Bos &" 5 
* 2 * * 1 Pr * Ws * * r. . 
* * 1 Y is 4 „ A 
* . ” — 
8 1 of.” 0 
mY | 


. 


” 


. viz. to find the amount o any — of :  —— 
Things when the * One or wg „ 


* 1 
: LY : . 
— 0 
* _ $ * ' D Pl a 
. ja Ss. A 
” , _ * E wy 
- —» 
— * I 
* — 4 
; * : E 
- = — 
% i * - bel 
— & 1 85 . 


3 8 only with this. ice when the price is 
1 «above. a Shilange” -.., 
„ Tuppole, 460, Yards at 4 5 the vas - 


+ here iS ſanzleſt 209 4775 Will be. 20-5, 
- "and therefore if 1 divide 46 by 20 the 
Quote 23 is the number ol 439 thoſe 
Yards wall colt 15852 Suppoſe 384 Ells at 
4 ab. the Ell, here every 12 Ells will come 
I. if. there ore] divide by 12 the Quote 
_ 54, is the number; of Pounds thoſe Ells 
5 Will coſt. © Underſtand the like if the price 
1 - * d. : 25. $62 1546. $56 55. 6 6. 8 dl. 
odr 10's. per Ounce, Dram, Ell, Tard, &c. 
for then it aA divide the number. of Oun- © 
| ces, Drams, Elli, Tardi, &c. by 10, twill 
gie you rheif price in Pounds at 2 5. each ; 
ach; if 
=” by s at z £14 4. ach; it by 5 at 4. cach; 
=; of of 7 each; if by 3 at 6. 84 
3 1 if by Fare 10 . each; Which is evi- 
dd eͤeent from the foregoing reaſon/in the Ta- 
* We. "i dle of Pence: 1 . 9. Ls : 
But if che Price of the Integ zen he not 
ks the *Aliquor "bf A Shilling or Pound, but 
uneven and compounded, that is Pounds, 
„ Sghillings and * in as in the ns 
V4 . N . F * e 
"fn $a WET GE 0G OT of 
Cochinele Wg * "3 1 e Sa Qunce? | 


* 


85 „ ; Jr; 


| * oF : | ; ö N / 1 4 #2 1 5 ” 3 * 7 i 2 
3 + F 5 ; 5 F * 2 
AA $15 oft 10 a8 SM eee, . 
is 2 —. F a ; * : 4 n 7 F 1 F 4 1 ; ay 1 > 7 - 8 
8 . . n x 4 5 . . Fg | 
„ 2 + o x 4 
5 SEE 
1 
3 + 
'#. 2 
1 , 


STOR * ö 
2 * ö 7 ” Lo RI od p Cnr on ß . , - 
** 


Ia furt prmieany' 0} Peritb api Ban. . 
gie and then ſhew by Moy l 2 


1 [ Wor Aha . "SP A. 


l 1. £3 A * 3 0 = 72 1 
485 12 ET Toy wth BY, Pe 
n N. RM : [1385 LON * * „ 
i $99, ob 1 e M8 . & 5 50 li 1.2 
0 571 AG * 8 ng 218 1645 Ji „ 
%% 
Irn 48 1 285, 25 2 a 311 FP RON 
4 . . ee eee 
. 2 J. . vials „n At it g at 
2 Ss 11 8 : 925 23187 dak 5 n 
uf bre . pin ame fre bet 
| £43, ene $ 


RP 11 * 1 4. og 2-9-4 213 ot 3 T 
23 "9 epi 2 aer 


\ N e g 3 * 105 net, 24-4 | w*, 4 03 


In che fr) piece, Pecaufe Hege 1 


— 


in the price 4 ite Integer, itiply the” - 
tren ere r Ke +82, oh 


(part of rhg price of ant Tnreper,) che 80 Gre 
dit" malt *ideritly be ker pop they” 
coſt were there no odd Sbillibg pod Pence, „„ 
for 489 Ounes at 2 J. che wut e 
come to 928 L. And fy ir kad be <4 
458 = 1 ot nds 50 7 ſt Have . | 
4b) e 68. the Pounds. 
ve plac 5 137 Which: becauſe © 
| 1 2 0 2 4 Pbund, I cherefbte 


e del next er Of Shillings that” 
; \ - : 1 | 5 A 


my - —_—y — = n P 
” « bk * 9 5 ” 7 0 3 * C - 8 va) * n 
» + r FUSS . 
r FRF: . ar 
| , 8 


alſo the 3 of 127. U. whit = . 
nn fi ids 

_ Laſtly for the /Farchings, Wh 

3, and therefore the ;; of 6 9. I take the 


* 


= - 7 - 
1 1 3 a 7 k 

1 0 +” 

* « 6 *% 9 : 2 
* — 
** > 2% f 
\ x * | ; 4 

' » #: 0 * 9 

* 4 ; , : 4 


— - 


are eſs than. the ſaid odd number, which in 


his caſe is 10, and therefore 3 of a Pound; 
I take 3 of 489 aud ſet under the former 


Product it gives the number of Pounds 
they would coſt at 10. the Ounce, which 


if added to the former would be the price 


t 2 l. 105. Each ; but becauſe there are 


Shillings, Pence and Farthings yet remain- 
ing that are part of the price, I proceed 
farther, and take 25. to be the 3 of 10s. 
which 2 I ſet under the 10, and then rake 


$of 2447. 10s ( which is 48 J. 185.) and 


place under it, next I place. 15. as 5 of 2; F 


under 2, and take f of 4874. 18 5. placing 
it underneath, this compleats the number 


Then for the Pence, which becauſe they 


ære not an Aliquot part of à Shilling, I take 


the next lefs number that is an Aliquot 
part, which is 6, and conſequently the half 
at a Shilling, and therefore take ; of 24.1. 
9 5. Which is 127. 4, 6 d. this I ſet under 
the 241 9. Then I place 1 under the 6, 

which is 7 J. and take it as 3 of 6.4, taking 
49.5 6 4.. which. is 2 . 


3 


* 
> 
, 


„ 5 +6 < ON 
which becauſc 


1 
ory 


— 


of:x2 1. 4 6d. which is 1 J. aos. $4.4, 
and ſet under the former, then I ſum vp 


© 
a * 
r 
: 5 
* 9 Uh 
_ g 
1 , 
! fe 4 4 


* 
* 


* - 
. 
; 


% 


£ * 
Y «2 + l Ks 


4 : * ; - * *. 0 

K - 1 

* - 5 . . 

* ba ; \ A — - = Ja 
is % 5 1 \ * 8 * 

— i po 
* 5 
7 - 
” : 
* + E 
W 

4 


cheſs ſeveral rates, vir. "NY Ry,” | 
at 10 s. the Ouince;'1 , the Ounce, 6 d. 


the Ounce, 1 4. the "Ounce, and 3 Far- 
things the Ounce, all which rates FI 
together makes 2 J. 13. d. z the price 
of the Ounce given, and the of their 
prices will be 13711 J. 12 . , „the price 
. N 


©: 1 


- 


Tan. x Y What N is Ab 9 


* ſame Name with the Dividend, as in ws 


the preceeding Example and firſt Diviſ ion, 
which was halving or dividing” bs 2, Gigge 
the 1 remaining was 1 Pound. 
ah, If there had been half or a quatter 
of an'Ounce, Pay; maſt have taken ern or 
_ quarter of the price of che * 
= to — — * Sum. 0 the "1 

341y, When the Price of the lavage i. 
above x Shilling, yet under 20 Pence, t 
beſt done by the Akquor of 2 Shilling; z for. 
any number of Pence under 20 is above 
the of a Pound, and above 12 WE 590008 
practically anne - 

922 if the number of integers he 


; > un- 
3 tis ily done by multiplyin; 
5 che price he ge by e BY 2 


ö - Iu 4 72 i: = bt i) 5 
ch 11 Ar Be, 2 
1 * 7 2 yo 4 5 + 2 of! 


N — A : F F 


: 


1 rw” | of ivr ar 555 745 1 the 


_— 
—— 


3 
"To a 85 „% 


wn Pr. . 


> ij 
1] 


I > 


: 


1 


. \ 4. 2 . diy bars 1 tt: 


r 


8 | 


"7 : od ek . 5 
be - = a i 4 


2 ee 
„ + wXF; 4 


HTS , W When {che Price of wo integer 1 
"HL ing off one Figure to the 
the remainder to tt Lc 
is the price in Pounds. Exam, 
pi r e 
0 9 ra- 70 e | = mp 
"+. Yet Le toy op (ny 
Infor ei 3 437 
15 i lt 
25115 11 " 3p 


*. Gtbly, IH. the Price oy 9075 gerbe toe 0 


* 2 
"> 


F 


* 


but balving or dividing by, 4 


e is Pounds, "nfs: de Felds 


* ts 4 E. 
f "A > * . ” i. k 4 78 3 39, 
. 25 4. „ er AL 


1 "648 Mag 10% ber, Man. eds 


— Nr ⏑—— — . ꝙ P —⁰· L. Ä 2 OR 
. N * TY 

* wx ** . 4 * 

mY * F 

— a GH. 2 — 2 „ 7 
* e - 2 IE * « WY * Ee r 

"7 * * PEST by” 25%. = 4 F N * x 
" 


N 1 4 7 ** ; 5 8 
1 e e a RE + # * 4 Os Wong x EH Hs os 4, Þ Yo ed 
dig TFT IR Via i an 7 od 


=_ :- "rhe. ir the PRICE. the tents 78 i 
=. E: arthings, chuſ e rather to multiply by 2 
= a 5 then will the Product be Farthings, 
A ch are eaſily turn d into | Pounds by * 
: K Arn by 4, 1 and 20e. 
Many other Contrationg there care, in 
1 I chis Rule, which would be 00 e 


x . $4 IE : I , = * 
| * | * hs po . + f to 
HY „ 5 i f Fs 

* 4 a 


NG OS + ” v — 


* 


to e in this 3 . ſore ſor 


Brevity ſake J omit them, ane al D 
up this Rule. with che fo ollowing G 4 | 
Wee and 51 Anſwers. 5 8 g EY: 


A 0 9 
9 * 7 45 * 7 2 * — 8 
42 . ” 3 a 2 
* , ; af q * 


3 N is w 3 414 12 dez 


"964 ins N 1s Lemont An 
ee ee wa 4 


"499 Ells at +4 the Ell > J 92 

305 %O oa Klee * 
576 Ells Flemiſh at 3 4 eki 4 "IBF 

Tr gt olgd 1 + OR 


by 


. 500 El 9 
"87 m the Pound [wer 
. 5 we tr ka 2 e 


Th 9 > age at -— rs 24 Pe 


Ir 
1 


hs 10 4. 85 ny 1 

4 568 3 at 8255 Fac May?” e i N 
a 6 200084 3 
„ Days at 10 Lehe Day Frag ver 
3345 5 10d. J WS 40 287 oft « "ow : 


F * * 
10 I * * & 3 1 2 13 * , * 4 * Rn. 1 


Ms 


- 
* 


* 


PP: 
* 


E * 1 o 
6 + 
* * * 


1 498 Hana at 4d the © pr : Vp : 5 
b g 1 6 4. Ee Ae N 5 | 
674 Pieces at 5 4. the Piece? Sug: | 


4 
= 


* 


1 370 Men M 14 ber May? ee, 


8 1 25. rod. 
_= 654 Gallons at 94. 3 the Gallon? 
Fey. we 9 5 54. 9g 


7M 


al. 


7. 7 d. 7 7. 


81 17. 1 . 12 f 
196 Penny-weights at 15. a benny 


* ht? Anſwer, 97. „, od: 314 


374 Scruples. * 1. 24. the Scruple ? : 


Anſwer. 211. 16 x, 4 4 $45 „ 


5 284 Ounces at 52 49. the Ounce 2 af. 

e Fa . 

; : 148 Feet at 85. 74 3 the Foot? ale. 
OT. x67. GE + 

. 425 Pounds at 1 3 4. 64 5 {the Pound? 


9 289 J. „ 9d. TT 


_ bs - 4 214 Guiness ar 1. 4" 3: 10 d. esch? | 


Anſwer, 235. 121. 44% 
4 9 2 Piſtols at BT's Hehe Anſwer, 
as 


96. 9 


1 1151. , EE £95 | 
= 2000 Ducats at 45 114 Lesch? af, 


497k 18 f. . ag 
+ 1700 Gelders atrs. 8 f. the Gelder? 


= fur, mark. 135. 440 


685 Liures at 1 J. 94-5 x Por. Liure? af. g 


10101. 7. 6d. 
95 Pieces of Gold a. 22 TY 


= Piece? fir, 444.” 6 10 f. . 


#* 
te 4 / - 
1 4 : | 
4 A 2 3 7 2 7 p 
— » . ; ; 7 ; 
J A i A 
4 "9 N f l 
1 ö N 4 
31 . 4 F ; — . l 
WW * £ | y 
* | 5 
& 
— %*. 
FR 


4 


98 Quarts at 11 4 lde Quart? Aal. bh 
268 Pines at 7 4 . Pint? 9 Anſwer, = 


436 Pieces 0 Eight at 5 9 4. 4each? | 


6 2 
* 


4 : the Hogs-head? Anſ. 961. 9 5. * 4. * 


at 41. 35. 6a. per Pound? Anſwer, 1101 


3 6 d. 1 Pound ? mn e Tack 


„ 8 ＋ 5 FW = * 
- Hogs- heads of Oyl at £75 OP 16 4. . 
5 19 Hundred 5 af Cochinele at 7 7. — 


64 per Hund. Anf. 1534.17. 3d. 
13 Ingots of Silver each weight 21 th. 5 


64. 10 d. 3. ; l 4H = $4.7 E 1 0 
64 1 Hoghe heads u 404. 7 | 
Ty * Anſ. 1395 l. . 245 1 
8 9 i e 51. 
per C | 182. 16 8. 416.5: $row 155 
5 66. 9 Ow, 16 Dwt. at 4. 14. Fg 

- 4 the B. Au, 23 J. — *. 000 
76422 my, at 1s. 2.4 K each Mang: 
Anſwer, 46961. #5460 WS 11 
alt wy 222 A» Fo, x 4. 140 r 
unce 343 262 $617: i 
What comes } of an Ounc f GO e 
at 40. 7 249 . me OunhoailWaiaegs, +37. , 
a - J. 94 * 3 i : = SME] is . 
What comes 17 A. 1807. of Carmina 


to at gl. 43 6 be. Ounce? Anſwerii 
„ e 


5 


What comes 3 Iran rn . 
arine to At. 7. 19. e 
by” = 26 J. 18 . 10. 2 8 e 


5 Wedges of Sold each z ths 3. 2-504; 


e 


orb an Mon 0 | 
Tun, 3 Hoghs-heads, 36 9 


14% 2 4 fer Tun? anfmer, 120647 . I 


21 


3 e 84 | #4 * 1 Ws - N $430 8 2611 ; — 4 _ r tak 2 2 


a * 
we” £4 4 


* P — 8 ee ————— a 


_— R 8 
"0 7 . 


IR 0 1 


1 =). 


2 A 
ug . Ls % uw > * „ 
. Lt : 8 * 7 
HEEL A 4 Þ 1 (ra he # = 1 
* 0 =. As 2 
bl y WA. * 1 : * 
x” 8 


A* wands + 1 wt, * * * 5 a® 5 4 8 is 2 


* 1H18 Rule we e annex 30 d Print 
3 N. dogs Ae Dire&ions given 
or thei - 
Rice... "= Pegs l K 1 W _—_ 
; *. to this yOu are to uhderſtahd;" 
. chat moſt: Commodities *which are either 
brought from beyond sea or Carried t- 
| ther, are put up ina Cheſt, Box, Bag, _ 
on ket o ſuch: like; and when taken out of 
ip are weighted! with the VelſeF 0 
Thin they are put up in, which weight i I 
1 _ Gall The Oe eb... 
dee isa allo Wänee made byethe Qucen 
d che Merchant, and of the Merchant to 
tme Buyer; for the weight 6 fich Veſſel, 
Bag or Basket Whierein be Commodity i, | 


11 * 


Puk. | 
Hen is an allowanice"df ASC ever ry 
12048. for Walk and Dirconfibine fort f 
: ** Goods and is allowed only by the Merchant | 
| 13 the Buyer; and: mor te 80 Merchant in 
* hg of Cuſtom. © HS N * 
, "EF. your Commodity be ſuch that'his an 
FL allowance for Trett⸗ then Havi & fe found the 
5 Tare take it from the Gröſs Weight, the 
mains is the Subtle weight ; then ind out 


— 
* F 5 7 - 
# , 
: 
: . - 
1 8 5 2 * 
* * s " 


\ 
* — 
. id « % Y 

- 4 $ 7 4 — * 
ate — e 
N ET. 

* - =D 3 

= - * g FA 8 2 3 


1 


„ 


* 


Ti VE 


e 


| weight, 


y 9 
n 
1 
72 


. 125 Y 


: the. Frert by the following Rule; avhbich 


dedutt fromthe; > bile, leaves the wen 


wy bo 1 


1 ac b 
Wt; note, hack 5 Commodities Cn 3 
ere-is no Trett to be allowed, "there ha- 
* ing the Tare weight from the-Groſs 
bac en are Nett weight. 


W N Artes IK 
Hum £67 dr d bits) 0 N 


| alin Jr 
Kul. 1a 52 the Haste, We: 7 7 Cheſts, 
Bags, &C. ahi Pounds. Tare. 25 for 15 
Hundred weight Cheſt, Bag, &. The Pre- 
duct is the Pounds: Tare for the aybole Commo- 
dity ; theſe Pounds reduc d into Hundred a 
taken from the. ga. $ angle 


W 37855 * Sugar at (h __ . 
| 80 8 * 


250 Ne 

8 1 25 i WA > » "pl \ + 381k 7 
e e 

— 4 1 C, = * e 


| eee 2724 . 8 2 2 


——— 2 — hon 
FFF 
„„ . | * Wo” 0. 4. . 
| | © 1 
2 887? £376 10.0 Gm," 
„„ a 
; — — — — 


9 ab re 2 1 2 Nu, 


* -_ N r 


5% 
W N 
: i : Peres he - 
* * 4 o 
f 
k 
_ 
"« jo 
| 7 5 
i 
21 
3 F 


30 


— 
— 
= 
8 
* 
* 
. 
FA 1 1 
. v 
4 - 
* 
= 
* 
* 
- 
f \ 
= 
** 
= 


4 


„ 
* 
F 
4 
Z * 
8 7 4 
"EY 
bw \ : 
* 


5 
” 2 
I 8 
8 
N £ 
$F : 


* 
9 4 
1 8 
* 
# * 
0 Bt 
A 4 
*. * 
_ 
* 2 
2 
* 
= 
— 
-. 


* 

* 4 
0 * 
2 
7 
2 


ne I. 


* 


fore 376, 


15 and the sum Will be the Pounds Tare ar 


> 


* Nere II. If there had been an odd quarter, 
half or three quarters of a C. then having 


multiplied by 16 vou muſt have added to 


. ene ner * * . 


the Product the 3, 1 or 4 of the Pounds 
Tare, Which in the preceding Example 
Was 16, rhe Sum will be iq Pounds Tare 
r che whole at PIES 972; 6 


e. U. . lt 10 were. 


- 
_— 


8 L * ONE. 2 8 2 9 „ N N 
2 \ * ; k 4 » a % | i * 
1 8 32. 39 Tang for the 1 of a Pound. 
8 . , k 
| CE ET OE: Tare for che half Cw. 
h £ ' 2 * y 
„ whole Ta. . 


> < 4 
3 7 


p . £ I x 
, "nM 
— : p , «„ hoy 7 * N * ew 1 


=y # of 
. 
* » 
* % 
wil 
>. 
& » wa : 
4 * >; 7 


e N N 8 + 5 39 4 EP 97 ; E ' oF 4 . * 4%. 1 * # 
4 ; : 


$ * 


e 


| Py 127 'D 2 
Note I. When I rake the Tare 10 1 
Cw. which is the 3 of 18 ; 4, 1 negleR ta- 
king the f of Lof a Pound, ic being "_ 
| inſignificant 1 in thisCaſe. dae. 
Note II. When the Tae is the Aliquoe © 
part of a C. 'Tis trueſt and quickeſt dene 
by taking ſuchAliquor parc of à C. a 
poſe 296 Cw. at 1 4 b. per Cw; Tare, Here 
I conſider that 2 19-3 of a C. I there- 
take ibe 3; of 296, it gives me 37 Cw. for 
the Tare, Which. I ſubſtract from 5 wi 
leaves 259 Cw. for the 3 


„„ 


Eu 70 "fad the Trax. = 10 


„118 rſt 22 e bs — „ 
Kal ,which detlu# from the a © weight vt rien 
the Subtle weight, as before was nt Reduce 

this weight into Pounds; and divide by 26, the 
Quote is the allowance for Trett ; "the Pounds 
Trett ſubſtract from the Pounds Subtle, the 
| Remains are Pounds Nett, which may be roſy 
N 4 fo 4 Hundred weight. £3 


| Example, 976 Hundred the of To- 
bacco, Tare 13 1b. . Hundred weight, and 


Trett * per 194 How: 200; Hundred | 
| 9 oo Nette 0 . Tad ion act cher 


rhe Tar found by the pred. 
0 ing fl rn 


; FM 


: ? 1 
. 8 
* - q * 


4 Ll 
8 * — 
n * 7 4 
: | 4 


* 1130 8 4 


< * 
ba 
* 
2 
1h þ 4 Y 
=. 8 
* x 
x 5 Te 2 * * 
wy * ö 
* *s 
* 4 b 
I * 
\ 
1 
* 
13 
* 
* 
* 
2 1 
0 
bn 
9 
3 
* * 
o 
=” 
- 
7 
3 
” 
» 
# 
- > N 
* 
* 
L 
: * 
I * 
4 4. 2 a 
* 
- 7 - 
, 7 
1 
; es. — 
. is 
8 \ 3-5 
22 
* 
* 
1 
* > 
A 
* 


: 


6 a 
s 


6900 „ 


4 


— * ada Wa 


„ 


"I. ; + L 


2 iis C 3089 40 N 


WS > „ * 


Aw 


_ N 10 5 


42 


56624 FA S, 164 


— — nr 


N by 4 third 


* 115 FI 


»-- 


lowance 


* £44 ” 
0 
* 
. 
* 6 


uſually | 


made 1 choice ſort of Goods in the Port 


25 (0 every 3 Cw. for Draught. * 


\ 


an called Clongb, What, 2 ts. 


88 
3 


1 Examples, 


3 C. 3 of. Cotton- Wool at 17. ber 0. 1 4 DN, 1 = 
Tate, bow many C. Nett? As. 2 
4 1. 23 P. 1 N 
3 124 C2 46 p. of Mace at 34 p 2 per C. 
I are, how, many C. Nett: 95 "nfo $6Q. 
10 p. 4 
by Bags br Peper weight 2 C. 1 each Tae 


' 37 p. per C. how many C. Nett! 2 Anſuer | 
1310. o q. 9 p. 3 233 
43 Boxcs of Cali a at 51 1 p. 4 Leer Box rare, 9 


how many Pounds Tare ? 4/ 2225 P.+ - . . 
17 Cask of Iron-Wyre at 23Þ. 5 per Cjjx.lb © 
Tare, how many Pounds Tarc # Anſwer, | | 
t Do Fus of Copper each 804 21 p. Ta „ 
Ip. A ber C. how many F. Werte . 
— ͥͤͤ dE 
X 7 Buts of Currants each 1 C. 4 8 a 
Tare 13 p...z LC, how wp C. Nett? 2 
Anſwer, 28 55 . 
14 C. 3 16 p. 0 Cinnamon at 14 p. 1 
C. Tare, and 4p. ger log p. Tret, how 2 ; 
many C Nett? Anſ. 12 C. 1 g. 24 P: ES, 
3 Boxes 3 of Cloves, geh 2 C. 5, at Rp. 
' 3 per C. Tare; and 4 p. P fo p. Feet, hr 
: many C. Net? Anſ. 7 C. I ., 12Þ. 4. 
10 1 of Amber-greels, a 5 .. = 
4 Tate, and 4 p. per 194 p. Fi how many Fr A 
= Nas _ 3 4 8 8 + 18 -- 


0 130 ) 2 
218 p. of Ginger at 30 p. z per C. Tare, 
and 4 p. per 104 p. Tret, how rn Newt? 
A my 2 * 15 near. 


8 + 


— = 
I 
The dae Rule Ie Three| f 
- both Direct and Inverſe. 
15 E compoind or double Rule of Three, 4 
1 > ſo called, becauſe tis a compoſing F . 
"of two Operations of the ſingle Rule ot = 
Three in one, or tis a Reſolving ſuch Que 
lions at one Operation, as require t] s of 
the ſingle Rule. 
In this Rule there are five diſtin Num- 
bers given to find out a fixth, in Proporti- 


on Areund; which may be _ 8 b 
Or Inverſe. $4 158 


" Dire#, When both Op ations of, the 
* Rule require a dir Proportion, as 
in this Example. 

1f 38 Soldiers ſpend 228 L in 16 Weeks ? 


n much i "og 30 Soldier ers «for 12 
1 8 2 | 123 | 


0 


"mah when « one of the Obcrarinds off '£ 


* ſingle Rule requires an invaſe 0 81 
tion, as in * * N 


ö * n E. : ; 78 
. ” «i. 4 *. % > 5 +. fs 
4 A . 20 41 1 iv ” w * : 
2 6 2 2 ' a 
1 — 7 : * W's ' 
. f * 7 : ; 
; „ 
* - C _ 
* * 
* 


e * * N . „**% ici 
» Oy - 8 . * MY . 4 7 erm — 
9 ” ERIE” 2 e : 
ws / W e 3 
. 5 , Pig * . 7 6a 1 


+ tzt 5 OT 
8 | 5 1 
are, 3 20 „ Graze _ IF 1 
ett? Dart ? How” many — 
e % en? 515 


. i 


ME © The thre? frlt Tenne! in tds Ne ext dien 
Na suppoſicion, as in Queſtion the firſt, Die 
38 Soldicrs ſpend 228 L in 16 Weeks) the 

two laſt a Demand, as, How ue will - 
| ſerve 50 Soldiers for 12 Wee | 

$0 alſo in 2 the 1 (F 20 
Acrees Graze 32 Oxen for 18 Days) is the 
 Suppoſttion, and (How many Days will 30 
Acres laſt 46 Oxen) the Demand. 

To ſtate the Queſtion in the direct Hole 
Let the firſt and fourth Terms be of one Name 
or Nature; 48 alſo, the ſecond and fith; and 
the third Term muſs be like unto the Term re- 
m- quired, which is the ſixth; or thus, that of the 
rti- three Term implying a Smppoſttion, which is 
ect like the Arb er term required, muff. be the 
third Term in the ſtating, and the remaining 

tuo, make the forſt and 3 Terms : It mat- 
tert not which is which ; laſtly the two, wh; 4 

2 the Demand, let be the ** and fifth 

Terms; not 2 08 which of the to 18 pr. 


The Queſtion bein ſtated according. 10 So 4 1 
einer of theſe Directions, Divide the pro- = 

du of - the third, fourth and. f b Terms, 4p, 
xo the produtt of the firſt and. 2 Tem; be 
0 re. 1 be „ to the * gee the 
| Ks folloWw- 


WS; * 


. 132 * 8 
following Metho- of ſtatin and workin 
| he preceding Queltion, a 5 


n < 5 Ss E <4 
. - 


Sold. WW." . gold. 
FN If 303 in N bat will 50 ſpendim i: 12 


1 


- - 
4 * 30 . FR 4 .. 4 
H) tf 348 s 


a 


13 f 7 9 if 
— 8 a * 
n A ne 5 3 
s 44 2 „ * 11 a * 2 . 1 N 8 
15 480 | ed 47.4 a Ke 
ert CCC 
' | ' : 's * ys 3 1 RY % 
* ; 1 — by 
OL * # 5) 6 7 
; 85 30 $00 0 ing nfs. 
2&4; 5 N 
nd 4.3" 7 *. ©] 1 by, WO Pe } oy * 1 is: 


in the Compouhd Rule oe” eb werte. 
Obſerve - among the Term. F 5 5a: vn 
Which of thim bath the ſame . Denomina- 
Hit with the Term required, and reſerve that 
* the ſecond Place; then fet the other two 
ent of the Supp An one above anot her in 
ide ß Plate; Ho lafly, the Terms of de- 
man one” "hour another in the third Place I 
| the") ating, in ſuch ſort, thut the wppermioſt Mm - 
the third may be of the ſame Name, with the 


ans in 0 bf Place, | 5 F * 


. 1 
nl 
4 ? . J . * 
8 "* DP 8 * ans 1 
D * 2 Fo. I * #5 4 8 nne * ** ** | '% ES, 5 
qv OE * * r e 5 PA» ; . * 2 
L 7 * 


5 FOI #511 ok » . — 2 ee 
. "tt 4 an,. 3 * N 7; bot 7 A 


- 


y a, Io 45 


— £ bas - 
, ba | ' 3 5 J l 
g : "g* 35 | 
| x K ** . 
h #5» "_ "1 ” 
5 2 
1 « kx oe 1 
1 * 5 
: 4 — * K 
4 7 * * 
1 N 1 
* - 
* 


2 92 „ 1 S 2 


The peeing Qin ha. 0 


"© a * wiper > 


1 . 0 D. Abe. | 


20— . = Eel . * 18 . — —_— , — ** 17 - | 


- = 4 - * 
OX 7 ONS: 
F - * 1 * 

| ——— —— —— 2 5 

* L —— —— 
5 \ k 4 


W "Ty. ER RED 


ds pd, TH 


OX De „ I n e 


ö 


The Queſtion being ah ſtared, Matriphy ; 
the uppermoſt Term in the firſt. Place, 
lowermoſt Term in the laſſ.; and the 


permoſe 
75 the laſt, by the lowermaſt of the 6: ſet- 5 


each product under 1 tower Tem, 

wheh it is produs . | 

If then, the Inverſe: Propoteton be in th 
upper Line, uſing theſe products as ſingle 
Terms, Proceed to find: the Term required I 
tbe ſingle Rule of Three Direct. But in caſe 
you — the Inverſe Proportion in the lower 
Line, Perform: the wor k by the ſingle Rule of 
Three Raves *. $ beg the following Opeth: 


11 * \ Bs <> 


** 3 13 
N 8 * 4 is. C * 1 1 1 — 5 5 0 
? uy % « - * 
* x 1 ; 2 4 2 4 £5 4 . 
nf S br * 5 ** 4 4s w Fo 
IA 4 I 
n : > . s * - A d A 5 
hong an 1 N x * * | 
- pt 8 . ” 
1 - ah - ®. 4 * 
Jo ; / „ ; n 
— ON ” i 
* 
- - 
1 
* * 
7 
* 1 * 


* 
4 
1 
AS 
be + N q 
l * 
2 < 
* 
— Pl. 
ag 
. T- 
8 ky 
\ 
: v 
# Hh «2 
* * "WV 
„ 
Bag 
4 8 
4 
3 
«Be 
* 
1 by F 
AY 
wy % 
. } 
*＋ 
: 45 
* 1 
* 
„ 43 


* q 
. 5 Pn 
* 
% L 
is N 
* £ 
* * 


r. 
! , J 
U 7 
i "uy 
* 
[ « % « ; 
Le 4 * 
i 
i; * 
; #3 
* 
[ 
! 
{ s 
| 5 1 
' 
i l — 
t1 - 4 
[1 7 
F * * 
Y ; F + 
* 
\ 
„ 
L 
* 
* 
” * 4 
* 
a7 5 
* 


je jr . 


e Examples in ; the Dirett Rate... 11 


Or chus it may be operated. 


* 8 
5 1 4 
3 Ya ——— * 5 
a 
A I-44 > te” ao RT,” a . 
«x + 1 * 1 
P 7 
2 {> , ? way # 
4 : 4 2 4 | 
3 * * * A t 
£ a 7+ 0 
* > 
* 
1 q N * £ 4 
: 
8 \ 
e b O 6 1 
; 4 3 * a hl * 1 
8 % 
4 4 18 
1 
— % . * 
A * 7 * 2 > ? v8 I + W 
71 3 * 


5 EY. Days.. „ 
W -800)172Bo(21 £4nfw.: 
The proof of 2 of theſe Rules 1 is per- 


form di by a back Stat ing, as were thoſe of 
__ the ſingle Rule of Wer boch 3 and 


%ſCÜÜRT M mot pee cs 1c.) 
— v If = 


1 A 
p 


«ab ＋ 1 be 1 
ry I C — I D * . - 


—5 * 


„ 4 
oY <3 


If .5o C. weight carried 35 Miles coſt 
48 £ what will the Carriage of 39 . 


N 2441 


* 


Ve coſt 138 Miles? Auſuer, 131 115. 


\ N 


” , & . * 
; 8 [7 
; : , 
. 1 — 


1 * 7 Tg 7 7 5 a „„ IF 


= 8 9 * 
N. K n __ 
F 8 1 "Y n 8 = * 0 5 . cs "YR * OP — 
* 3 Fx * 4 * * 7 1 
J a a = 1 - W 
\ : 
we... * 
2 * - 
4 i * 
* , 
: Z 
N * 
. \ i q 


if \ Wes 1 VEL of Wikeai is d . 
for 7 s. I can Board 9 Men for 42 Ms „ 
How much will pa 80 y the Board of 36 Men. 
when Wheat is ſold for $1 . 6 d. the Buſhel 7 „ 
3 7.4. Th. ® 


. 


Examples in the Inverſe Rule. 1 Do 

1 36 Crowns 3 in 10 Montbs gain 24 Shil-⸗ „ 
lings, in how many Months ilk I 50 Wo 
Crowns gain 8 Shillings : 92 Anſwer, 40 1 
Months; ; 1 
If 765 Yards of Cloath of 2 Nen N _—_ 
100 Men, how many Men will 150 FA 
1 7 quarters broad ſerve; 7 , Anſwer, Bu 1 


' - 7 % 0+ 28 of P * 
"7 4-4 1 i 9 . 5 7 = 
A £ * N A # * 385 
” : * 


o N Mgt 
, SSP . 
a K "y 
4 — a 1 ae *＋ 
— ** . 1 F< A - - 
7 5 2 1 — — 
— 


1815 Kk 
Inereſt gl an Confei 4 
"with the Valuation of aner d _— 
| Penne in Reverſum."' See e, 


2 
700 98 


T0 ſay 8 iht wget 4p oY of this ll 
” Tubject would. make a Jar ge H by 8 = 


x 2 5 _— 
„ = Dp 
7 - — 
3 E _ 
- I 
h _. 
« 770 
4 * 
1 


1 Win therefore only: give ſome ſuort pra- I 
ccical Rules for 15 55 theſe Things. Pl 2 --" 

In order to this I muſt acquaint my," 2 
. YM Pr BIR pr rhe Mo-'+ 


I 136 57 
ney put out to Intereſt; Lig Money 7, 1s 
the Loan, Præmium, Or uſe. Money, paid. for. 
=  theufe of ſuch Principal. £2 
—_—  - | Intereſt, is Simple Or Conpoond:; Simple, 7 
when the Intereſt of the fum firſt Lent is 
only paid; Compound, when the Intereſt 
wo. not only of the ſum firſt Lent, bur alſo of 
ſuch Intereſt, as is not paid when due. For 
Example, Suppo ſe 100, J. be Lent out for a 
_ Ycax for 6 " than at the ſecond Years 
WE - end I reckon compound. Iffrereſt, which 
is the Intereſt of the 100. and of the 61. 
we, that ſhould' have been paid for the Interen 
ot the 100 f. fog ihe firſt Lear. 
n * of Interęſt, is the Money that = 
paid for the Intereſt of 100 J. for one Year : . 
and from this Rate, the Intereſt of any o- 


= Sum for any other time is compu- x 
c 


Ded. 1. Hrereſt, ( ons in simple 
Intereſt may be wrought ſe 20267 Ways: As 
by the ſingle Rule of Three at 2 Operations; 
bot part by the Rule of Three, and part by 
Practice, andfomeoth rs: | ſhall give. an 
Example wrought theſe two Ways. 
Baut before I proceed, take this Rule for 
ſtating the Queſtion; if the time be longer 
+ , Or ſhorter thana Tear, and the Sum more 
or leſs than 109]. The firſt. Term muſt be 12 
Months, or 365 Days; the. ſecend Term tbe 
rate © Intereſt; FP "nd. the. third the time 
2 ed; X70 ing this * ile Rule of Tris, 


-- 


4 4 
8 $4, : 
— "ca 3 4% 
ff & LS 24 5 4 * 
1 i: EIS . 4 9 
1 * I - 


1 


C12) 3 

| a Facit comes out. 8 2 ſay, 3 
that Facit, what ſhall the 
working here as before x th 
the ark of the given en ow 
me g hi e 


R * 45 


th "oy time re- 16. i 
5 Ay: 3 2 * Fc T | 4 1 us 7 *; » ah 4X 7 3s * Y | A | oy 4 
> £8 wm» Oe 92 5 + * . ons | 3 


; | Example 1. What's the Intreſt of 240}. 5 
n for Months at G1. OY Ry - EM 


o 


$ ö ri. By the nne . 
bt - 1f 32 Mon, give wa bit ben Mon, . - Bs 


O _—_ 7 K ; *" VT 


* "4 

d k 
: * 
0 8 
a 


12. f 8. . _—_ 
. 7552 55 01 et 


wy FA. © : | | 2 
1 7 A 5 | 3-4 
: WIT . 
* * ; [ : * 


- 1 
* 1 5 wn WER : { - 


151 105. hei. rug 


* 
* Vw 


F This 11 10 x. that comes out is the Intereſt 
of 100 J. for 9 Months, and therefore, if. 


1 On give A 5895 a hat hall 0 1055 W 50 ö 1 


oO Bo 2 — . 
i 4 2 IK 4810 > $33 1 - 7 
501 6 290. Ar A 


1 8 x = 
4 „ . 
. a * 
„ oer Gee a 
# ? kv 17 "x ö 
* De ts 1 2 


Fn 


ct At 5; Or, EO $414 


#4 % #4 + % f = EN „ 2 3 
„ Lge | ; 


F £ 
L 2 8 4 „ 8 Ry F 4 ' «lh & * Lean 
42 , ; — k 5 — e : 
/ 1 I WI | 
«#1. k . f : 


iy 


-* * A 5 AZ 
/ Ps . jv 4 * * — OS : +26 <A 


* 


Sescondiy, By the fel. Rule of Three ad 
g n Practice. 


A \ 


# 
Eq 

_ 

"4 


We” A give 6 1. What ſhall 9 Months ? 


19 4. 28 before. N 


* * Gs £ * * x v 
* 1 * 


* F4 4 DT 


2401. 10 f. at Al. 16 7. O. pong 


- - ay 


2 _— $a. i - , 


r TE A Curr" 1 


of to the 15 
5 1 105: for 9 Moths. | 5. 
: 22 ; Reaſon" of this laſt Operation is 
*hus, having found the Intereſt of 100 J. 
Es a: . 9 Months, which is 40. 10 5. ſay, as in 


* 


- 
"AJ ; 7 ” 2 
0 4 of : 2 : : % % 
a * 2 G4 
== . 
3 5 21 wh { 
* "REN 
3 ; 


being © 
e Intereſt of 


7 
q 
* 
=" 
X 
8 
TY 
* 
"- 
. 


0 


* 5 . 7 * 9 2 . 
- - o 2 * : * N e 0 n n * q —— 
p 2 3 5 9 * MY ES by ' Ke: 


' 3 $M, ac 3 * 
7 * . 
«4 - 


25 9 4 


5 9 
” a \ 
2 
(4 
01390 


che firſt Way, if 100 J. give 41. 1053 bat. 


ſhall 240 l. 10 , give. Here I am to Mul- 3 


tiply the ſecond Term by the third, and di? 


vide by the firſt, which in this ſecond Caſe 


I do practically. For firſt, I multiply 2407, - 


105. by 4, it makes 962 l. then, becaue! 


have 10.5. more in the Multiplior, Which is 
rhe half of one pound z J therefore take the 


half of 2401. 10 4, which is 120. 5 and 1 


place under the 962 J. the ſum of theſe 

_ which is 1082 J. I divide by 00, Which is 

done by cutting off two Figutes to the 

Right-hand,ſo are thoſe on the left Pounds 

the 82 cut off is part of a pound, and muſt 

be multiplied by 20 to bring it into Shil- 
lings; this done, I divide by 00, that is, 

I cut off two Figures to the Right, again 
the Figures on ihe Left are Shillings. The 

43 cut off 1 multiply by 12, and cut off 


two Figures to the Right, as before; the 
Figure or Figures on the Left are Pence, 


the 40 cut off* I multiply by 4. and cut 
from the Product two Figures as before-31 
the Figures on the Left is Farthings, and“ 


the remainder or & of a Farthing; whieh, * 3 
becauſe is ſomething more than half a Far- 


thing, I make the Farthing laſt cut off a 

| Half penoy So that the lntereſt of 240 J. 
10 4. for 9 Months, is 101. 16 8. 5 d. 3 near, 
being the ſame as it came to before. 


. 


* 9 
A , TIS 8 
, N 85 
- i ; ; 
. F ; 
: ; * . "Lat 
Uo : 89 - * 4 o - : % 4 
5 1 : « 7 # ' © ; 4 s 
A 4 Y 
* o * I. 
* b f 8 
- oy 4 . 3 * . 
: 5 8 . K , < 
i 
* 


4 4 
* * 


A 
: : 
i 
© * 
«7 


r 


5 : 
* 
. * 7 
A 4 - 
5 __ 
. . o 
_—_— 
. 4 x 
: . 7 17 
4 +2 2 p 
„ 
% 4 . 
f is 
i —_— - 
_— 
L "x _ + 
: . 
£ W * 
1 4 
—___ : wy 
—- 5 
* * 
þ 5 * * 
1 & 2 - * 
n => 
v7 4 - a $3 
e "3 £ 
I R *y 
' % £ 
1 » 4 * 
+ F. 
L ; 9 
4 


HE 
: ** * 
„ 


4 8 —— —— 


Fi r 
is 7 £ 2 
f * 15 
4 4 4 1 , 2 
iff 5 TIC. 


= 2 — * 
—— — — 0 


- 
—.— 


„ CI 


2 


— 


— 2 + wo a g 
— — Ts 1 
8 4 2 i 4 
. r 
* ** * 4 £ JOS 3 . N * 
n 9 \ 9 9 * * hg * 
_— 9 (+. Tb 
Wet #4. 8 N 6% p * * . oe 
4 e | $47 WES N 1 
CET ws.” 
f 
5 
L 


. 


„ FS he 


RY. 
S * 
7 * <> 
p 
» ; 3 
1 
' 2 
XX 8 
1 4 « 
* 
5 5 
4 » 


12 ” 
Pre gp 7 


N 
} 


7 
4 ; - 
ni 
8 
1 e 
* 
» 
A 
5 
* 
* 
by 
* 
% 
= 


x 


. + 


Ts 


Money be requir'd: 


iF# 


x1 


* m_ 


the * any Sum 9 
for one Year, one Sta 


ting does it, For 100 J. is t0 61, as any gi. 


ven Sum is to its Intereſt for one Fear. 80 
allo the Intereſt of 100 f. for any time a- 


bove or under à Tear is found at one Sta- 


* 
£— 
* 


* 


* l. 


11. * * 


45 


121 
3, 


- 
- 


ting; thus if one 1 n . What Mall! 
gs other tĩme give. | 


1 4 


4 4 
9 5 


» V4 


5 


Ls 


112 1 
1 


found 


 theIncereſt for 2 Tear, Tale 3, 3 or j theres: 
of, and it will be the Interaſt of the pro- 


#7 * 1 
Wh 


2 if 


for Days, then inſtead! 
" 365; the Da 


Days to 64 


7 = 

7 0 
17 5 8 x 
z* 2 # 
> "SR: 


poſed Sum ſor fuch 


wit $274 


? N 


of 
1 03 


the Thiebteſh of: any om ber 


equired 


of 12 Montt ſet 
ys in one Frar; chat; 175 
fois any other Nu 


a5 369% 
mber of 


Days to a fourth Proportional, which is 
00 J. tor fuck Number of 


7 1 2 oo 


CS. the ee e 


ot r 


1 "I k 5 ; " 43 © 215 
5 * as „ 211 


%. 


* F 
22 * N 1 4 * 


2. If the Intereſb of m be required i 
for A Quarter, Half, or 'three' Quarters of a 
Lear, one stating does at, for having 


- 


1 hl 9 * eee e — 5 "I 
wo ft the "ſhorteſt Rules, for frad-. « "8 
| 1 ing the Simple Intereſt 75 all 2 | 

2 any Rate, and am * 


4 Bult the Firſt.” Aleph: 5 3 * 
| ven by the . Rate, and the - Prodiufs I the 
„ Number of Dajs.; 3 this ſecond P roduct Fade 

. 365, and the, Quote: ener * =" 4 A 


ion. e 25 
Kulte the Second. Multiph the Grain pro- 
poſed by the Number of Days, ani that Fre- 
wilt again 7 7 the. 4 K of one Ne fur one © 
%;; the Pro : | Anſwer. : \ 5 N * 
2 1 . n K 2 Kd bY, 


" as 5 xerciſe of the Rulesis 
bel perfe med in Decimals. 
9 20 er Fe as ee of - 
ePoun ne Years by ſaying, - 
71 0 J. g 180 what ſhall 1 J. give Hete 
adding ede to the 6, and dividing 
by loo, the Quote, according to Decimal 


Diviſion, will de os of Pound, afterubis 
Method you'll find. T hos: "I 75 0 CR 


* 


I "AB, 1 | 
L- 4 21 ; : J f 
9 . 5 N 75 8 . A F 23 "MTS * - 
. _ Tx? * A 1 * y * 1 872 15 , 
F K 8 ” * * bi * - * —— y 1 x 
+ _ 2 : br, \ . f 2 4 
. © 3, 1% . 5 4 . 2 1 
* 1 « + 4 e 9 
12 : : 5 5 A 4 4 
3 5 of : . „ 1 
- * l s 
__ =_- * 4 
5 1 
. : | . 5 
5 — 25 * + 13 I; 
- - % * by 9 » 
* - 2 
0 T f 
> . 


” - = 
— * 5 > 
—— 
my 


— 
ns, ation — 
2 >. 


— — more 
— — 2— 


— 
—— — ↄ Py = 
_ CT 
e n 
X. 3x mw _ <4 5 


4 1 
F 8 : ; by 5 255 A 
* ” x ” 
& * 22 45 1 * ©4p 
* "_ 1 F- : ” 
* DAL * * 7 * 
\ } , 
% 7 
c 
2 
Mig 


4. W. en Shillings, pence or Farthings;. 
be joined with any Number bf 
onda, they muſt be reduced to the De- 
imal parts of a Pound, and fo ſet to the 


Pounds with a point of Seperation, Which 


buſineſs is very readily Effected, by having 
in mind the brief way of valuing aDccimal, 
mentioned i in page 105. 

- The Intereſt of t J. for one Day, is 
found after the ſame manner, as is the Inte- 
reſt of 240 l. 10 f. in the firſt Example of 
his Sefton, by which- method you wil 


= N . ” „ 5 4 | « : - : PR | 
os . 


„97808 N 
e i: 


FA: 4? 


: N ' , 5 
1 1 
* 4 7 9 > T "_ * 


22 5 
5 wo 


e 7. „ What's hs ts of - T1 71 
4 2 for . at the rate of 61. P. 


* 
7 


. 


, ' TP - . . . 
* * 0 8 * ** OY : 
n * 4+. ” . 4 q 
N. « . 


A 
* 
0 of 
* 


* 


- 


; 88 1 173160 


838 
86580 


4 > 


365): 1861460(324. 497 Anſw. 
RET, > EE ; | 


211 Or 321.9 41 * 


- _ - 
a N . E © N 4 5 
A N Pd 8 vl * * 1 s 9 * 4 * 1 a n = 
4 vi "I £ 1 1 5 5 & £5 £3 1 * 5 * > 
* iS 4 / © % XX #4 . a w 4 o * 12 
* 43] 
| x f . 8 
* 1 
* 4 PE. + * 4 : - 5 N . * * y * 2 
1 — a * Y 
— * ö 1 3 : — 8 
* - g v 
7 LF 1 3 
. * FP 5 N » } : TR 4 = r 
* f . Oo * a 
8 * « * : , 4 1 5 > — S 2 4< A 5 FI oy 4 | * sf ſe A 
* - 33 
« > q 2 
* | £4 $ 
” : * 14 * 7 . 
4 8 
2 L J 
0 2 "I 
* 3 5 1 
5 * 2 
2 .* , . : 5 = 8 
1 2 4 < . 


— 
o 
. 
| 


a : 
_ . 2 5 
2 


the Second : 


000164383 5 Intr; of 1 l. for I day. 
720 . Principal. DEST ox 


3 I } n 


1643835 T 
1 . 73 | 8 3 


A, =, 


* 
% 
— 


4 
* - 


4 
W wma" 


N eee TR og t 
- . . mids ae q . 
*. x ; 1 | PF 


% 
* * 
: 


8 Dee fi LAs D 
„ 2 9 : | 


* * Or PTS air m Before. 1 


. : i 


He 24 


RN * 
* 


Wobtre, 'Tis no matter which of the Terms 
=: you Multiply Firſt, and therefore for Con- 
bvbeniences fake, I put that firſt, which has 
the moſt Figures in it; that 5s, I make 
3 1 2 that the .Mulciplicand, Which has moſt 


— 


. N + 
5 ; A * . - 
. 


* 
* 
1 


e 


Wy Engl” 8 ee We 


Wbar sthe Intereſt of 176. K id dp. 
for two Years and three Months, at 67. per 
Cent. der Ann? Auſiben, 2384. 15% Vs, 5 
ng ; E 

What's the Intereſt of 896 J. TW 2 d. 
for 256 Days, at 6 1. per Cent. Fer Ht e An 
ſwer, 3 Th 36A To 

What's the Intereft of 1 00005077. for one 
Day, at 7. per Cent. per Am | ? Eur 191 7 


155. 1 0 1 7 n I 0 


Steck. 2. Rebert 7 or "Diſcimj 1. echt 
to Simple Intereſt, is to Fad how much 
preſent Money. will ſatisfy a Debt to be 
paid hereafter ar any Rate, per Cent. per Ann. 

For Inſtance. The preſent Money that 


will ſatisfy a Deht of 106 J. due ond Lear 


hence, at 6 J. per Cent. per Ann. is ro. Te 
Reaſon is clear, for 1001. put out for one 
Year will amount to 106 J. at the Tears 
end, after the rate of 6 J. per Cent. per Ann; 
So that 100 /. is thè preſent Money that muſt 
be paid, and 6 J. the Rebate or Dice 
for ſuch prompt Payment. 
And therefore 1001: ready Money i is e. 
qual in value to 106 J. to be paid one Tear 
hence. 

ow for ſolving of Queſtiofis in this” 
Rt ule, * take the following mac 


R Gd * by } 
4 1\ \*. . 2 
” 2 
2 . * 
4 wh of : 
Z 2. 
—— 
— 


A 0 9166 55 7 
The frp Term muſt be 12 Months, the ſecond 
' the Rate of Intereſt, and the third Term. the 
time propoſed, working this by the direct Rule 
e Thrce, à Faeit comes out; this Facit add 
1390 100 l. and mate that, the finſt Term in 
- this ſecond Stating, 1001.:the. ſecond Term ;. 
and the propoſed Sum the third. Working this 
as before, there will come aut the. fy. 


whic is the preſent May that muſt be paid. 


0 \ 
P 5 
9 D n 2 —— - $4 n * 
—_— wy A's : LEED "0 mY ET oa 

of g 

N * * 

- of 1 4 
. 3 
, 7 
Age \ OY 


Exam. What preſent Money mutt -be 
* paid for 210 J. due 8 Months hence, Re- 
bating 61. per Cent. per Ann. ih \ 


2 „ I SG Es 4 
. n . , * 
W - 3 
*. | * : * 
8 8 * 


Say, IE: 12 Mon. e 6 L what; ſhall 3 Mon. 
e „ | 


F THF 


1 ' C . 
3 ö 3 ö 5 
5 + U 0 
: a 7 
ESO 1259080 8 . 
4 ; F . 4 £ 4 4 FE » 
a, i : * , 3c ) 1 „ - 


Wm, Thus, If 104 pay 100 what Gall 
0 wy: pay. 8 
S A 


%. 


— 104 A. : 215 


; 1 93 5 
A; s - Us-- e _—_— | | 3 
5 n 


\ 17 
© * 1 Cl 
#4 | * Font I * > 4. . 
8 : ; 


Ga e 1 1 


; 
3 * 


104 . | „ * 


ee == ocagol 1 : 


. 


- 


* : 
©4738 
- 1 7 


© 


E 


- 
. 


21 Days, after the Rate of 71. per Cent. fut 
per Ann? Anſw.-151. oo f. 3 d. An = 9 


paid 99 Tears hence, diſcompting after 1 
the Rate of 5 U per Cent. 15 _ 7 {oo 
847. oO 5. far r, 1 3 


of Money, to one time for Paying of tje 
whole Debt, withour inzuty t to Debtor: Of” 4,0 
Creditor,” 3 ng 


by its reſpechide time; then! add their ſeveral 


i the Payment of the whote, Debr. k EAA 


"More Branpler, 8 
- Whar' rn Rebate of 175d. 15 5.06 4 Suk] 


Suppoſe 2000 J. be to be, paid 50 Years 
hence, what is it worth in ready Money, 
diſcompting after the Rate of 6 1. per Cint. a 
per Ann? Aunſu. o l. 2 

What's a Legacy of 5004. Nene 0 15 F 


% 
45 * 


Sed. ; K quarion off Pod 105 hs 
G ign of this Rule was to teach how to re- 
duce the times for Payment of ſeveral Sums 


For doing. of Which this is od Rule. "4 
Multiply the Sum of each particular | Payment 


Products together ; the e rule by 1h# whole 
Sum of Money; the Quote is the equated Mime. 


But Note. The 3 of ment in not { 
ſo given, muſt be reduc d to one Denomi- 
nation; chat is, thex muſt be all Tears, YI 

| & 3 > 8 þ . | 


1 * 
; 


a 9 n 


; 0 ( 148 5 „ 5 
obe Se. And then the Quote will ac- 


cordingly be Years, Months, &c. 


edo dow 


the Falacy of this Rule, as ſome'Authors be- 
fore me has already done; and therefore, 


1 have Oe it, more for Variety, than 
for Use. | 


3 we 105 J. to . paid at the 


end of 12 Months, and 2 101. at the end of 
24 Months, What's the equated time for Pay- 


ing all at once, ſo that neither Debtor nor 
Creditor may be damnified? 

In this Caſe, as in all others of this Na- 
ture, ſome Rate of Intereſt muſt be impli- 


ed, elſe any Day at pleaſure may be aſ- 


en. d. 


Let therefore the rate of 5 per Cent, per h, | 


be underſtood in the preceding Queſtion, 


then reaſon will require that the pre ſent 


worth of the Total Sum payable at once, 


(Rebate being made according to the aſ- 


ſign'd Rate of Intereſt) muſt be equal to 


the Sum of che preſent worths of the par- 
ticular Sums; Rebate being made ar the 
ſame Rate of Intereſt, which ſhall be Exa- 
min'd in the following e 8 the 


2 . 


3 j v ; 4 af We, * ; i 
OF» . 47k ; 8 „ 


A „ 


- g 
Bret? J 1 
L % 
£ = 
; ; : | 
© 4 . 3 
r 7 105 . 
* * J ” 
\ - N 
r 
A 7 Av * 
4 . 


1w 1 8 mw 


( 149). 
105, at 12 an 1260 
210%. ar 74 eee 
3% 1 630 


— —— 


1315)630o(20 Mon. the time for pay- 
; ment of the whole 4t 
| | once. 


And bere 28 That had he Rate per | 
Cent. per Ann. been 6, 7, 8, or any other, 
The equated Time would have been che 
ſame. TOI 

So the equated Time for payment of the." > 
whole Sum, wiz. 315 l. at once, is found io 
be 20 Months, according to this Rule. 

Now the preſefft worth of 315 J. ro be 
paid 20 Months hence, according to the 
preceding Rule of Rebate is 290 U. x5 5. 107 
near, at 5 l. per Cent. per Ann. N 


And the preſent worth of 105 J. to he. 
paid 12 Months hence, rebating 5 per Cent. 
per Aun, is 1001. and the preſent worth of 
210 J. to be paid 24 Months hence at phe 5 
aforeſaid, is 190 J, 18's, 2 d. near. The 
Sum of theſe two preſent Worchs make 


2901. 185. 24. Which is more. than the 45 


former by neat 25.8 d. And ſhoweth that 


the Creditor, or he that receiveth the 5 


WAY, Sym at the end of o Mont 
1 N e FP RE 


3. 


Fs 


—— ů 
COTE 5 C 
232 
4 ** 


— — . 
— Ao ami ves rig ited; 6: ib. 4D AE te 
WY TA "I * * n 8 . 
, * MY Es yy — * 8 +. 8 
. y bs. <> 
- _ a = 


* S —— oo OT ROT 
i Os 
ot * 0 * 


% 


90 x50). 


loferh near 2 5. 8 7. which ſhows that the 


Rule is Falſe. 
But tho' the common way of working 


0 Queſtions in this Rule is falſe, yet, when © 
- there 1s occahan for the Solution of ſuch 


Queſtions, he that will take the pains may 


1nd out a wean time, at any Rate of Simple 
Inrercit. Thus, | 


Find the preſent worth of every particulay 


Sum in the Queſtion. payable at a time #0 come, 
_ by Se. 2. Then find in what time the Sum of 


theſe preſent worths will be encreaſed to the To- 


ral of all the particular Sums due, or payable 


at Times to come, and that will be the true 
3 ene Time for payment of the whole Debt. 
| Sed 4. Annuities at Simple Intereſt. The 
5 Bufineſs or: computing the amount, or 
preſent worth of an Annuity at Simple In- 


tereſt by common Arithmetick, is as trou- 


plüeſome to Work as tis Ridiculous and 
D Uſeleſs. Becauſe, as ſhall be ſhowen here- 


after, (in the Demonſtrative Part of this 


Treatiſe) the preſent worth of an Annuity 


compured according to Simple Intereft may 


amount to 200 Years purchaſe, which is 


more by; than is commonly given for any 


| ie, or Penſion here in England.  * 

But altho for the reaſon before mention- 

ccd, the Computation of the amount, or 
6 preſent worth of an Annuity or Penſion af- 


fer this manner be Uſeleſs ;* yer, becauſe 


Fs , A Naber Authors bare W Rules che the 80. 


* 0 


_ en 


0 ” atk . 


% \ *I©@ 


SO 0 * 1 Fx 5 3 | 
| Jution of ſuch Caſes 3 I ſhall 12 in the 1. 
lowing Trac of Demonſtration ſhow how eo 
erect a general Theorem for doing: the ſame, 
and alſo how. Hoe Authors: hae miltaken. 
in the Rules they have given upon frag: 
caſion; particularly Mr. Kerſey in his 2 


pendiæ to Mingate s Arithmetick, and Dr. 


Newton in his Scale of Intereſt, page the 


2oth, and therefore I ſhall tay Bo. ak. 95 
i in this 9255 


wy NET 


" Sec, 5. cage Interefh, or Intereſt. up 


on Intereſt. - When tis requixed to know. 


what Sum of Money any principal, forborn 
any Number of Years,will be-encreafed un- 
to, Intereſt upon Intereſt being reckoned at 
a given, Rate. Tis done by ſaying, it |. 
100 J. amount to 106 in a Tear, What ſhall - 
one pound àmqunt to, Working this by 
the Rule of Three Direct? You'll find 1.06 
for the anſwer ; So that at the Rate of 67. per 
Cent. per Am. the amount of 1 J. for 1 Tear 
is 1. 06, which Sum in this Caſe iscall'd the 
Rate. Then ſay, if 1 J. give . JI. 06 What 
"ſhall 1.06 ? The At I. 1236, is found 
Dy Multiplying 1. 06, by 1. 06 the amount 
of 17. at zwo Year 8 end. Then Multiply 
1. 1236 by 1. 06, twill give 1, 191016 the 
amount of x J. forborn 3 Tears; again, ol: 
you Multiply this laſt product by 1. 06, 
'twill give 1. 26247696 the amount for 4 


TY: ; 3 fo Ui 
4 


* 


WY 8 — 


* 
*. 
. 
[+ 
1 
ST 
23S 
' - 
_— 
1 
. 
ö 
* 
WAY E 
— - 
* 
11 
3% 
= 
. .»' 7 
0 . 
'7Y 
& 
1 * 
1 
[ " = 
LY 
1 
| 3 
$ 
4 
j 
1 
* 
1 
3 
14 
1 
: 
A 
TH 
14 bo 
; 4 
I 
or 
-Y 
[ 2 £ 
+ 
'i1ZY 
I 
wy 
. 
5 


14 

1 
8 
1 le 
4 
114 
1 N 
17 
1 
$ 


oy 
a — 
—— 
—— 4 — — 
— x 1 „ 
R Monat da dc" * 
* * n P 
7 1 3 
4 #5 


= 
gap erp Oy» 


9 ob 
= - r 
r 
A * 
„ 
8 * 4 


00 


This gone. 10 if 1 10 give its! amount 
"for 4 Years, What ſhall any other Sum give 
here working by the Rule of Three Direct? 
There will come out the amount of the pro- 

een Sum. 

From a Naser Confderaion of whit 

Sis goes there ariſes this general Rule, for 
folving of Queſtions in Compound Intereſt. | 


Rule. I volxye or Multiply the Rate ſo 25 
into il Jelf, " as' is the Number of Payments 
ke . n Et Product 5 V by the pro- 

poſed Princips d the Reſult Boe au 105 
6 Tony of the Jaw pro poſed. 


Exam. Whar' sche amount of % J. 10s. 
5 * 4 Tears, at 6. per Gove, act 49: 
e e e 8 


: Lr 


. $ ; 
3 \ 4 * 1 : 2 : 
# » Nas F : * : E * 4 + a : 
44 = 3 | | : : : « ” p 1 * » 


450 9 


42805 amount of 1 TL "for I Yau! SDS 
1. 0 Se Ya 


636 5 
1060 * 5 


— 


1 80 amount of 17. bre v ren 


1 = Pats 
| 112360 


[ - þ a t — 
o 2 © ; 
— RR 4 . 


2. 191016 amount of 1 J. for 3 Tears. 


106 8 1 Toes : 
. 7146096 *x 2 „ 


* ? ” — Z 5 8 a | / 
1 TP LOPOY! 8 „ Ts. 


_ "4 


72 amount of Ti for 4 Years, 94 1 4 

0 : 395 - 1 85 e e | 

631238480 | (9, 1 
1136229264 ' «» 
N aud „ 


112 7525 amount c fought, 


4 N 


80 it —_— to this Method. the a 2. © 
mount ff 89 J. 103. forborn age 1121, 


1 $2.9: 3 5 1 
$i | Aker a WY 


Aſter this Merkad . 4 
_  - Jowing Table, ſhewing in 
botborn any Number Th 


— 
* 


, The on: if the Tabla is PA: The top Role * 3 
F ſhows the Rates of 356 and 7 per Cent. The 2 


left fide Column the Number of Yeats, and 
the Angle of meeting, the amount of 1 F 
forborn ſo many Years; and at ſuch a rate „ 
of Compound Intereſt. . 
For an Inſtance, take the foregoing e... 
ſtion, What's the amount of 89 J. 105. N 


| born 4 Years, at 61. per Cent. per M. 
Seek in the upper Row for 61. the Rate 3 55 — 

of Intereſt giben, and in the left ſide Go 72 2 3 
lumn for 4 Years, then at the Angle "of /-$3 ove 
meeting is 1. 26247 the amount of 41: for- 1 
born 4 Years at the Rate a foreſaid. This, © 4 

_ Multiply'd (as gms" by the: gl.. 

ven Principal, vis. 10 5 will give 1121 J. 

f 195, 9 4..3 near, TE of 89 J. 194 


forbotn 75 Years, at the Rate of 6 1 "per 2 
Cent. P- Ann. Compouiid Intereſt. ” he wy 
1 | 
"Notes 1. "Having got the amount * any 
Sum, ſubſtract the Principal there from, and 
the remainder Is the Intereſt * Intereſt $15 
offuch Sum. . 
of, Bs | N 5 7 N 4 2 2 of 2 
"2 the teten be at 45 I, 75 8, ge 
Cent. per Ann. then the Rate will de U 
108g, 10% re8, Sg. and is . ua * W 
| preceding Deeden. . 1 LN 1 | 


a 2 2 
* . 5 = 2 1 * 
"of K 5 4 L . 
4 c + 3 2 RY $5 * N. * 22 
w IX A 2 £ > „ q 1 2 9 . ** 1. 1 * 1 8 E » * F 
& # * 9 , - 3 77 1 . * Mer 
— * . 4 3 3 8 LAS EZ Af _ 4 le „% ˙· — * 4 '* 
. 
© R$ : 
1 * + wr 
* D 
Bend, 
* ö oy > "A 
3 
. 


C66 "4 | 

4. If the payments are Yearly, then if 
there is an odd half Year, the laſt amount 
"muſt be Multiplied by the Square Root of 
the Rate, If an odd Quarter by the Biqua- 
date Root of the Rate; and if there be 


odd Days, then by the 365th Root of he 
e. 


More Bramples, 8 
What's the intereſt upon Intereſt of EN] 


ſorborn 5 Tears at 6 1. per Cent. per Ann. Com- 


uud Intereft ? Anſw. 1691. 25. 3 d. near. 


What's the amount of 3650 J. 10-5. for- 


„born 7 Years and: 25 at 5 J. per Cent. per Aun. 


; "Compound Fes 1 ah $5524 11 5. 
8 * 14. z ear. r S 


\ Sea, 6, But ſu ppl 4 Sum of Monty, | 


2 hereafter, and tis required to know 
What preſent Money will fatisfie the ſame, 
. Eompuring after. any Rate of Compound In- 
2 Tit done thus, 


ind a ſeries f Geametrigh Propotionalsmont 


Fore in Number, than. the, Number of Tears 
*. _ Mentioned, decreaſing from the Sum to be re- 

luated in ſuch Proportion as 100 Degrees,” from 
' . Tod added to the Rate of Intereſt ; the laſt of 


_ theſe Proportiopals ſhall. be the priſon 1 5 | 
"1 Demanded. 


Exam. What's the preſent worth of 540 7 


5 the paid $300 8 55 in after 


the 


| 
( 


3 F WY 


9 
WY * 8 


| We uh —490: It: 3:7, 
« 17 27 2; . 14:11: 4 | 
the Rate of 61. ee er, 155 Lu "Comput N 2. LY 
COON ITED 
5 106 give 100 J. what "ſhall 
= 2 The Anſwer, is 390. 5 66, . * e 4 
what is due at the 3d Year's end. Then 4. 
gain, if 106, give 100 J. what ſhall 49g. ©: 
5662 The Anſwer,” is 46%. . au % 
much is due at the end of ae Tear. 
proceed thus with the reſt, and you'il n 
the 5th Proportion to be 4x1. 888 or 4117. 
175. 9 d. Which is the preſent Mone that 
„vin ſatisfy che aforeſaid Debt. 
8. But the preſent worth of any Sum of Ma- . 
rey due hereafter, is more readily diſco- r {$0508 
„ vered by the foregoing Table. 7, Find g, 1098 
che amount of 1 J. for the time, and at the 2 l 
g Rate propoſed by which divide the Princi- en bi 
pal, the Quote is the preſent worth of the” 9 
ſaid Principal. „ was , 77 * 


„ ĩ³ Mom Rt ith 


* Let the dees ding Example be on 
What's the preſent worth of 5 20 J. ph 1 
, Il Years: hence, diſcompting afler the RRE * 


of 5 7. per Cent. per Ann. Compuimd Intereſt; 
Here I divide 320 by 1. 2614 the 5 5 

„mount of 1. for the time propoled; the i ” 3 2 2 

N Quote 41 1. 890 near, is the preſent worth A 

: as before of 520 J. to be paid 4 Years at | 

64. oF" Genre fer Amy. Componald Intereſt." 


5 


Set. 75 Ok dna and penſi ons in 
Reverſion at Compound Intereſt. The method PERS 
of valuing 31 Annulties and Penſions, after this _ 5 25 8 4 

| ; manner. — 


a £ N IP ö *. i 
* 9 3 5 — 
os = he \ 
4 "+ a” 


WET 1560 


——U - 


manner, depends upon finding the preſent 


worth of any Sum for Ore, Two, Three, Or 
more Years; the Sum of which preſent 


wWorths, is the os: worth of. the An. 


| _ 


| But Fig. 'To find the amount of an 


| Annuity or Penſion in arrear, allowing a 


certain Rot of ce eee, Do thus, 


* - Find as {fans of Geenen Proportionals 
whoſ; firſt Term let be the Annuity, and the 
ERatit, as 100 to 100 added to the Intereſt of 

100 l. That is, if the Rate be at 61. per Cent. 


= Ztwill beas 100 to 106, the Sum of theſe Pro- 


portionals ſhall he the amount RI the Annuity or 


enfin ſo'forborn. \ (© 


Now to make the Operation more uni- 


verſal and eaſie, Reduce che Rate of 100 
to 106 to another Rate equal thereto; 
whoſe firſt Term let be 1. (as was taught in 
| Compound ' Intereſt) thus, if 100 give 106, 


what ſhall 1 give? Auſiver, x. 06. 80 that 


- 


i 


1. 06. isthe ONTO Ratio of all the A 


Exe. Pee ef 00 b ke 60 an 


Heir of 17 Tears of Age, what muſt he re- 
Ceive at the Age of 21 Years, at the Rate 


dl 64, 120 Cent. per Aw Compound 1 . 


# | a " * 53 4 
4 2 £ 4 © 2 : 4 * ' £4 
. . Fan 
- 3 * 2 , R , * f ö 
= * 
+ a \ 


pb 


W 


a©@ BJ 


C159.) 


p rap, Becauſe. the Time is 4 Lau: to 


make him of Age, tis Evident: there muſt 


be computed the amount of. I 3 en, 


Jears. : Dy 8 02 IN * + 
1 9 8 IF | 


3 There muſt be F. the | 


amount of 150 l. for two Years, which is 
the Rent due at che end of the fec : 


e 2 There muſt be computed, chic 5 
amount of 150 J. for one Tear, Which is 


the Rent due at the third Year's end. G 331: 
Laſtly, The, Annuity it ſelf, which is "the 


Rent due at the fourth Year's end, for which 


no _ Intereſt is to be rec ned, the Sum of 
theſe four Amounts, is the amount of the 


Annuity. See the Opern of; hy pre- 


1 Fee j os as 11 1 * 


7 "+ . t dis IE 


FE * 1 FT 150: (159 - 62+ 1 \ 11 
I: I, 063159: 168 1900 50 7 60 


* — # — . 


656. 54 "hh 
E „ 1 * : 
FP | 3 
2 M , 45 — 
2 ED. 

= 

*--. 
+ w 4 


? 
I, 
E Cath sang b 

R. £7 l : : : : Fer c 
1 lt {1 TH ent „ all e 
— re, x 2 4 8 


_ 


by 
— g 2 
—_— non oo —_— oo 


5 * _— 1 = — — 3 
by — — —— — — — — —— 2 
"TE ES > Le — — — — 2 
= — r =_ — — l 4 Gr —ů—ð— Ps — 
— . . —. . K ee — 
_ x — —— — I = —— — ws. i, — 
3 N * K * 2 
a 47 R N - . 
Ae RITTER TNT on n = 
me . 1 5 * N 4 F Y * . 9 ä +; 9 N 8 
'S V PIP, CEE TIRES 2 2 
— - y 


"een 


80 that by 6 ane Work, 1 nd 


the amount of 150 l. per Ann. lying unpaid 


for 4 Years to be 65 61. 3 5. 10 d. 5 near, at 
the ang of 6 l. per Cent. St Ann. Com- 


puns Intereſt. | 


After dis manner af Proceeding nity the 
following be Conſtructed, which 100 the 
amount of x J. Annuity to continue any 
Number of Years under 2 1, at the Rates of 
816 and 7 per Cent. per Aun. Compound In- 

tereſt being * 


[ 


„ 4 , 5 
” * of 1 
1 to. . os 
— — . 


Li ne I: 12 36 


7 


1 —+ 1. os the ſecond; and 4 f. 06 + 
1. 1236 the third and ſo on. After which 


Method yon may Calculate a Table, that 
* ſhall ſhow you theamount of 11. for as ma- 


n 8 Years as dart cron! 


1 123680 1. ese. 


The ; Operation is for 61. fer Cent. per 
Sg And from it tis Evident, 1 muſt he 
the firſt Number in the following Table, and 


1 


= 


. 


; . 1 
N 
: ' 


— 4 
2? * 
* 
* 
9 
” 


* * a . 9 — * 1 P EE 
J * F 4 — 0 * 
A % - we YO IG; 
, 5 2 5 5 a \ ; SET, 
4 9 A ls 8 p 8 A * 
— \ 7 £ 5 " * 3 | A : 7 * 
8 k Y GD * 
* * 2 : _ 
f * 1 8 
0 0 Me 2 — 5 A a xp % * „ 
1 . *. 1 - _ N 
0 8 ; ; i Et * 
* 
5 ; P : = * 
J of * 
1 7 * U = 
7 4 p "a 


* 1 
1 * 0 


| | nujty for any Number of Yea 
_ 21, at the Rate of 5, 6 and 7 


- 


| — EO 5 
A Table ſhewing the amount of x 


vp 


"NE. 
, * 15 v9, 


. V 


＋ 


a 


An- 
rs under 
per Cent. 


” bay * * 
* 


2 


Years 


bs Bs cer HR 


> 


3 


der A. Compurid Intereſt 


1 — G «ha »4 | 
_w— PS Ye ; oY: 

; _ 1 - * 

* 55 
0 4 ” 4 
4 x k 
; r * 4 
2 4 
* L * 
A 


8 


LS } 
Ate... pw 1 


12 


— 


1 


- 


6; 


7 2 2 Es, | 


1 


2.05000... 


3.152355 1 
- ] 5:52563 


> 


vo. | wu aways = 


Bug 


* 
$- * 

7 . 
«I. * + 


4427759 


1. ooo 


1697531˙ 
17˙39383 


| 2.06600- 0 
3.18360 
4.37461 > 

5.63709 


— a 


1. 00 
2.07000 | 

3.21490 
443954 
575073 
2.153291 


9. 64910 | 
If.02656 


15.9 1712 * 


2 


17.712989 


11.49 131 
13.1807 


9. 89746 | 


10.2984 % 

1787756 1 
13.841644 > 
20.1404 


88 


845 


s 2.87856 
23-65749 2.67252 
25.84036 28,21287 [ 
| 28.13238 


30.5 3900 


30. 90567 
3375999 


2 
bay 
S 
+ 
O:. 
8 
OY 


+> 
| © 
\© 
\9. 
> 
8 


2.88 


A 


| 36:78559 


FIRED | . 

bs: . 
ARR s fy E 
7 % : 4 

1 7 * A 6 > 
: * 
* 
* 


. ; 


25 — 4 
— py bs . 


— =] 


* 
7 


A J 955 * N py 20 * wh, 123 wy 9 28 > x * FR. 2 * * c 0 
8 r 2 IF Cn. EO 1 

« 8 * 111 8 a \ 

x J 4 : 2 a e HS EM . 1 

w.; 2 * * 9 
1 * "es t Re: . * £ 0 2 
+2 * 8 * * 'S) * 4 > 8 1 \ * l = x « : 

\ — 1 7 * 4 J : K * 
j +5 wy WA ; . - ' 4 N : 3 
_—_ * R TL k . ; x . 5 — Mp, 
"I OD. . * Wy — & 

"i \'% 5 Ia . 5 2 — 
Nen g PPT : + OE” 64 ' 
=. c 3 

IF" 3 1 * 2 5 
= 2 . . 2 We 
3 - + 
* 2 Ky Pi; ; 
4 41 3 : 5 . >. a : . 4 
1 2 * e 
* 
mw . a 
Þ 
! : 8 1 14 1 » $4 PR * 
1 P 4 0 * n : * 7 Fi 
* * 


. an n to continue any 
1 1 of Years under 21 to find its A- 
mount, Do rbhus, look the Years of conti- 
1 "nuance onthe Le de of the Column, and 

the Rate at Top. Then at the Angle of 

meeting is che amount of 1 l. Annuity to 
continue the Time, and at the rate propo- 
ſed, this Multiplyed by the propoſed, Annui- 
ty, at the amount of FIC faid Annuity. 
4, W An' Annual penllas of gol. per 

Am, is in Arrear for 12 Years, What doth 

ir amount to at 61. oy ape | i Ann. Cam- 

= Pound Intereſt. © | 

wo oe 0 5 5 Againlt 12 Years in the Left: Column un- 
| KC EW... der 6 I. the rate per Cent 1 find 16. 86994 
—  -. rhe amour of 1 J. in'r2 Years; "This 1 Mul- 
_  _  riply by 77 it gives 1 12225 or 15381. 
= 294 — Sg s. 114. near, and fo muchis 
1 2 78% — forborn 12 Teats. ö 
=_ Sed. 8. If you” world: fm Pe? * 
—_— Wat of an Annuity to continue any Num- 
= ber of Years; that is, how much ready 
= oF money will purchaſe it, allowing. the Pur 
—_ be 2 certain rate of Compound Intereſt. 

Proceed #hus, © $0 0h 

— Fed « Rank of . 5 8 Pro- 
= — n (one more in 8 than the g1- 

y a den 


. 8 


= 
PO 0 


* 


A JEDI IG 
* e ZI © =, 2 2 
: hs 9 L 
N PIR con 8 
* ; 


5 


Ven Tim An Years) decreaſing p40 the e | 
ſed Annnity in ſuch Proportion, as 100 "doth 


from 100 244d to the Intereſt of 100. That 


is, if the Rate be at 6 1. per Cent. till be as 


| 106 to 100. The Sum theſe Proportionals ex- 8 
cepting the firſt, ( (which is the giuen Annuity) 
#s the price, or pred worth, of the propoſed 2 


Annuity. 
Exam. .Suppbſe an Anndity of gol. per 
Ann. to Continue 4 Years, what is it worth 


in ready Money, diſcompting after the 
ray of 61.- * per Aun. Compound In 2 
wok OE as in the foregoing Rule you 5 3 3 4 F 
muſt find the preſent worth 27 501. fort - |, 
One, two, three and four Years, . 2 Eh 
them e the Sum is the preſet 

50 l. to continue 4 Yeats.” ; BY the. = 
| Wee N C 


worth 


: is 8 5 — * "vow Lo S945 3 
1 1 * * j 8 = a . 
. 1 


0 e 50. | 2706p 
1 106; 100 CPR : 44-499. 


e e, 5 5 5 5 


41-971 2395 


A 173. * 
af > 19 55 ö 3 Be 


By which | find he 8 Heth of a 
A of 50 l. to continue 4 Teats at 6 , 


per Cent. per Ann. ro be 75 J. | oy Fs 74 1 — | 


rechoning Componnd * 


7 
LY ol 
; 3 2 4 


. 
7 


* 
* 
4a 
D 
—=— 
4 
4 
* 
* 
— 
* 


„ 
” 
- _ 
A, 
* 
* 
* 
＋ 
7 
8 
* 
* 
1 
* 
«4 
2 
\, TP 


of Pr 


be Conſtruc᷑t 


* 


nt Wor 
y Numbe 


ma 


k 


anner 


© 


Table 


per Ann. Compoun 


preſe 


ing 


OY 


mue an 


fer th 
be 
8 


Akte 
following 


** 
ate 


— 


ſhows. the 
b 


4 
4.» 


to cont 


= 


re 


7 


— 
— 


. 


oF 
bs 
8 q 
* 

4 
= 

PR 

8. nt 

, o 


- 
* 
2 
$ kv 
1. 


2 


Be 


din 


75 
5 
5 

— 


e prece 


= - a 
Ls 
*. 


—— — 


8 a 
— phos 


8 


t. and tis Ev 


ident 


uſt be the firſt 


Number 


381 


ing m 


* 


o 


8 


r 
rr 


able 


—— > 


— —— 


. 
* 


And ſo 
that 


LOI 


952 


* 


proeged 


all ſhow 


0 
ſh 


many Y 


— 
3 


vou the 


fo 


74 


Fg 


e 


ars as y 


* 
\ g _ 
7 
o 3 ke” 
* 
a gg 
* was Ti 
12 133 * 885 
N of 7 * 
* 
* 3 
p ® "x x 6 
n 7 3 
; 2 
8 O 
&. 
* 
* * 
© EF 
A * 
* 
x % 
{ * 
x 
— 
* 
% #4 
* % 
{ > 
my 
. 5 
© 
o dh, * 
4 1 \ 1 
* 
— 


Set 
n 


r 1 
—— 


-. — * 
15 - Ks 
=» 1 
- Ly 
* e =. 
. 4 1 # 
— . « „ 
ws 
p . 
1 1 
$ 5 7 - * * . , 
We * | 
# wah HT 4 s 
** » 
* 
* a — 
2 6 
* 
- * * 
by 1 % * 
- 
— — ** 
* * 
LED . » 
1 7 { 
* * 
on 4 
7 3 
* 
N 
* * a t 
5 „ 
- * 
— 7 VF; 
4 
* * 8 
+ as : 
- ho # 1 
4 * 
2 - 
* 
* 4 
Pg 4. 
b * 
* * 4 * p ” 5 
„ — 
W 
* 4 F 
bo * 
1 $5, 
4 
—_ 64. i # 2 
* * A I , 


r 


* 


* 


. 
3 
— 


Ld 
94 
7 
y 
* 
* 
v 
* *, 1 KO 
>> 
— 
* 
A 
- 


J 3 7 
% ” 8 5 t 
g He — — * x * 5 24 s * 
wy WY . 
; *. * 'v 8 a f $ 4 p Ss : oY 

, 0 "by 2 > 5 | "FS 5 S 2 = — * 6 8 ; | - 2500 TEA 1 . ' 

F * 5 ' 2 : j 4 4 bc EI % 4 6. ey p ts ng th 
rss MS . = 
1 wh N = ; Ws p ” of 4 74 — — 0 ; 3 * 9 
C“ VV 
1 8 ENR «SD. ia ke RSG 8 „ 8 £2 "IB 1 
—_ S „ d oo, . * 5 
R I 5 * ROD TN Oo „ JJ ͤ I 
] * 2 mg oy 8 A pe} ee 4 | Bu : m_ 4 of &: | * | 25 wr 1 4 4 * I . * WE : | 
j SS 388 SS 338833 V 3 

; . . „ CCC „ 2 
2 3 . 0 UV 3 3 1 '#; wo ; V+ a * 93 3 3. 1 2 2 5 "Tom, A 
l ; mw I 4 5 g 2 K 0 : EF ” | : 1 : 
: Vs = — 8 N 8 — = ©) 3 9 8 1 . „ . 
* 8 2 5 28888 5 0 | 3 
_— 28 ZE 8 J 1 
a I 4 3 . wee ES who by g yy Y 1 2 > 2 4 Fw 2 «Ay f - 1 
848 
— — 
UL 


vs. 2 * 
* 8 * 
N , ; 
% ; x 
* 1 
<1, * 
4 v Z 5 % 
.. 8 * 
F F 3 
= 
- 
1 
14 
” 
r 
3 
* 
— 
— 3 = 
* - 
- . 


* 


| This Table ſhews-the preſent worth of 1. 
| Annuity to continue any Number f 
Tears under 21, rebate being made 3 
5, 6, and 7 per Cent. per Ann. Comp. Int. 
— —— —— — 
| Years. |. ; 1 ps f 1 15 f e 


n 


E 


494339. 
1.83339 
262552 


2.72324 
3.547595 
72254 
1 
A 


* 


oþ> ve 8 * 


# 


491732 | 4:76653 
5.38233 


A 


8 
S 

9 

8 
od 


* — * 
n + Rr 
kd * — 2 


OOTY 
* « 
'P, 


* 


6.46321 
272173 
8.3064 


6.2 0979 * 
6.80169 


0 
JP 
2 

= 

O 

5 


— 
3 
N 
22 
- Jon 
x 


| 8.85268 . 35765 
9.29498 8.74546 


1 <4 
8 


8 4 ” 8 
_ ot 1 r 1 2 . . ad 
2 —_—_— "i k 
PR * 1 
OY * ** 7 7 * vx c * 172 
* 


9 


* 


D 
8 
0. 
_Y 
© 
— 


10.379865 9.71224 | 
10.83776 } 19.10589 | 5.44664 
I. 22406 | 10.47725} © 9:7632% 
71. 68958 | 10.82760 | 10:05g08 
12,08 53541 31.15817 1.33553 
12.4710 11.469902 [1059401 


* 2 Is „** . N * N 
: A. £54 = Oy — p ˙»¹1 ··⁰·˙² af 2 83 ** 
= 4 3 Ws - 7 i gm «oe — — 


»„— 


_— 
> wa * 
— 


5 
1 * 8 
5 8 
1 * ” h 
* _ * . CY . 89 
* — 1% A . 2 4 
6 =. | „ 1 "24 * 
£ a - N 0 "= Ys * 1 G x 4 F A 3s ; 
; . 2 "ds A - 5 8 , 
l 5 N 7 3 Y . e # y : . 5 
th X 4 $ s of F . 5 d 
x 5 — > N + * N 4 * 1 1 7 ? ** ) > . 
* 93 * 5 4 4 : ; 
* WES * - 346; l * 2 F $ a 5 4 * 
= : : 2 A 
8 cas. - 4 o 2 * * 
* »_ SJ g . - 0 . 
: . % $I - A ' g 
# 1 - o h * F 
. * * * - #7 . 
$ on . 
a q oy g ” — 4 
* 


4 «bp to continue any Number of Years under 
1 be requir'd;- Seek the Tears in the left 
ſſde of the Column, and the rate of Intereſt 
at top: And in the Angle of meeting is the 

N ee worth of 1 J. Annuity to continue 


; N * FP vF : * 
— W 5 
hal Ras ba „ 
* * 
* 
o 


Wi 166 50 * 
"of 4 the preceding Tal 


"opp. the Poeten worth of an * 


r: the Years, and at the rate of Intereſt 
propoſed, by SN" Multiply any other 


= Annuity, * "twill give the W Wortn, of 


ir 2 the zo cla Time and Rate. . 
Eras Whar's the refers Snare | of 100 31 


5 eres to continue 9 Years, computing 
after the rate of 6 1 Nc 


1 C 
Prone Intereſt? . hg * «ij 


Againſt | Years in te left Column, and and 
under 6, the rate per Gent. I find 6. 80169 
the preſent worth of. 1, age to con- 


er Nes rere 


This Multiply by 100% 5. gives = 


5 5 e, Which is 680 l. 31. 4.4. near. and 


ſo much is the preſent wexth of 1 po J. ger 
Ann. to continue 9 Tears, computing Alter 


225 dhe A GARE r 1 — 7 me 


DO 


8 N 
j 


* 
; * 


N 9. if you. TRA Tt, 1 8 Mn. 
u 5 or Fenliop, any Sum or nd wil 


& 
6 N ; : 
| 4 * 


= 
— 


n 


k 4 


. continue any N BE, 7 Years, * 


and at any rate of Ingereſt. Do bu, 


| fo found be the preſent uvorth fd. dAnmuty.;. 


ſuch Sum will purchaſe one pound ana fer 
the time, and at the rate propaſec. 


wt 


Then ſay by the Ruſe of Three. i "ny g 


Sum Purchaſe A I. Annuity for the time, and 


at the» Rate e 8 4 bars 
. Purchaſe ? M8 


. tb . TEE 


[Exon 1 baud kpow! as „ *$ 


continue 7 Years, 500 J. will Purchaſe after: 


the rate of. 5 1. 101 Gents fer Ain. Compound, _ 
 Inereſþ. | "> Mſgru-105W:: 7 
By the precrding Table, I End, the i 


ſent worth of 1 J. Annuity to continue 7. 
Years, 51. 22 7 à near. Then if 8 15:4," 
8 4. 3 Purchaſe 1 J. Abnuity to continne 7 


bus + what ſhall: 500 l. Purcbhaſe? The 19 1 


Anſwer. Is 86 J. 8 5. 2 d. f near. and do much 
is the Annuity, - that 500 l. will Puichaſe 


to continue Tears, after the ee 5 per 5 


Len. per: Ap: e naar an 


Fn Iv 8 7-5 


More Eramples, © 1 


"IP D g * I} * 


2 What S. the preſent. worth. of an 3 
Jn of 20 J. per Aim. to continue a9 Years, 


Ha 6 15 * 12 . W 


Int ert 


4 : 
2 q 
— 
* ry . 
. * 


Find the preſent worth of l l. Annuity 80 
continue the Number of; Years, and at the Rate | 
of Intereſt given; then is Evident, if the Sum 


* | E 3 5) 168 5 2 9 
33 e 92.1 10 . near. by 


wy 
«I 
| - 
% 


, a7. 


* 


=> 
282 * 
1 ES k < 
-'* 3, 
3% 5 r 
N AN; 
7 

Ss." 

Oe: 

* 


FSeckion 8. a .es 


. What Annuity will 6604. Purchaſe, 
<4 continue 9 Years after the rate of 7 l py 
75 Cent, per Ann. Compound Intereſt? Anſwer, > 


ry rs. rod. neat, by Section 9. 


An Annuity to continue 18 Tears 1 

ſold for 7600 l. What will it let for 
on Ann. to bring in Principal and Intereſt, - 
.. computing after the rate of 6 J. per Cent... 
ee Compound Intereſt 2 Anſwer, 7⁰¹ 1 2 


2 6. 1 d. 3 by Sectien 9. 


A Leafs of ſome Land i is to be let for 
8 5 *tis Worth 1460 J. in ready Mo- 
y; now ſuppoſe, he that takes it can pay 
but 7450 0. ready Money, What Annual 
Reènt muſt he pay to equal the remainder of 
the Money, Compound Interefs being com- 


bes at 6 I. er Cent. per Ann? e 
des J. 13 1. 2 d. f near, by Section 9. 
© 5« A Leaſe of an Eſtate to be let t 1 


4 Years, tis worth 206 J. Fine, and 36 J. per 
Ann. Now admit, he that takes it would 


lower the Rent to 10 J. per Ann. The Que 


ien is how much the Fine muſt be En- 
haunc d, Compound Intereſt being com mY 


= 100 ber Cent. yer on. "A. 


'F 4 ene F the x nah ah which 
26 J. rhes the preſent 'worth of an Annuity 
of 261. ro'contimue 7 Years at 10 J. per Cent. _ 


5, by e e 125 115.64F_ 
Ia 25 3 "0 - 


ES +. 


tb Rabanne f Fin THE, "this al to 4825 the 5%" 
mer Fine makes 3321. 11 % 64.2 the whok 


Fine the Tennant ought ro 72. To 7 Ea rhe | 
8 onditions required.” 


py 5 . * 
. 27 * 54 


6. What Aunuitp f to continue 15 Years, 


will 1000 J. due 4 Years hence Purchaſe, 10 


allowing Compgund Intereſt on oy des 
2 61. 1 85 er Ann. : © 0 ; 
Find by Section 6. the ent wort 

100 J. due 4 Years bence, proſe 792 1. = 
11 4.5 near, then by Section 9, what, 42. 
nuity to continue i5 Tears, 792 J. 15: 11d. f 
will Purchaſe, which will * 8 FH. x 15. 1 1 
wears, the Anſwer. TRY 


7. The Leaſe af a Houſe i is. PIER 30 „ 
* 7 of which there is 4 Years yet to 
come, what preſent Money muſt I pay for . 
a Ten-Yeas's 17 to commence at the 
Expiration of the old Leaſe,” comput 


| en 
Find the piſeat 5 
continue 14 Years, which 3 9.29498, and » 
ſo the preſent worth of 1 I. Annaity to. conti 
4 Tears, "Which it 3.46510. Thes difference of 
theſe two preſent worths, viz. 3.82988 5s the 
. worth*of x1. for” the Ten. Hars in 
en after 25 4 47 Fo z this" "tp , 
30, the propos d Ann 7 e, 174 * 
x 14 ns the N * 


3 Igtereſt at $6 7 Conc: „ 
f 12 4 to 


N £ + 4 : bn th + 
9 N ern 
* 9 = ; 
Be * 
3 
. 3 
We N 
Jo oy 8 5 
Oe FOE 
- = 
2 4 ou 
: 1 - F400 
F 
$ | * 3 
* 
yy g 
2 
þ 2 i 
"i 


9 


8 


g 


5 
o \ * 1 : 
: : 
: 
*\ 


5 


— 


** 
— > 
+ we — =, 
a yn —— mos, 
2 
— 
* 
OY 
* 


= 
— — 
TOI —— 

—— OY © + _ — 


l * 
— — — — — = - N = 
=” — S= L T EG Ag” 
mm. — — - — * as 
- —— ach a — 
. vn — 


N 1 
8 . . 1 
S N 
i x 7% 3 N 25 
1 8 a : We ae 7 * 8 . 
[IF ; * 5 - F : : 5 | : * n 
9 a g + * 5 x 
" : "+ . F, * N * * » 7 1 * Pa} 
if- | - ts # 2 4 ; ; p n 2 i ; 19 
is v4. r «A 2 8 k 4 1 e 
Th! + x eie z — 4 1 * 35 * 
' „ bk + 7 h ++ & 0 : 
„ * 7 a * 4 4 
141 8 3 | x 
£ F.2 * * *, - . 
"PEP F "x" % ; . 
F 1 | . 
z bg . * * 8 by 
1 af / Py 
| \ 
\ we i ', 
* 
8 5 ; 
2 8. * a 7 1 
H i, of 


Fan Ye br 2 veiety, 


10 called: Peel it "WOE 0 find 
out the ſeveral Shares of a Gain or Loſs, 


| | reſulting from a joint or common stock, and 


that in ſuch Proportion as are the Shares. 
And therefore this Rule is of great Uſe a- 
mongſt Merchants, 80 Trade in Compa- 
ny. with a Joint Stock, | 

Of Fellowſhip there are two Kinds, vix. 


DENT. Single and Double; that is, without, and 
e ith Thee. 


Single Fellowſhip, © or Fellowſhip without 


Time, is when divers Perſons make a Joint 


Stock, and each Perſon, concerned therein, 
receiyeth a ſhare of the Gain, or heareth a 


ſhare in the Loſs proportional tq his Stock, 
- Without conſidering the time tis in; that 


4 it ſuppoſeth all their Stocks 40 ye che 


ſame time in Bank. 
The Rule for working Quitions-3 in sin- 
get Fellowſhip is this, 


As the Sum of all their Shocks, to the. toal 


5 Gain or Loſs, eig ach Man's particular part, 


to each Man proper ſhare in the Gain or Loſs. 


That is, 440 the ſeveral} Shares of the Per- 


- bp toget ber, the Sum is the firſt-Term in the 


Rule Tbree; the whole Gain or Loſs the ſe- 


= and each Perſons _— Share! be puts 
| 4 Into ag Stock the bir x; a 


lere 


"7 171 » e 
Here working according to the Rule of 


Three direct, there will come out 4 3 - . | 


Proportional, which 18 Fw: Gain or Lols 


requited. 


And here Note, chat hs Operation md 
be fo many Times repeated 2 chere are 


Partners. 184: Io 


Exam. Three Perſons make a n A 9 6: 1 Y 


of which A put in 194 7.. 101. B 96 J. 15 "> 76- * 


and C76 J. 5 5. gh Trade; and Gain 220. 
124. what muſt cach Forge wave of this aſs; » 


Gain. 


* 


* 
* 
* 


172 EO 1 10 4. 


Fe 15 . | | | 
7150 442 6% 
; 1 * 3 he | 


\ K 


— 
bea * * 
© 1980" 4 

8 5502” L338 1 - 


r eb pig kh 16 » $A'sShare 
. | 


| 0 
RP? , | 2 — 


. . * : d + 2 * 4 7 4 
4 SY - i * . 
6880 EI = 
. ; : 5 g | I 
» © 1 0 a f 9 k 1 


* 
— 
— 


"4 N 
A * A 
* f a 
9 * * . 12 . 
4 * * A 
* . Ws « 
- 1 . f 2 P + 4 
* - * 5 2 5 


Hos 
o(1194 


9 


3722 


> 


008 


3 ant. avg 
7 
* 


2 


715 
* 


* 


— 


4 
2 4 


e „ 4% 2 ' \ ' . bats WE: 


* 14 ' 7 «>: 4 I * 1 * | 5 2 " T * 8 * . , . W% 


: n a 


a — 


SS. 


dee "1 ITE. 13 


2933 47.01 1 Gy 6 
— 4 F 2 
ba 3 + „ REEF; 
- » 1 a N TY * - 5 x _ * = 
. * 5 F ö ; z 2 24 1 F * #7 0 4 
2 * . 4 1 
FP 24 4 * ; 2 74 > [ 2 aj 
— 7 8 * - * » - 
17 - 3 5 1 2 33 
- o pf 9 8 9 * — * 


- 2 8 £4 & : 2 , 
*. + " Y 
L * * I wo 4 
4 ** p ” 


Na, This laſt Stating i is needleſs, 1 
are fure the two firſt are work d Right, for 
having got the Gain of A and B, add them 
together, and ſubſtract the Sum from the 
whole n the remainder will = 


* E "OBI 4 LOS Y n Er 
TE) «EO my * * oF I Rr n * fo 
8 WY * 


5 The Proof of this * Rake: is 7% * f 
for the qum of the particular Gains, muſt 

5 make the whole Gain. Lg in the preced- 

ing OR 3 W 

ws „„. N 

A's ſhare was 113 16 5 


mn. a 


B's ſhare was 39 "wy 8 


er „ 


C's ſhare was 2 or LY 


* 


220 12 2the wholeGain 


*. * 
F , ” % 4 A 
* * — . . . 
-A * J J ” * n 
3 4 « Oo 3. ** Y 


—_— " More Examples. 
ni 80 Company, the firſt put 
5 in 120 J. 12 5, the ſecond- 98 J. 145. the 
. . third a certain Sum; they Gain 110 J. 10 5. 
of which the third perſon is to have for 
his ſhare 344.16 5. what anuſt the firſt and 
| ſecond have of the Gain d And what did 
the third put into Company? Anſwer, The 
eſt 43x l. . o d. 2386 and the ſecond 
© bn 4 * 4. . third put in 1000. 165 
o. eee 
- + Bras berfors A:B and C ER. a en 
Stock of 400 J. A put in 198 J. '14 5. = 
Gain 2261. 105. of which Gain B is to 
have 30 l. more than C; I demand ach 
Man's Share of the Gain, and whar B and 
QC por into Company! ? Anſwer, A's 1121. 
104. 


Doe 


—_—— 


— es EESS — CR rr $o- Ons | — 2 5 1 — — —— l =_ _ by 
— = T * AF ins — — Le} 5 r wad \ — , 8 =" — 8 9 >, as ltr _ 3 1 1 Ton _ __ 4 
7 2 2 — 7 = Wie l > 2 _—_— 2 wie So — ___ 4 — — wy — 
= * — — — — 2 — * — al 22 0 — —— wif So lod ea, PR — — fas — 9 9 N 3 N 2 — - — — hp — 5 . 
. = —— OS». gu I : * — - 4 CET + + audi * 88 5 = 
& — 5 « —— 2 < — —— —_— — — - a — — * 3 x . . * „ * 4 — — 
— —— — 2 DD — —„- — 1 — — 12 — > * * an — * whe 6 
I * , * * i — - — 1 an * 8 = 
ISA. eb BG eee ' AS 2 4 . = 2 : — * js - 
X 0 — * — — 3 „ — N a , — * 4 — 2 jt > 6 n ——— * 6 4 . = 
* * N 1 * 2 * * n n - n CEE _ 4 PU * * * 4 8 . — . — — 
= 7 Mx, om EEE ms A * 3 y i ; ” "% . 1 * * xv ba * 22 8 C5 
* 4 : * = * * — * PR * 
F bs : . N of * F 7 
* * — # os d . * 
; = Nen * * . _ 
i - 2 8 * 4% 7 1 
. -— * 


nn tm Doe WEE nan nite — , 


g ö 
1 mT 9 


© N 4 50S 
N WES N 5 2 


* 


$ 
; * 


_ \ a 
* = = — - yo 
EPI wk . — — — 5 
rn ee 
Lan” N * en Wm * * Fo 4 * 
I” * 8 2 A . 
* A* 
4 8 


1 +4 . 
3 


_—_— 
3 . 
2 : 

21 —— 
* 1 


- 


* 4 ee 
*% * 
2 £ 
. ” 
Aa : 
= — N my 
. 1 
= 
< 7 
* 
o 
. 


105. r ot: 197. 100 — C 


41. 19 4. 104, BY and Bputin 127,025, 


098. Tat. 8 'C: 1 in we 93 5. 02 4 


Double F ellowlhip, 0 Rübe with 5 3 


me, is when ſeveral Perſons make a Joint 
Stock, without an equality of Time; but each 


Partner puteth in his Money, or taketh it ot 
of the Foint Stock as occaſion reſuires. a) 12 
118 working of Queſttons 1 in this Rule, | 
do thus, Mulizph each Man's Stock. by the | 


time it lay in Bank, and add all the Produits | 
together ; the Sum ſhall be the firſt Term, the 


whole Gain or Loſs the ſecond, and each Per- 
1 5 7 rodud} 225 Stock and Time fle third. 


Kean i 1. | Thres Perſons lake A Srock, 


the firſt put in 96 J. for 8 Months; the ſe- 0 


cond 58 J. for 14 Months; the third 40 J. 
for 22 Months: They Gain 2407. What 
18 each Man 8 e of the ny * W 


43 1 
F f 65 © 


$4 we 7 4 
, 
= * * 
1 Mult, by 5 Non ves „ e 
2. 
£ 5 gi o "a 
* 0 8 
6 . 4 7 e 2 = - E 1 
—œê — * * , — p $f F 
29 a | a : ? | - % 
& wo > : 2 4 3 a ” 
mA Py 5 * * . ; | 1 7 ; * 
* A . * 1 : 3 A : 
4 N i beg C . Let 
| , 1 
. - 
, F : # * * 9 
2 : - 1 . : 5 6 


Ag 1464 * Bags | 3 25 5 WR 
_ . 185 6 64 K 


® 


m 
% P44 * 
a i io 
. - A. 
i 
% 


Again 1 246 — LEY 
82 w. 79. 45.44 5 


„ 174% 2 2460 — 4 


« f 


Arſu. 851. 174. 275 8 


N . 5 kee three Sums added. AS wil 
=_ * the whole Gain, if the Queſtion be 
4H . wrought-Right, and is W an infalla- 
_:. dl Pr of chis Rule. 
i Fiſt Share Fry 18; 5. 6 4 25 we 
ne Second Share 79 L. 4 46 44. 2. 
1 = Third Share 85 l. 17 04. 3 0 
920 4 | Proof 2401, 0:5, 0d. 


1 te 2. A Garriſon bath 4 Py 


—— — 


' 


Ert, and 60 Soldiers in it, the Yearly pay of 


I᷑1 is 4000 J. But each Trooper has 6 times 

. the pa ph a Zauner ou 2 of this 

X _ Yearly charge. muſt be paid to the Troopers, 
and how 5 the Soldiers. 

in this Caſe you muſt Multiply the Num- 

55 bee of Horſe by 6, and the Number * the 

7 9 . YO W r, as followeth, | 


40 by 6 makes 1% 7 
69 by 1 makes 60 


— ——— — — — PO — 0 
8 9 — — — n DN CD = 2 — 
2 ——— , — — - — 2 — . _ — *. — . ̃ 
by 5 == DEI l & 2 — ͤ̃ͤ ä — — 8 3 2 
— — — — y — — — — ——— — — — TIES — - o — , , — — o 
— — — 7 — — — 5 - = — — oat — * a — . : 
— 94 rT TAIOAEYY  nn <-ws 7 ren RE hn — , CC — — — — — — — — ” ä IT a » 
— at Be © bac es ad, a am. Les , * 8 . we. 4 2 — 2 — 
a — ———— 3 — — 
* 7 3. a * . "my N N * #*. > 1a FOO TT PREY 
4 * 888 9 
* ( y * 
Rok 
+ ' 
C < * 


2 — a. r . <a, io. 64 4 Ouran Ate 
— — — * _— 4 N > by PRIN . r X. _ 
W 4 5 * 7 * < * - * 
7 FF 4 1 3 , C - g N 
a * 4 . *. 
1 0 


x4. - Wa 


998 


— } x o i . . 
p * \ * * . 
2 - . 246 vs — 
1 * FR a 7 IP we 4 yy cn 
„ v 5 
, * , — a4 1 
= 
- 8 +3 
; * - 
* 
. 3 q 
2 
- 
- 0 
. 


From this tis i« Evitent 4 ad Yorks 


Mony to the Foots is as 240 to 60. ſo that 
the 4000 l. maſt be Ade into two ſucli 


Parts, that the 


eater may be the HET 
240 to 60, to 13 


o which n 


As: 300 to 4000, ſo is 440 to nel the - — 


Horſe- mens Money. 


_Foots 3 of dns 


"Mere Es, wa > 


V 


| Thyes e A. B. C. enter 8 7 


fot a Year,/ A put in io, hut on the 
fir of April follow ing took out 20l. B put 
in the firſt of March 60 l. and the firſt ot. 
Auguſt 100 l. more. C put in 140 l. rhefirit 
of July, but the firſt of Ofober takes out 


40 L. Ae the Year's end there was gained 


142 J. what muſt each Perſon hade of this 
Gain? Anſw. A 51 I. B 55 l. C36 l. 
In Caſes of this Nature, Mulrigh the ſewe- 


ral Diehurſements by the proper time of its m. 
tinuance, and becauſe within the limited time 


they took out, and put in again; therefore Then 
you have Multiplied the Su Sum put in by thepro- 


per time it lay, add the Produtts together, ſo ſhall 


the Sum'be 5/4 Product of Stock and Time. 


For Inſtance, f in the preceding Queſtion, 
A on in F100: which continued In three 
N 


Mons; 7 


As 300 choad 10- 1 6% 10 80 4, the 4 We 


2 


8 a and C 


ö n * 
$46. n 
5 * 

* * 


S ">. 1 
- 8 
* been * 


"TY 


; Months, which Multiplied made zoo, and 
then taking out 20, 1 was left but 80, 


Which continued in 9 Months, this Mut. 
tiplied made 710, the Sum of theſe two is 
roꝛq; and thi is all A's Stock into his 
Time. Do the like for B r 


d Ne If chete be dls Days, all muſt be 
"uct d to Days, and ſo Multiply by thoſe 
Days, juſt as you did when the time was 
given in Months. Es * * AO TEM 1 > 

There is an Army conſiſting of 30000 


| Foot, and 6000 Horfe; the Foot have 9 4. 


Day, and the Horſe: Men 2 4. 64. per 
they take a Booty worth 15000], 


which is to be divided betwixt them in ſuch 
Proportion as are theit Wages, What muſt 


each Party have of this Booty? Anſw. The 
Foot muſt have Her; and the Horſe 

00 N . oa Na 

Three Shepherds take a piece of Bee 


Liter 206“. 102118 Which A put 860 Sheep 


for 7 Months, B put in 75% Sheep far 6 
Months, and C put in go Sheep for 4 
Months; ap muſt each Man pay of the 
200 J. 10s? 3 +35 ary Oo fel: 5 
. wy 3 1 a 


8 3 £8 * 7 : n whe. " Sy 2 i ? 
CELTS "$236 684 981 


N 0 
1 # 
mw 4 # | . £ 3 W a 8 RR 6 # A 
r di 3ι.] 1 
*. * c 3 A* * Ts * A * ©. ; 
- I : * N * 


. 3 Be 
* 1 * 
3 1 Fl 2 * 2 * er a” : 
7 Fi 43 * 8 ba = 4 4 i% # N 3 4 1 A 
gr” 2 WY 
& 


9 


* 
a 


oO © 


1 


Ae bx 


58 8 : £ 1 


8 0 called, ede it Treatetli 0 4 
Mixing or Incorporating of divers Sim 
ples into one Maſs, ſhowing how much yon 
ſhall take of each Simple. It conſiis of 
two Parts, vir. Medial _ en. ©; 1 


Aligatian wedfal, Is N wy Quan- 
tity and Rates of ſeveral Simples are given, 
and "tis required to find-a mean Priee, that 
the whole Mixture, 'or any part thereof may 


be afforded 2 at. For ane which, this is 


1 - 


mn Relay": Yu" 


a , 


505 the whole ih of * PAI TH 15 | 
To o the whole Value of them; © / ö; 


- 


So it any part F the PT kd e 
* the mean Price Wars: At ates 


„ 5 i; 
7 5 


For a There Is mine 4 5 10 Buck 


* of Oats, at 24 d. the Buſhel; 7 Buſnels 5 
of Barley, at 30 d. the Buſnel; 17 Buſhels 


of Rye, at 40 d. the Buſhel ; and 22 Buſh» 
els of Wheat, at 48 d. che Buſhel. The 
Queſt iqn | is, what one Done} ory this Aus | 
15 Worth 5 


0 180 > 
Having added the ſeveral Quantitics tos 


/ 


| ee 8 make 56 Buſhels) find the 
Value o 

ber of Buſhels hy the Pence they coſt, thus 

doing you will ſind that the Oats coſt 240 d. 
the Barley 210 d. the Rye 680 d. , the 


them by Multiplying each Num- 


Wheat 1056 d. which altogether make 


21 _ the Value of all rhe of this M then 
to ſind what any 1 this e 
as hs e n 


| In s Buſh. (be ee, 
To 21864, (the Value 


of the Simple; 221 


Sa is any gere, ſuppoſe 1 Baſh. 
25 39 4. (the mean Price e * 


Op; If che price by: But ane aire Or 


Part be required; take this Rule, 


Divide the Total of all the Prices which 
7 2186, by the Total of all the Simples to be 


| mixed 56, the Quote it 39». Ihe Free required, 


near. 


ec to 8 of theſe 


Rules, you will ſind that one Buſbel of this 


Mixture is worth 39 d. and ; of a Penny, 


_ whichis For of a Farhing 850 the” 58 
| mn We Operaion, A „ 7.3 


AsÞ 


by the firſt Rule; 


- Le d 3 2 REY WA 
o 5 * = * 2 5 ; * N S VI 7 | " 
” L * 7 1 2 5 | 8 0 . i f 
9 2 » ? * 7 \ '1 1 
1 : N , 4 l 
N 2 1 - 8 9 1 
7 g 3 
5 \ o —M 
„ 8 7 * - * . — N 3 * þ th *. 
, ? 
5 22 | 
* | p ; a” 2 x I 
: { * N Re 
6 : 
. 
» , x | | | is 
5 n 9 8 . 8 ; 1 1 * * TT . : 
" . * 7 f f | | , | F 4 . 
+ B. 4 5 N * »;? - FI „ Ny 1 F- | £ 4 a 
2 , 4; : n 
12 117 95 * FE 1 
—— : F «. x * RX, * 
N 3 7 
% * F 3 © 


1 th 4 


* * 
4» x po? { LS % 1 3 7 0 
8 * 4 29 


b ae 45 v or TY 0 


* 
© * 
5 


New , When che Pier dt ge NJ. 
quired, then the two preceding Rules . 


# ow, 


come one and the fame, becanſe one does _ 


not. Multiply ; but, if the Price of 2, 3, 19 
4 Cc. Buſhels be required, it maſt be dogs _ 


2. If you would: have "of the formet — —_ 
Mixture any Quantity, 9 200 Bum. 


Fe to 2007 [a4 it 10. "he Nun ber g * Buſhels of "Yo 
Oats,. te the Fourth. Number, which 1s Th \ 
Buſhels, the quantity of Oats to be mixed. 
Proceeding thus wich the reſt: of rhe i8- 4 
ples you will find, that with the e35 ? i Bus © 2 = 
of Oats, there muſt be mingled” 25 Bufnels 
of Barley, 60 £ of Rye, and 7 8% of Wet; 
the Sum. of which will make 200 Buſhels, 5 
the ( tity required. e 
Ik you have Two, Three, Four, S:. Wo 
beer Things, and N mix equal Paris 


3 3 ka 7 
> * 1 


3 . x. ( 
* 7 X Fl » 4 } 

3 wit. > 8 - 
MI”. 3 
r 

wh 2 bag 


2 12 
2 & 1 * — ; 2 Mc 
8 2 . 19 * 2 hx * F 
33 2 Ip nenn * ; . 4 g 
=o * i Son 9 * 1 
2 CS \ * 
a + 


— 35 3 

. * , 
4 WP * = 

. DR q 
* © - r 
2 ( 
6 1 0 
„ 


* mr” — : mms ed 
* * * E 0 

"> 4 5 7 

* pl 4 


005 (abr 5 ) 8 
0 mem 3 add their Prices, and 
take ; of the Sum, if you mix two Sim- 
les together, for the Price of one part of 
1 ch Mixture; Take; if you mix three to- 
gether; and the 3 « if you mix four, &c. 
For Example, If 20 Oltrices of Gold at 4 1, 
an Ounce, be melted with 20 Ounces of 
Silver at 5 . an Ounce; what will an 
Ounce of this Mixthxe be worth, 80 5. the 
price of an Ounce of Gold, 5 s. the price 
of an Ounce of Silver, the So of which 
3s 85 , whole half is 42 . 6 d. or 2/. 25. 


6 4. the price of one Ounce of this Mix- 
ture. | 


1 the price of one Simple be given % 


Sg, another. in Shillings and Pence, 
and a third in Pence; they muſt all. be re- 
duced to the loweſt, e 7 


"I. 


— The Proof "of LT Rule is is thus, 115 11 


Pen of the. Compoſttion whoſe a5 you ſoughr, 
4s to its price, ſo 3s the. 2wbole.Chmpoſition, to 
tbe whole Price. As ini the preceding Exam- 
ple, Where one Buſhel of the Mixture was 
Worth 39 4 23, therefore, 1 ſay, if 1 Buſhel 
coſt 39 4. % what ſhall 55 Buſkels coft. Here 
working according to the Rule of 'Three 
direct, vou will find che price of the 56 
Buſhels to be worth 2 186 4. which is, 48 ir 
WMWu,js given in the Queſtion, and ag 
= (ae 955 Wor 0 * e 45 


1 7 * 11 iS . 4 " 


* 


inn 


* 1 ua 


xz PQ wk TD TD 


SD 


5 4 More: Examples, 


Ounce. of qr SPE worth; ? * 546. ee! 
7 4.4; K 5 


|. 507, at — the 3 70 l. at 1 te 


of the Gompoſiti tion 1000. Pound weight; or 
And hat will the price of a Pound of ibis 
1. 6 d. the bound, 183 at 13. 10 l. 
: of the Mixture 24.5 4. 15. n Co” 


q 3 


£ 0 | 1880 3 


2 


A Goldfmich hath- 756 Quince + 8 5 4 
Silver, worth 6. 2 d. the Ounce, to "ol = 
mingled wich 68 Ounces of C Copper, worth 2 

three Farthings an Ounce; What is one 


7 


1 3 12 ; . | 
ho, 4 15 of, S . _ 


10%. 112 l. at 2 4.6 d. and 1: 50 J. at gs. the — 
pound; all theſe he would mix, and have 


how much of each ſort muſt he take? 
Mixture be Worth? Anſwer,” 130 J. at 
293 Wat 2 6 d. 392 7 3 6. Ae _ 


Y 


Aligation altevaate, Teachath whan _ 
having the Values of divers Simples, What 
Qantities of each muſt be mixed, fo tha: 
the whole Compoſition may bear a price 


n ? _ thus * mare are £ 
F n RI - * l Dies 


Fi 15 When ch price of ok ci 5 i 
xmas, bur no Quantity given, and tis 
required how to mix the Simples, to Sell 42 
N at a mean e R 


# 


( 18g) » 


For . Rye at 16 s- the Quarter, 


Batley at 18 s. the Quarter, Oats ar 13 5. 


the Quarter, and Peaſe at 10 f. the Quar- 


ter; How much of each muſt I mingle. 
together, ſo ee the whole Maſs pt be 


worth 14 . e Quarter. - rf, 


; ' Secondly, When the, 8 of or one = | 
ple is given, as alſo the price 1 each Sim- 
ple; and tis required, what Quantity of 


each of the other Simples may be — 


therewith. ſo as to Sell the ſaid Me at 
à mean Rate? 


As if with 70 Gallons of C at A 


tbe Gallan, I would mix Sherry at 3 the 
Gallon, Ois Hock at 4 . the Gallon, White 


Wine at 21. the Gallon; and it be demand»: 
ed how many Gallobs-of each ot theſe muſt 


be mingled with the ſaid 70 Gallons of Ca- 


nary, ſo that the whole e _ oe 


| fold for y 5. the Gallons "vp 


© Third, When. the price 5 nh Simple 
is given, but none of their Quanties ex- 


preſt; and tis required, t Quantity of 


each muſt be taken, to make up a certain 


Wut, to be ſold at a mean Rate? 


As, fu poſe, I have Silver of 7, 8, and 12 
Ounces je, and I would have a Maſs. of 
159 Qunces, of 9 Ounces fine; how much 


: each WP of fie: will make, the  (aid-Maſs. 


Notes 


0 oy „ 


Notes 1. That the ſeven Quant! es 10 «. 
1 ſame kind. that is, all Pounds, Ounces; 
Gallons, Quarts, Sc. 


2. That the price of the mixt: Quantzy be | 
beta the given prices. 


Tbat in Combining them together, 5 
a greater and leſſer than che mean is always 
to be joined. 5 £ 
| 4. That the Exceſs bin che mean and I 
grear Extream is ſet againſt the leſſer, and 
the Exceſs betwixt the mean and leſſer 4 is er. 
againſt the greater. | 
When there is more then one greater 
or leſſer Extream, they may be often linked 
together, and have different Exceſſes ſor 
one fort, whence there will be ſeveral An 
ſwers, vet anne, oy 5 
6. If either of the Dr be ſingle,” 
ſuch Extream muſt be linked wilh all the 


reſt, in Which _ coy wil it but one 
3 Anſwer, , 8 


Theſe Tviogs OST the DiceQion . 
| ing ase and working any of he ce 
ee 15-4 falloweth, * - 


"« * P — 


"The e Combining . tet, Plas 
the Prices of the- {ror Simples, ſo that” the 


greateſt Stand in the higheſt place, and the next © 
8 Price under the former, and fo proceed * 4 


: with rhe _ N Peng” the mean 
| _ Rag 
as 


F (58659 > 
; Rate or Price on the — hand of the  ſoid. Rates 
vv Price. 

dTDibes i the 61 Caſe, Aligation Mare," 
x2 Pra Anſwers the Queſtion ; In "the ſecond 
Caſe, Aligation, and the Rule of Three ; In the | 
- third Caſe," Aligation, Addition of the Ex- 
ceſſes, and the Rule of f Three e the Bu. 


,” TY 


f 
(meſs. Ay | uf 


oy — ** * N . 
3 "7 6 Kin: . 
* ny yo. $ > Wale 7 2 ew. F b 
} | : 


* 


* BL LS = gg hoe at 46] 4. r bites at 185 * 


* ter; how] much of each muſt be mingled, 
ſo that one Quarter, of this Meſtling may 
be worth 1 e | 


Fr N ; 4 6 
; ' * L - 1 nl 4 54 
1 ; 2 x Þ r 4 
y : 5 | + 
3 3 * * 5 as. 4 
4 s " * +: 1-/ * 
1 5 1 1 
; ” 1 d E. 4 * * 
. 4 : * - 
. 


nee. RS 7%; 
J apa. 


| hence you ſer chat 4 Quattchs: of Bar- 

= LPs of Rye, two of Oats, and 4 of 
Peaſe, at the Rates above mentioned, muſt 
e mingled together, to make a Maſs to be 


1 


19 at WA 25 8 Vurter. ; ces Rs ; 50 5 


EST... : 
SR * 1 TI 5. 3: F _— & £84546.» * 

% "OM" * o *. . A 2 * xt 

. FE * * Ns * Fa . 8 LF) * 4.7 * 4 - x ” 


we 
\ 
WA. 
I 


MR. NS i wo 
„ ö a => S 5 X44 2 e Fo. 
P. 4 . W 4» W-> : | 1 1 
N 8 a * =. 4.48 


6 , » I , 
* F ͤ˙ ˙ T apa odor Wan * Nn 4443 + Thy 
% F 4 * =" 8 1 A ** 


F- 


— —_—_ \ _ ==, : — 5 : \ m 
_— - = 2 1 D _— = 2 
— 2 — 3 = n r — — 8 — I 
I - "2025 — —— — —— > _ ——— — i = x EIS ICS b 
8 A - * ls, "TE IO rene 0 - 3 8 4 $'22 — * — * _ * LE e - © = — — — — «<= — 4 * 
2 1 * I —_ 2 8 2 * * e — T — Wer * mw 2 2 1 pac — 5 — 2 * 
# X 2 — —— p > — r 3. 2 - 1 5 * $ — 
. by * 4 - — > — wm — — — > __—_ wow — 2 — I LY : AAR Ba. 
— 1 * 8 8 — — a —— by 2 — 2 * 4 « 2 l ; 
e — ph GG — al 4 r * Lr 9 5 _ g 1 W — 
5 a6 tioned. oe a - N on I x 2 r 1 p K N 7 3 3 9 TS ET VET ad — 
4 1 _— - Fs +I a=. 3 r ** 4 a - » * l = 4 Yy * , x SS 9 
> = 2 a l $ £ 8 e > 225 * 8 5 8 FS." 
2 - \ * 3 4 2 i - IT's : RY 5 4 8} x ! * # 4 IE >" ” * * — : 
A he Rd \ 5 v by 4 3 1 5 - As - ROE 
_ * 4 1 1 85 A $4.4, 6 IK . F N * r af : 5 * ; - 
4 ) * , eee RY F . « : a + Ke l S N 1 
* 8 : * * x 4 7 r 1 a 
F ” 4 ta mers £ : 9 f : * 8 4 
7 x — * 2 A * 
* . @ Synch — . " s . 


», =, - = 
* 

— * 
rr * 
Oe N RV FS 2 by hn y Te 
* = 
* * . 

x 


* 5 F ; ” : * 7 \ *. 4 54 , * N a * * 5 3 %. 1 2 : \ &. 
2 5 * "<< 5 % * SY 2 a. * + * — F = % 5 * 5 2 I 0 { x 3 5 8 0 
9 Ly * "x s kT OWED 2 * # * F * 1 * 1 23 8 - 4 F — * x 8 L 1 * * 17 


* 
* A 


2 
— 
9 


+ 
YI + — 
er 


3 
a 


, % 


: 8 x 
ets 7 : | 7-0 9 "> , s 5 ” 


Oars at 13 s. and Peaſe at 105. the _ 


1 enn n 7 b-" 5... 


4 


5 1 11 A 5* ” VET” | * 
3 Gaze W # 0-643 at Bu 


"te. 1 3285 Kind dr and 
With 70 Gallons of Ooty: at 8 5. Frag 


| Galton, I would mix Sherry ar 5's. the Gals 7 
lon, Old Hock at 4. the Gallon, White 


Wine at 15 the Gallon; how much of 
e mingled wich the 70 Gallons 


each muſt 

of Canary, laser the Mixture may be fold 
for. the Gallonꝰ F 
| Combine them together juſt as in the \Fremes, ; 


without conſidering: that "OG Nee of = 
OO a. PPC 


10 Canary. | 


6 3.2 

1; 7 12 I SOckry- 
LnþT 5 Jv Þ Hock. 5 0 
42 1. | 1 W. Wine. 


Hlere tis een e no Quantity of 
1 aſſign d) there ought to be 10 Gal- 
. lons of Canary, and one Gallon of each of 
the other Wines; and therefore to ſind how 
much muſt be 2 with 70 Ne- 9 


. . 6 | NM 

8 r Gal. RE: Gal ls: | 
2 2 As 10 —ä70 > Þ 

100700 Salons, 


EA bene all the Differences are a- £ 


like, or one W does the —9 5 | 
elſe 


TR 
iy 
18 
. 
[1 : + 
. 7 
ö . 
p * . 
i * 
N N ta 
T 
* 
g 
ty 
= 
* 
5 
* 
a 
— 
* 
* 
A * 
is * 
U 
= | 
. ; 
3 — 
4 


(1889) 


py dle there a have been z) and ſhows, 
that with 70 Gallons. of Canary, there 
muſt be put 7 Gallons of Sherry, 7 of 
Hock, and 7 of White Wine, 10 RES: 8 
e n we, Eau | N 


"The Third Kind. , 8 


"There is ; Silver, af, 8 ad 12 Ounces 
Fine, and I would have a Maſs of 150 
| Ounces, of 9 Ounces Fine; how much of 
each ſort will make the faid Maſs. 50 

. Here alſo Combine them after * ſame man- 
ver as . 1 + 


1 


Gs bf x2 Qubces Fine: © 
33 of 8 Qunces Fine. 
( of 5 Ounces Fine. 


In this Caſe "is evident, chat did my Maſs 
conſiſt but of x x Ounces; then 5 Ounces of 
x2 Ounces Fine, and three. of cach of the 
other would Anſwer the Queſtion; but 
fince a Maſs of 150 Ounces of chat Fine - 
9 is I, * e 1 


* 


n . : 
* 4 5 "2". 
— Te . 4 
4 
K it 0 pet 2 1 3 x A 
Mo os, „ * * 
1 5 
[4 
F 4 
. 45 
ef ”, 
8 33 * o $5,» . . Wop ih ” 
8 = h n * * . T7 568 ee => os, 8 7 
39 2 + # " 1 21 wy 49% Þ x 7 
4 : C205 
E 24 | ” £ — 144 . 2 % — ; 
2 
hk =. 


3,4” 


cans ys I r 
4 1 4 i 1 ** 
: a 


» | * * 
A # '% ; , F 


A8 11——I50— 


A 
ö * 
5 o 
” * * 
2 bs J N 
J 3 It : 
4 £ : | k * 5 La Kolb 
Y 7. "i : 
4 1 55 A I . A 5 . 85 
| 7 
1 | E. . n 7 Py” 5 * ö 
e , ; * | — x 
f 2 x * 
— 4 | : 
* . Is - % 
ny , 4 % 
o „ © * . þ ; — 4 
k f $ ; a 1 
2 * ; a 5 x .# 4 ; a ry Py 
4 6 * 
” x 6 FR * 
— 5 ® ® 24 Pt 7 A E x <4 44 : 
* $3 > N 2 + 94 1 TAN £ 2 © 
: * — FF "I ED: g % 
8 . * " 
* 4 Sar r * Ee $a * . 34 f 
. ; > » ; " 
4 . * 
Is f 4 "9 8 
N 3 e _ 
D — - x3 1 1 x7 FM * . N 42 4 * 
. 7 K Eq * £4 1 
6 oo A NY 2 
2 me * = 
_— * & N . b 
a f 9 7 7 <2 R * 8 5 | 
8 FT * 4 . 42 'F PEN — O * * 4 
% Py A 7 K j r £ ZR 1 
7 1 © 2 1 
e 1 K l 
- - 8 * 7 5 - 
o — x 5 
f > Wo 2. "+4 > 5 
4 f — A - . 
5 95 | 
* 2 
7 


- 
* 128 
- 
pa 
: 
: « ** 
o 4 
P - 
8 
- 
As 1 
I ; 
1 4 i Y . 
; * 2 — % * 
4 


s f | N F 1 an l . 
: 8 * 1 1 a 72 "FE . 5 23 2 4 F< 3 1 
. 4 Fs 0.4 * SS 
n ff : ; 
9 . 12 1 1 0 0 11.5 | : 
J A | 
* 
* ww. 7 r 1 ; . | > 
5 5 4 * : * 5 . 4 | 
7 i 
* f 
* a 1 2 Us 1 «+ * * 4 
OT * « y HE by f — * * $ K 
. * 
ae - 
: 1 E x — a = as ; 
4 5 oo 1 ICT e ; 5 
5 0 > * F 8 * ; of * e 


And of 5' Ounces Fine, there Will be che 
ſame Quantity as of 8 Ounces Fine; which 
three Quantities, viz. 68 f, 40 E, and 40 
R, of 12, 8 and 5 Ounces Fine, Will mae 
up the Maſs of 150 Ounces of 9 Ounces 


* 
P A 


, oy 
= 
* 4 


% 


4 The Proof of t y a | 
| the Toral Value of the feveral Simples of - 


* * * 


* + \ 
2 : er #* 
E 25 1 * ; 
* * , « 5 
4 ot ” * S N 1 0 
* — 7 
” * 
2 % 
A 8 * — : N 
- 3 ,—» 
* * 
1 * - I 
* 
. 
5 * > 
— — C 
= - 
* 
© * f 
A s 2 a8 
? - 
* * 
« 
7 . 
— — P 
— 
o | f 


. 
. & 
* * . * _—_ # R : 
" . 5 Z 5 
* > 
= — 2 
* 9 — 
8 2 
7 ? ö 4 
5 2 : - 4 # 3 
- . 1 * 
w <br * 


. 
©. * 
* 
* 
x 
»$ 
j - 
* 
» +? 
. 


, 
+} 


o 


- 
— 


+, 


* — 
1 
%.. 
7 
—— 0 
o 


+ © 


1 : 
* rt to a 
* . 
1 
I - f 
Y % 5 2 


4 = 


; which the whole Mixture is -ampoaſed; 


with the worth of the whole Mixture ſo 
compoſed, and if the Sums vtec, che work 
„„ : | 

As in the ſecond IRS The Nele of 


; 79 Gallons of Canary at 8 . the Gallon, is 


6d c the value of 7 Gallons” of Sherry at 


4 5 . the Gallon, is 35 5. the yalue of 7 Gal- 
lons of Old Hock at 4. the Gallon, f 28 5. 


and the value of 97 Gallons of White Wine 
at 2 s. the Gallon, is 14, s. - Theſe 3 of 


Money added together make 637 4. 


This done, add the Gallons together, viz, 


5 70. 7.7 and 7 they make 91. Now the 


Total value of 91 Gallons at 75. Which is 


the mean price of one Gallon, will amount 
to 6375. alſo, whence I conclude the 
Work! is „ 


More Example . 


A a Ct hath 4 ſorts of b of i 1 6. 
-64ahe pound, of x5. 2 d. the pound, of 11 d. 
the pound, and 3 d. the pound what Quan- 
tity of each of theſe muſt be mixt, ſo that 
one pound of ſuch Mixture may be worth 
27 + Anſwer" I J. at 1 . 6d. 1 . ar . 
2 d. 1 I. at 11 d. and 65 l. at 3d. 4. 

- A Woolmonger hath divers forts of Wool, 
one of 11 d. the pound, another of 9 d. 


. | bg? pound, another of 8 d. the pound; 


e * pound of each of theſe prices 
| 5 muſt 


Fon cg 


1 = OS PER"? bs nat l * * 1 , " 
2s Se _ 3 * . 2 
"Ne 3 * * 7 e 
. | 
* . 2% = 
1 * g 
2 5 


k | "©: 191 ) 
muſt he mitigle with ſome of 3 4 4 „ 
to make the Quantity of 00 pound 
weight of 6 d. per pound? i Anſwer, There ä 
e 4. and 8 4. 789 of. 
each, n $1. of 34 _ Fo ke 


. 
5 | F! 


The Rule of Flſe, or. .- == 
85 "Poſt . . _@ 


HIS Rule is ſo called, Pe we = 

put a Falſe or Suppoſtious: Number, +." 

to . out the true one demanded. 4 

Of Poſition there are two Kinds, vix. * 

Single and Double. - = 

The manner of operating in ſingle po- _— 

Grion is thus, Suppoſe a Number at venture; 1 

and with vw ſuppoſed Number work in all 7e. „ 
ſpects, as if were really the true one, till at © 
laſt a reſult comes ous which reſult if ãt be 

true, Anſwers the Queſt ion, If not, it muſt the | 

: rate by the ſingle Rule of Three direl. 
Thus, ag the Total arilingfromihe bd, 


do the true Total, fo is the e Pays 

.t0 the true A | — 
ae 

For 5 le, A perſon dying. left pgs: _— 

to be diſtributed among 3 berſons, viz. 

As B. in * manner, A Was ta have a 

Certain 


0 N a 
oo 4 N 2 ” 8 i 25 1 
1 


nen,, ks | 
Eerrain Sum, B twice as muck as A. and fs 
C thrice as much as As be and Was each C 
Man's Share. / 2h et, 
WE: 154+ L . 2 
1 „ Suppoſe 7Y to have 50 445 
—_. -. Then B muſt have MM 1 
11 5-54 4. n y 1 
_ = 5 1 2 — 4 
„ n "Tora 39P 1 4 
| Thenas 3000 504. ſois 507. b 
N . CC 
5 ä . 
8 7 0 3 84 ae FE. ” 
JJC 40S B'ſhare.. WO H 


= =; 
PH + E 
- W 
* 


d, 


5 . The Opt ce; A rory hin, for 
_—— © having Muitiply'd the ſecond Term by the 
= . third; and divided the Product by che firſt, 
== there comes out 84 Which is A'strue ſhare, / 
1 this doubled gives 168 B's true ſhare, and 
S8. ipied gives 252 C's true , and the 
Fee |: 
3 More Examples. | AL I 
FRO r «© L 
=. I; Profit bought 45 Yards of Black, and 
of So 60 Yards of- Red TIE whichic 


5 . 
1 4194 * 4 


r . * 9 
2 7 # 4 7 4 * N bg, > "= 1 * * Fe N * * 
4 WI * mw e 
$f „ wo COT” 
1 n 5 : Pl 
9 


1 
„ 6 
. 


roge cther 241. i; 1% But cyery ad £60 7, 
I Cloth, was double the pries A a Yard of | .) 
Black; what was the price of a Yard of 


Black Cloth? Anſwer, 3 * W 
One heing aK d the M 7 hie had 1 in. / 2 3 
his pocket, War that” the 30, _ 


5th of it were 2 5 together, 5 Tous : 
make 188 J. what was the Money he . 8 
Anſwer, 240% e 8 


4 X's. ; 
9 * «i * * 


Suppoſe a Ceſtern with 1 8 
containing 6 un, if he eat Cock be 
{et open, the. Water will vo i chan in one 
Hour; at the ſecond twill” require two 1550 
Hours; and at the third in three Hours: 
In what ſpace of Time will it void, if all 
the Cocks are ſet open ? ba he 3z Minuts z 1. 


4 here Note, Both in this, 55 that 5 

p Doble Poſition, That you take care to 
* chuſe ſuch a Number for che Poſition, ag 
* Þ hath the Parts expreſt in the Queſtion Wich-. 


, I our a, Remainder, aud then 500 will „ 
F Fraftions. yh Fe IT 15 b aq frm. 12 1 . G 35 WY 
Double poſition, l unbeg ut Mi W 
Falſe Poſitions to arkiue at che Truth, a4, 
thus, , £4 


Having ſuppoſed 4 Number, and wich! 8 
proceeded to chte Solution of che Queſtign;” 


| by trying whether ix Will Apwet All the 0 pr 
Properties thereo?,” a Po! 


. Fo 


TO oe. 


4 — 


* — =. "2 ht Res > 
I» b by Ti 
* 
1 „ 
\ ” * 


tte is my Suppelitioncoo much or too lit- 

tte, Which hy comparing it with the Truth, 

I find the Difference, and as it is too much! 
bor roo hire, Note it as my Hrſt Error. 
This done, I again make a new Suppo- 
Ition, and working With chis, as with the 
former,” (if not the Trüth) a ſecond Errot 
ariſes, which by comparing, it with the 
Truth ſhows me whether tis too much or 
too little; and accordingly I note it for my 
—_— ] Pc ĩͤ 
e,, 1 Multiply by their contra- 
22 Poſitions; That js, the firſe Poſition by the 
4 ſſecond Error, and the ſecond” Poſition by thi 
=. ni Evruor, then F the Errors are à like; 


4 * * 9 ST * 
K . + 
7 * 2 


4 


; * 
4 = 
* 9 7 
* 


1 
R 
* 8 


* * * 4 — 1 


tles i both too much, or hath too little, I ſub- 
ralf the Jeſs Produdt from the greater, and the 
5 | r A ee pe 
RRRRemainder 1s #he Dividend; but if the Errors 
Were different, that is, one too much, and the 
ae 
% keep the Sum for a Dividend, which mußt 
be divided by the, difference, or Sum of the Er 
. rs, according” as they gre Ae or unlike, the 
=. - Suorient will give the Number ſought for, 


wo ip ; * 
* 2.05 x 5 


— _ Which will Anſwer all the Conditions of 
For Eadmple, K Göldtmith Bath two Sil. 
dier Cups, wi 5 n6hing 
YT ke pur” on the - firti 


WW  #Oubccs, fas "Coley on the 
eser Cup, end ae weight of the 


- 


oy £% 


| $6 11 «4 5M R a ; 
> Mat © e Ercater; 


* 


5 2 2 a 
; % 
| 2 : 2 


creater it will be 4 times che weight ol. 
the leſſer, what s the weight of each Gu 1 


"TB 10 fie@Poſit: firſt Op. DO Oe, 
8 weight Cover. LAY ge = RO ba 


0 74 WE & : 
* BY 1 5 


— — GY #4 8 | K © 3-3 


18 weight f firſt Cup arid Cover, 3 2 | 


* 
4 


W ö g 
* „„ CEA? PF 18 wot KR. 


ken at weight tend Cp. , | 
= „  B ( Eo PITS c 

5 - l £03 0-206 e co BY 1 3 2 
0 32 weight ſecond Cup and Cover, . = 
* 6 » 25 four times ert Cup: — Ol 


- * 


F n 1 \ 


ll -: '8 firſt Error too little: „ 


* | | | 
— , 1 i 4 | 
' : ju £ . = ; 8 2 | 4 - 
; ; 2 5 * 2 * 3 5 4 N 


1 ——- 
. 0 * x 
©) * A . 


er, . hb ; % 2 d a — Bs 5 . N Ra > ; I 
74 5 f - 2 Bal be X4 1 4 FE dec | l 2 - LS 8 _ 
* „ Hole 2 0951 Ooh © EE 4 


, © 2s act's wh 1 > 
5 * : 2 * 1 a * 4 
or, 3 BB 0 ib d . 
1 . % 0 '2 J my 2 I 7 — 2 ' 4 . : 2 
01 1 5 2 — 8 
| « vx - ; * . | : | 
To - 0 4 4 * f — i * 
a f a * : N 7 - * 
4 ö ; 14 | 
: r GILES 4 ME a. - 
* + $43 #53 e 8 | 
— py » by. 14 15 ; . np 5 
N 4 8 * 14 8 
„ !( ͤ AC SISS 
> 1 - - 
A < : 98Z＋qꝙtnö . 
Py Z . 
1 . -» Wy * 4 
"I > * XL 5 20 a f 5 a / * 
. * 2 4 72 3 s ul _- 
* - 
55 5 x # 3 * 
"I, 2 2 ; * 0 
5 ulgiw 287 7; 5 
* A St 94 * 5 44 * C * 


- * PEE 


. 85 We | 2 S 


1 
* 
& — 
. 
- 
N 
88 
— 
* 


— 


JF ( * 7 the weight of the firſt Cup. 


* 1 - 
o ry = 


5 53 weight 2d Cup and Cover. 
. o four times weight firſt Cup. 


' © 8 
— 8 2 


34 f ſecond Error to hte. 


g $8 firſt Errot. - * 


343 : ſecond Error. 
o firſt Polit, 


2 firſt Product. 


160 ſecond moo =" | 
ſecond Error. 
if, Errors. 9 5 | 


\ * 


| 


times ſo mach ' wanting 81; | 
_ muſt each of them have? 4 5 Fir 235 TM 


Number of the Army? v. 380 0/%/%„2»“/kO 
One buys 2 Horſes with A Burt : 


'T 297 J) 1 


de Examples 


Ace certain eiten left 1277 Crownk to be 
diſpoſed after this manner, the firſt was to 
have a certain Sum, the ſecond twice ſo 
much wanting 54 Crowns, the third three 
how many 


fun 63. and the third 25. 
There; is an Army to Which if you add N 


there Fill Remain r00000 ; What was che 


100 Crowns, if this Burthen be put on the 


firſt Horſe, it will make him of equal price 


with the ſecond; bur if the Burthen be pur 
upon the other Horſe, he will be double 


the price of the firſt, the Queſtion: is ihe 
price of each Horſe ? Nane F ol | 


e ny #5 = 8. 


* * 
Ei - 1.9, , 4 9 k-4 2 


4 OATS 8 * 7 . p07 . „ 

* - - , 4 by 1 

F * 0 . W 
9 1 * 


a - 
* 4 2 , * / ** 2 * N 
„A. „ 2-H 4T 5 
N ET 1 
x * = 
£8 37 4 55 ys 7 7 
3 14 N . ew 1 . 
= * on 
3 T F _ * + L 
* + 269 53 4.233% 5 3 2% 14. 


* n LT 
Ts . 2 


Le > TA 


645 3 
K-45 5 13 


FF any Number be .propo oled. chen is 
| that Number called the Rot, or fir 
Power, and if ſuch Number be Multiplied 
+ _ by ir elf, the Product is called the Square, 
dt ſecond Pomer; and if this ſecond Power 
* be Multiplied by the Root, or firſt Power, 
tetis called the Cube, or third Power; and if 
cis Cube, or third power, be Ninltiplied by 
dh Root, or firſt Power, tlie Product is 


% 


— 


= power, than 16 is the 8 or fond 
© © * Power; and 64, the Cube, or third © ow: 
3 1 'F p er, * © 3 1 CE” LN a * 5 Ty ne : 


; X ; * . 


5 When chereforg a Wer is given, an 
s Square, or Cube Root requir'd, the O- 
' peration is called the Extre#ion © of | the 


e Cube Root. Which W | 


- 


- Nu 7 E&P wt VV +7 


. 


— 
— — 
IF 1a 
\ 

N 
1 
* 
* 
. 
— 


3 A | e 3, OBEY 1 195 2 . e 
is no more than the WAY or manner of 


ing. fuch Root from 2 givent 


Sed. 1 1. In order. 50 the 3 che 


! ſquare Root of any Number, the following: 
Table . will be 2 which e you 
the. Wege N 27 man n ee 

6 . 24271 15 N Wiel we | < 8 


- _ % Number Ader 108 be 5 8 an 
its Square Root requir'd;” then : 

expreſſed in this Table; take the Squar 
| BO of the Number that is the next let 
| thus the Square Root of 72 18.8, for, 64. 18 
Ke next leſs Square, 
The method'of operating), in che ſquare 
Root is thus, When a numbers given,” and 
che ſquare Root” of it requir'd, you mpft 
firſt prepare it for Extraction, by puting 4 
oint over every other Fignre; beginning 
t the firſt Figure next the Right- hand, an 
fo proceeding! to the Left; hat , To 
Muſt pur a point over chef, z sch, 7th, 
9th, « c. 3s the Number $56 is thus pre WW. 
pared; $76.) and"fo of any” other. "Which 5 
reparation ſhows you the Number . | 
es the Root Will contain, 


4 n * 1 P J 
: 9 8 82 . 
l woup 4 : 0 . 
batt *, : £ „ . * . as, SOM — 4 4 
- \ of G | O - 7 fn ” 9 
oh 2 ö N. br >, 
Pp of ” . A > * oy 
. ® „ 
4 5 A. — 
* Ws 
x * 
4 : : . 
N 7 
, » 2 
; 7M 1 1 
| =Y i | 5 
oo E | 1. 5 nate 
R 3 OA ; 
„ WY 1 * 
2 2 4 ws 


* Vr R 2 
ES. ns „ 
© r 
* N 2 
3 WY 
os 


a , ater 3 ded. ts. 5 
— ** e 9 R 
5 = 1 "$2 3 Lad " 1. Bk a Tae 
** * < 
> 4 
* 


« - 


"a0 * ” 
1 200 9 5 
TheNumber bells be 1 and "+ 
crooked lde dr gun on the ight hand, ass 
uſually done in Diviſion, Proceed thus, ſeck 
the ſquate Root of the firſt ſquare 5, this by 
the preceeding Table I find to be 2, which 
| Figure! 21 ſer down in the Quotient, and 
„tze ſquare of ir under the firſt 
3 576 ſquare of the given Number 
4 8 which is 5, this I ſubſtract there 
— from, feting che remainder un- 
eb, you e (ce A te 


> agent. | 


Z Mie eg I bring down to che remain- 

ger (1), the next ſquare. or period of rhe 
- given Number, (vis. 76.) and fer ic on the 
 Right-hand'thercof;. it makes the Number 
# ( 176 Wrüch 8 N el. Aung 


= On 7 "Double the. Root (2) placed 
4 in the Quotient,” and ſer the 
—  faid double (which is 2 on he 

9 Left: hand 45 the Reſol end like 
2 Divifor, which. wall make the 

© 90 * ſtand as you ec in the Margent. 

Having done chus, Le the ee Reſol- 
2 3 the place of U pies, * — is. 
t next the Right-hand,. : med a 
Dividend) then ſeck how 2 8 the Biviſor 
(4) ) befor+: found, is contained in the Di- 


r 


+ 


.- Vvidend (17)? The .Anſwgr," (4) place in 


1 * ang. allo on the. b 


* 
- y n - — 1 
1 6 V 2 k - 
— * * he : — 
4 * 
* | > 
4 $- r 
i » 2 7 E ; W 6 
. 0 . 
©, " . 1 . - * 
. 1 o 9 
= 
* * 
q = 
- : 


vend by the Figure (4) laſt placed in the =” = 
* 9 rhe Reſolvend; ; that. 18. U- 4 5 | 


| Les - (x76) placing rhe remainder. (if 3 


the MEFS (24) in the Quotient being t the 


N 8 


r 1 3 1 n 1 „ * * 3 9 


of the Diviſor : oe 15 between the Din. oo = 
ſor, and the cooled Line; as may! Nn „ 
in che adjoining e „„ =» 


3 * 6. 
„ - - * - 5 


e K yo 1 
e - 
ae 


| Then Ang all th wir (dit l 5 ; 
ſtanding on the Left-harid of the Reſol- 


Quotient, AY the product (176) order- Bs 
+. *  nites under Unites, and Tens 4 
under Tens, c. Then, ha- — ol 
133 ug drawn à Line under tl _— 
Cl product, ſubſiract rhe ſaid Pro- ©. | _ 

| Al duct (176). NE. —* 


was ; . day) under its proper Fi 147 * 
— 2 3$ common in the Cale. 
Wt tl Sußbſtraction, and ſo is your 5 
— work finiſhed, becauſe there: is YT 
1 more Figures to bring dow, 


exact ſquare Root of 576, Kecayſs there." 28 
. n . 3.99 


Nw 1. The N E ments 43 
po never be more than the Reſolvend ; 


- M if it bo ſo — * is falſe. 1 


wo 


owing Example. 


rettec 1 


R < 202 * 3 
2. That br every particular Square, dt. 


auen n by the Points, except the fiſt. 
there will be a particular Reſol- 


— which is made by bringing down 


the following Square to the laſt Remainder; 
and ſo off as there is a new Reſolvend, o 


oft muſt there be a new Diviſor, which 
Diviſor is found by doubling or multiply- 


ing by x all che Root in the Quotient, ſet 


the Number of, Places therein be never ſo 


WN. 


3. The Operation for fading : a new ME 


1 folvend and Divifor muſt be repeated, for 
3 9 figure placed i in the Root except the 


I ſhall conclude this aan, wich che bel. | 


. wk 3 *. ; 


eum. 2, „ What's 8 the 10 Lodi et TY ; = 


3 the Number as before 


ek che ſquare Root of 74 which 


7 3 find to be 8, this. (8) I ſet in "3: Quori- 
| ent; and che {quare of it (64) under - 


and ſubſtract therefrom ſerting | the Remain- 


We, Cie) .cxaMly underncath its reſpeRive 


Figure. To this Remainder (19) L bring 


down the next Square, (viz. 63) which I fer 
on the Right-fide ( of week it e en 3 
N PTE . 


ede; 
5 64 1 


- (a6) 


Figure laſt 


1 "#2 3 


KY A, 
” _—_ & + 


Cap)! 


_ This ang ha 40 uh 
Root, and place its double (c Ke 
n a crooked Line before u - 
© _ - + /Reſfolvend for the Diviſor, then 
III ſeek how often che Der 
is 8 in the Dixidend (186 
Which I ſind to be 6 times, this (601 8 
the Quotient, and alſo between the DNA. 
ſor and crooked Line as before, hielt | 
being done, 'Mulriply (166)the Number on 
the Leſt hand of the Reſolvend, by (5) the the 
placed in the 
Product 729701 


e 


&*- 2A Wh 


94 


12 4 


bane ATE 


996 © 
wt . * 


A by 


A Ta! 
i 19 7 "OE" the Right-hand; 


which (3) Tpiace in th Quotient, ard mo 


a 
” 5 0 * 
5 
45 ws 
-- 
» * 


135 


2 Ae 


r 


Then 1 Ke 
before, I double the N 
(86) for a new Divilaqs 
ne the double (7 
min a crooked Line Be 
the Reſolvend, the Divi 
"for being thus 
eek how often it 18 Eats 
. tained. in {65 


Quorient.” n 

place under; and fabMir&t 
from the Reſefvend (106 3.) And to the 1 
mainder (671 bring don the MATTY 
& 2) 4 Ln Bhs in Tye Mes. 


* 
5 — — 
2 1 


1 


74) the Di- 


* Vidend, Which I is the 


Refolwcnd 


Except the 
' bt; times, 


W 
* 


= 


of) 


* 


— E PORE 


n 


*- of Decimal Frat}ion. In ages to his, See 
that the Decimal confiſe of an even Number of. 
BOS - E which if it doth not muſt be made fo 10 


„„ 
© wixt the Diviſor, and crooked Line; 5 


chis done, LMultiply (17 z) the Number on 
: * Leſt hand of the Reſolvend, by (3) the 


Figure laſt placed in the Quotient. The Pro-. 


duct (5169) 1 place under, and ſubſtract 
from the Relolvend (6742) the Remainder 
1 is(1573) which hiniſhes the work. 4, | 


From this Operation i it appears, that the. 


ſquare Root of 746342 is more than 363, 


0 yet leſs than 864. But haw much 


more it is, is impoſſible to diſcover from 


any Rules of Art yer known, tho' ſome | 


7 have aſhrm'd the Contrary. 


But although we cannot know. the call. 


Quantity, yet we may proceed. infinitely 
near, which WI ſerve. in Practice, as well 


zs if we coul abſaluteſy come to the 
Truth. As 1 hall ow/ in the * 
. ts Ents {5h 


won; 2. To al 1% „e Hare ; Root * a 


do, by annexing a Cypher to the Right-band. of 


3 thoſe that want; and then Point, and Bye: 
F rate as before directed. Wa v4 


1511 


Exam, What's the ſayare Root 1 57962 
. Here becauſe the Decimal confi 


- odd Number of Places, I place a — 


'M the TROY" Ge, * then it Will 
MER "Han a 


0 205 5 - | ; | bs 5 12 Ke 5 4 NY 
and thus 579620, after which Operate _—_— 
juſt as you ch in whole Numbers. -— 


7 4 2 Rs og | ey | | 
57962076 1 FT PR Root. 
n, VVV 


10 N 
od % \ R x FILES - - 
W 1521 3 
8 : : i g 90 - * 
N 8 a & oy 
75 F 3 * 


4 x4 ® -V * 
' * F Vo, 
£ \ 
* 


ES 
W * „ 3 F N # N 4 . " $ 
- - 1 - g #  — 
— | , . 
3 * 
L * p * $ 4 * 


= = by Fe 4 * 1 ö As 
— S N wat. a 


_ Wes 1 "= _ 

l 5 > 5 * 5 
: — — OE N 3 — "4 
r 22 5 - a” — wn I 9 
©, * — * 34 EAR 9 


my, 


= « - - 
= \ fl * 
5 
WR +. 
* ” h + 
x 8 3 15. 
ue , "+ 
3 * 


— 
0 5 
24 | 8 
. + E o * * 1 2. 4.4) + 
| : R888 IS . TE 8 
© WE; än as oF, Rt en tt * N 
. „ a r & * Ko. * 1 Pls 1 * . 2 £ 4 pe on N 
* 1 1 * 4 [EY * 8 n.. 7 4 _ ) >> * 1 — > 
g ** 4 
. 


TE 80 chat 761. is - ths chte Root of 
| 379620 which was required. 

But becauſe: there is a Remainder 1 
zs not exactly the ſquare Root. 579620 9 cad 
1 the exact ſquare Root can never 

obtain d) but as I hinted before, vou 
may come ivfinuely near, Which thing is 
done by adding of Cyphers; fox ſo many 
pairs of Cyphers as you add; ſo. many 
more Decimal. Places will there be in the 
Root; and therefore, the more Cyphers 
you add, the neatecr you will come o ine 
Truth. 
L ſhall to the Remainder of the laſt — 


ample add two pair or fous S and 


11 


then proſecute the Operation. | : = \ 


mY 
LT IS 


F <4 
\ c 4 e k ' 
TIES. CR 7 mag l 
„ ox 4 


1 p k p 
4 2 
N * 
4 , — 6 
| z '< * 
N 8 * 
> \ 


. - Y 
F . * ; F. 
F* ” 


* 


vendor . LEM 
45% «AP — 8 ? 


by: 3 | . F 5 . bo; i# * , 
ng ud 4 


- 1 1 
: . L AE 8 Tl 
1 * * 


Te two Figures 3 to ihe fore- 


8 Root gives 76132, which i is conſid - 
J nearer than the former. 
? And if you will get the Roor yet nearer, 


7 3 
74 . 2 # f boo 
3-5 « 5 75 ? * + 
1 %% „ „ 
a ms . 1 is x [4 4 , 
5 ** l . * — N 8 IP 
* = r PEE ; + . 
— 53 59 8 8 bs PS 
5” „ ; n 2 
fs ? ys 3 : j 1 SS. "#" "x 
LY : $4 * » 7 8 | 4+ I ; 1 1 144 * % . 5 74 I 


7 may do it by adding more Cypher, 
carry on the Work. 
| ” After the ſame manner may you obtain 
5 the Root of any whole Number (that hap- 
pens to be 'Swrd) infinitely near by adding 
'* of Cyphers, and pfoſecuting the Work as 
1 — preceding Inſtan eG. 
gut that nothing may be difficult, 1 ad , 
' ["allume the ſecond Example, of whole 
umbers in Secbiam 1. where there remain. 
ed 1573+; In which, Example ts Quote or 


 ' Root was 863, and to the Remainder halt 


2d 3 pair or tix a er and: fo carry on 


the Vork. A We =o favs UE HOT 


IS EL FISTS gs 18 


8 IS A. 6 eB 
75 K - g * «7 4. 7 FX. p 


* 
: . FORTY 
"0 1 W # 2 * ». j 72 4 6s 4 * 9 1 * 15 4 
R 8 3 ; 4 2 * 4464 t * 79 1 21 


* 
{ 


A 


* F K * 
AS 2. 
N * P — - 
: : - 8 N 
; we” ” ; ; V3 
hs hs | — 
f p * N Y % *$y 
hy is «LO g — _ Le - 
. 822 Ve i b 0 > F 

7 . a 1 > g | | + : 
: 7 * - f s 
oF : E ? 7 2 q * 
6 4 , : 4 
. * V $4, a ; f 2 
* | * ; [ 1 ” - - I 

vw 
. * — A * — * 
N * 4 9 — 

& > + : | 

| if 
1 . 
2 

_ 5 


N voss; TY 
155421 : 


5 ene c EI IO 
55 1778 VVV 


17448:0)r 511906 


+ 
Cy 


#4 . 


By which method I have FR the. Rok St 
to leſs than r part ot Unity, whereas be- 
- fore, I had got it to but 2 little leſs than 
Unity. For every pair of. Cypbers vou 
add, ſo many Figures muſt yon cut oi in 
the Quotient, as Decimal Parts or Places. 
It the ſquare Root of a mist Number be 
J required, "en that the Decimal Part of it cont 
fiſt o mY an even Number of Places, Which if it 
not, mut be made ſo to do, I a, = 
* Ypber to the Eigbe: band thereof ; e Hott 
| it be pointed a before directed, and then w 
7 it Were a whole. 12 Baer: © So et add 
" Example... Ir 115 1 rl i { 10 L | 
rr r ng 2758 ;b ane 
What's the Naa! Robe of 25: 642: 914 
| W this Caſe 1 add a Cypher, becauſe. the | 
Decimal confiſts, of an odd Nambes: . 


Ces. „ ; 8 he FEI CR F . 


b_ 


i — e * ** a 
AY : „ * 8 m_— EY f f 
: 25 1 * 4 my 2 7 F 4 2 £7 © ly 55 . 74 * - Tat FI 2 +; N / 
* "4 , a 8 ; 
4 , * % 1 * £ ö 2 1 34 = 2 2 0 wg e's $5: 
| , 2.3 * 8 27 8 : pg” : KY =. 7 > "of SI 39G — $7 3 * 4 
N ©, (- oa EE 38 * 4 * \ 
) : R | - 70 
* - ” * 4 8 1 4 * a 
nA? F * e 9 G ö 
Ft 2 3 10 7 
: T7 n p b 
8 
» 
% 


* 


"© 5 


5 F | | > . . | ' 5 . 7 « « 
: _- ; 
; ; N "4 £92 5 - 
I 


WE e 5 a 
ER ̃ ̃ Ü—wNVWV , 6 


7 


e „ : 

WR: © Ave 1% — FE is two poinis over 
tte Decimal, therefore there muſt be two 
Places prick d off 1 in the Right-hahd for De- 
= cimal Places. s | 

. That he Gpernich may be carried on 

Ge fatchiny by adding of more Cyphers ; as in 

the g e Examples has deen directed. 


De. 3. If you would Extract the «AY : 
Root of avulgar Fraction, Extra the ſquare 0 

Noot of the Numerator, and ſet for a Nu- vx 

- merator, and alſo of the Denominator, and 

ſiet for a Denominator ; the Fract ion thus ; 

mg is the . Root of the for- 4 


* . Whar's the Ty Root! | 7 


f. 401. 5 4 
POT: But Note, If either 1 or hens!” F 
-.. "nxnator, or both be Surd; that is, ſuch | 

Ons that the _ Roots of em 15 


ES 
CIS f 
+ F 
N * 
"4 
. - 
. 


— a 
r 
3 
e 


( 209 F 
cannot ba . There. i 
way but -to, reduce. it. to a Detiy 
then Extract the ſquare Root. af it... by ; 
80 alſo, if the { Mare Roor of a mize: 0. 
tity be required; Tit beſt done by.zediicing = 1 
it to a Decimal prixt Quantity; and then ny 4A 


tract the ſquare; Root 
Arete 80 400 f itygs nt, 


-:The Proof. ofthe 1 t | 
46 Evident from the -Definitign ” 


ration. For finge the Exits ien of Po 
uare Root is. to 23175 ſuch. a Ni I _ 


whic if Mulciplied b Vit ſelf ſhall give - = 3 
Number out of which the 1 5 _— -, = 
made; if therefore u r 

or Quotient by it ſelf, taking in the Ne. 4 
ainder (if any) "will giye you photon.” 
er 50 Extradtcd.) iS is 57 ep? of ca 


Ack 165 | 72 5 Mor 24 
What's the ine, 


* 


2 
2 m G "»% > = . * 94 n 8 4 
e 5 r n 


a2 REIT ELD en 2c; 


8 Q n n — 
„ abs tor en 1 


5 
—— 


80 = ; 1 


pe 8 4 I” 
—— 1 Ty 
bot + 1 1 — 1 n 
. bo * , 
0 2 - — 


AE i 434 Cu PS 


r 
Ling IB 
ſy a, 


My ND 


As ai * thx; 
n 


8 
or; by _ 


. 
<8 
a», 


28 


es 


. 


3 * . * PN 2 

re r 

er 
1 20 — —— 
2 


a n 4 
** 
n 

* 2 I” n 


I” 5 150 1 ns 2 10 1 5 | T 


| WE wwe penis _ 4 f | : E 


eee 


F. 2 . 
7645- 7536 Ow. * „ 


Lo 


. 


- 


$4.27 ag! 27 near. 

| ehe 
oy Mun 24 > ge 
A. 0 801 21 
tis Exträckon ef the Cube 
DOT. 8 Operation, h by Which from 
| 1 ven Nurnber we find another Num. 
„ hien being Muktiplieg by it ſeif, and 

Pre gain by ch e faid ger Nb | 


1 E zuy Number that is 05 
. K Cube Number, 
| 1 "Nt may” be eltticr or 

| 093 1 0 


8 AN] 7. 
a... pry is Eb 696: of 5's 
| | 24 - — OR. 10, fuch, are an Cubes enn » | 


. corps wi = Roy of "Wh 
7 umber wen is more t nb, uch are 
ons above v99: © 1 | 55 8 
The Roots all Single Cabes, art expreft in the 
* "Hi Table. ! 


A „ 882 — 
. 13.5 b 8 Fi 


mbar 


; r 8 oft 2 + 214 5445 C7 + Ws 
. — therefore when a Cube Number 
be fa in che Table, — take: 8 
| ane 3 
i ample, let 463 be g e 
how” Gar? incarh 


; 
—— — firft 2 Gon chi 
band, and then another point over the 3 _j 
Place, another over che ſeventh, and ano- 
ther over the tenth, and ſo on; miſſing wwoũ 


ny points as the Number Wit admit, the! 
points ſhow ho- many Places the Rogt ' 


5 


buted into ſrxveral Cu 


en e i 


= 


| $0621568, „ 3 
08} NOV A ws W Us rr WES EA 1 Ta. 
Fi The Numbet being p ep 0 
cording to the preceding Birtction it 
pears that the Cube Root of it will confiſt 
ofthirce Plates, and that tłis xt Cube bf 5 


| 3 +, hekeon@eth; the third 568, uh 
deing noted (having drawn a crooked 1 5 

for the — Qube Root of't 

Ark Cube (Which 


| . 
* * 
. z 4 
* 4 : % 
: * i be 2 
A * 7 
— 2 4 _ 7 F 
* | N 
- > 
ou : 


Places betwixt every point, puting as ma- 


Conſiſt pff. pe e ict 5 * 
By thisiPrepar aidh the Numbet: is alt 


For Eanpis What hel Cube Rope = 


Al Cube, and ſet the Remaitider 


| Ji % i 


3 ö n 
. . yo, 
. 
5 n 
* 


Bot (which 1 is 67 K 80) the k t 
Cube, ſo that Units may 2 under 19 


| Bite and Tens under Tens, this don 
Saving drawn a Line underneath; fübftrad 


SMis:Qubcſot: the Quotient (64) from the 
* 
. d (oy 1 nom 


TS Tay Brag Calan: 40 


4 nc b Bs #7 as To this Remainder — "g 
| $64n568(4- 


down. the nent. Cube 


E CY 1273 „thereof, and by will 1; a 6 make 
An 125 (16622) the Number called 
We Re/aorods 18er tbe, ark 


8 Lan 20 L 
e al . rh nt ht e e 


neee 
hi donedraw a Line under the Re. 
and triple the ſquare: of the Root 


1 Ay 3 Tering the faid triple Square (43) un- 


der de Reſo/nend, ſo that Units in the faid 
triple Square may and Yaſs the place of 
1 We &JpIbe: teſalxend | 
ö do 


q- 4. Subſcribe alſo the * FELT (viz. 
120 1 1s 0 


PR * 
21 


295 15 (1662) is el —.— then?” 


op oa 


| Gies; wen which. 
wh : 2 cheforme: Root. 


i: This do ove, Agra! 2 Une node "4 

Woes, and Mukiply che triple Square ( 

re ſubſcribed b 

od? in the Root, and {et the Product (143) 

under the triple Square, fo that Units may | 
ſand under Units, and Tens under Tens, 

8 * 745 1 ' yuh 

Net ! pare he Figre (3) it ; . 

Wife triple Root (12) derbe 8. 

| ſubſcribed,” 99 5 the Product ( 108) 14. 

that Units in this may Rand” unger: Units ian 

the triple Number. * 

z N. 7 ow nad a +. FA 

9. L ede ie Cube (as) or ft 

Figurelaſt placed: In the 7 88 th. 

Tens in this ma Ed unde 


he HormerProdud. © 


$4 ail # £ | 
„ $5 oy 


+ 4 . » 


1889 

| ow. f- 46. MA? 3 

"Y ; 7 
7's * Vo LF 


* * 
4 * 
; . ; 


ro Fg e U 7 ves . 1 4% 
NY 64 ER, 


ol 6 3 . 0, 


> LOO 


3 (except gethe Ace ce of % 


by 3 che Figure laſt Pg. ” 5 


ler Units in e xt | 5 


7 * 
7 3 * F J 2 #2 qt 1 6 * 
I, fo 1 3 3 47 1 
: | ; Aa p < * 38 
"ry 7 x v2 7 
N 4 4 


. Wn 
4Y 
NF 


. N 
x — 
. ——__ 5 % : C 1 
ol , 8 2 4 l 4 als 


our - Prey 1 the” 3A 
on men Fablt 4 wy 


„ Tolvend, and place 
8 N 1 
Ta 2 ID 7) in Order underneath, | 

a >) 88 in common Sub- 


| ; _— ! 4 wg 4 
_ | 4 8 * a . 3 5 3 — 7 a 1 1 3 | 
"i * pee 88 r. 
. . 2 , 0 
» * 1 1 . W 1 x * * N 7 
4 "PS *y F Sg * — ; N TY * 4 644 WE x - ASS. i l ; } 


* 2 * 
KL 
Pu 
EY 
15 1 
: 0 
I = 
*. 
**, - 
. 


> oy 1114 Fig bri 
© down "the third 5-1 


IG 143 bh 1 45 3 24 


1 l 1 Rules Alf 1 5 2 N 5 
e draw a as jad this ſecond Re 
and tri 170 the ſquare of the Not 
whic ſet under this 
its in the triple 


7 * as 7 708 Lader eo alſo the rriple 
2 2 . 


* : 5 . 3 - 


_— _—_— „nm cogr 
—— 


. 


„ 


Sw — wat 


8 hm 


| 
+ ava 


4 


— 


rheſe two added together giyes 3559 
Diviſor, and all the Raſolvend (wit; 111456) 
nen n ee Dividend. 


dec 1c: Root 4 13% en 5 

641 „ 8 1 * / how often the Divi: 
— Ws /.. ſor (55599) Keen 
16621: we 


8 we” The Ane 13 2 


1 to DVii- 
on, Which z biet in 
he Quote to the fbr! 

a "Roby chen 

e W A Line un! 
ä PiviforMul: 
.7- - tiply the trip ere 
4+ Ge by Nina 
ny 4 +. , Figure laſt placed 
"> od, F 1 ey the Wotient, 5 4 


oy 
''S 

25 

5 


W = N | | 
. 8 ou ney 


* 


— — 4 N W - thetriple R 
1255399 Dixiſor- by (4) hg 
es . k 
e SEW  Prodybt er 
N 87 21 8: 8 "En EM. unser en for ; 


uy 3 2 7 


IF as: 1 1 5 68 | f * ; r Fe . 


* 


- gained in Ln, i 


"+ 
4 
11 
- 
: 


rr 
* , 2 
=D 8 
6 


: 9 
A 
22 . 7 ' , 
W . : 
4 G 1 1 I 1 = 3 . 0 
Mebat Units in this an 
: - of 


ſolvend (1 114568 and there Remains no- 


e I dhe Sum gf the left 3 


r 
F 


in that. i 249 a” DAN, N * 120 | 


1 1 53 F 7 r SLE 


Laftly;' Lſobſcribe. 650 Ihe Cube of hw 


1 laſt fer in the . e ſo that Tens 


of this Cube may ſtand under Units in the 
lat Product; che Sum of theſe three Pro- 
cuts (111 4368) I ſubſtract from the Re- 


thing, which ſhows that 432 is the- act 
Cube Root of ug” 568. | "HR r 


ie 


bers be greater than the Reſolvend, the work 
is falſe, and muſt be rectified, by puting a 
E Figure in che * AE e 
22 8 1 
— 4. The Cube Noot 462 a Decimal 
1 is obtain d, after the ſame manner 
as that of a whole Number, only you muſt 
1 the Decimal to conſiſt of ſome Num- 
r of Zetneries or Three's; that is, the Deci- 


1 nal muſt conſiſt of Three, Six, Nine, Tavebve, 
places, Which if it doth. not, muſt» be 


— wade ſo to do by adding of Cyphers 
80 alſo; it it be a mixt Number, the de- 
n muſt be made 10 conſiſt of 
12 2 of Ternaries of Places 
In like manner, if a whole Number 
happen to be Sard ; - that i 75, ſuch where 
"RR 2 Remainder, then may the work 


| o | * % * F 
1 2 3 ? 3 * 24 2 . * 
1 ; * , F ; as af 2 \& * * « j 


K 7 Þ Mev; * 1 
„ * 9 


6 Ape) = 
be . on 1 farther, by adding bone 
Number of Tirnariat GI Cyplitrs, and __ 
cuting the Operation. 
HH Wee cCt 013-160 208 ue 725 bo A 
Laſtly, The Cube Root of a vulgar Te, 
Qion is goten by extracting the Cube 
Root of the Numerator: for 1 Nütef abr, 
and the Cube Root of che Denominator, for 
a Denominator.” The former ſet over he 
later will make a Fraction? Which thall De 
the Cube Root of the 1 * . 


« Root, is alſo Evident from g the. Def mmition 

= eration, which ; 10 find a Nu 
't] 1 Multiplied by it sind W. 
make the Number firſt g m 


again by the ſaid Number, ic 1 | 
. therefore the Root found i in the * 
otient by it ſelf, and that Prgduct 2 
x by it ſelf (taking in the Ren gde 
any) then if the ſecond product K he 
ſame Number as that is out of Which the” 
Extraction was made, the work” is" e 
me nor. * . * * „ A ＋ 2 N md 
RT UTR © 1 8 Wo - 


. 4 TR OT EONS TW * 3 4. 6. 1 con 5 . oY 
7 4 * W S * F F 5 i 4 F "SEP mg "I _ RR. * Ps 2 1 5 1 i T 


* 
FR 0 
2 o 
" 
- % > 
Ye 
e x 


5 
* 8 4 
* — Mw 17 * — . 
F % * So # op" . i £ * MM, 4 
7 1 Þ 1 9 * : "IF T4, 4 3 1 8 $2 ws 7 
. 2 2 x 2 
' ws: ea 3 4 l 4 ; 
N 3 EX 7 ” * q . * 
? Ss * * * my 1 72 9 * T ; 7 FEES F 
11 : 4... 4406; 4 n 1 Pe * 
p 1 * 8 Ly 4 wu $57 & 1 * 
* 
£ 
” * 
* - 
* 4 
5 * 
* * 
* 


25 0 0 
l ab x 10 2 * "+ 


Grids 31 3 


. * 


"ot 115 be 


— What's the Cube Roots of the following 
; | 2 * e 2380 er ee 
1 =P n eg a 
2 * Alz en 4 > | Sho 
Ed 3 2 ——— e 5 
1 31036217776 Anſw. 3176- Wig? i; 
_. 6825359102483 e W 
: ih 253691022824 Aufi, ** 
= Bit > ob 3 HO 1 "uh 1 tes 4 
4 ' alley for. another, 25 10 r „ 
+* non of the Rates and ane * da Wei 
1 cher ſhallfuſtain Loſs. „ 
2 3 be Rule of Three is the onal Rule 1 
3 * ſaving Queſtions, c of this Nature. 
| ample * Two Merchants. gg * 
| 4 "bath 24 C. of Ginger, at 3 J. 145, per ( | 
he other has Cotton at 1 4. f per pound : 


F How 


1 F 
= * ö 
23 2 hd 2 
1 * + > 
oe « $ 
j o 


ney; theſe he 3 with another 


tan anch 


8 2 . 
109 30.4% 144 L236; oy „„ 
1 


14's. "Anſw."7 . 


much Couon 10 be PE 0 oh the 


# „911 3 * $2.8 3.5 
1 5 
Bk: 4 * 5 15 \ \ * * 5 Wo A 8 % 4 . S Tor 25 1 87 * © 
75 Fo * v3 us © 8 I 8 4 Wee A 8 8 * LEN 24. 15 * 


ay 


* % 


% F 
Merchants Barter one 135 4 
4 8 bny 2 ot, weight E N. 
ney; but in Barter he will Rade 300. 15 
pe Gi weight; the other has: r 
Worth 23 L 14 5. per C. weight” xeady; Mo- 
ney. How. muſt che latter ell his. Cinng- 5 


then er C. weight, to N . 
qual be he firſt, 


e 
® the prige « of one Of wei ght, of 


3; A Meteharit ahh one ML a mY 
elver, worth 3 J. per Piece ready * 


Chant at 44. per Peice for Spaniſh Wool, at 1 
10's.” Weight, which is worth ur 74 2 
. ready Money; the G Queſtion is War 


. 


” 
1 e's 70 
« . 
1 . 2 
FT we 
IF 
*” 


5 E W : * 
TP" A 


0 I 
5 104. 'give \ 


I 

5 e 5 thay 

dale: $32 Mods kan Vow 
* {0 10 5 855 6 8 . 
Ne mal, 5 Ae. 308 J. | ) ot | 
hence It " mabifeft, that the true 2 

of the Wool was 32201. and the truc wort 
of the Velvet hut 300 l, and. therefore the 
Merebapt that i the” A . 80 155 


| "TH the reit. 4 S434, . : 1 
A Factor AR) = } bat it. | 
# on Condition: N 0 ſhall add to * 


286 J. of his own Magey, as allo his tro} 
Ble in Managing the whole Stock. Por ' 
of which he ſhall have; of the Whole, the 
Quekiion i 18 What e Fac Qor's Service 
Valned at. edt cap oy" 
. Egge; what Hall 18587 Pl 1 


| Now dedu 8280 from 500, there will 
E OO Taue F. the Factor: 


TOO wh, s 


9 'A Ubtchant Remijic to. his 1 
Sum of 6; o1, with allowing E Factor to. 
put in 128 J. of his own, AP. by A Ste 
ment the Factot's Service e a 
certain Value, which is” 0 gh, 5 

t 


Wie „ 


whole Gain be divided prop 
J Ws to thole three 3 the Factor 
| 6 | 


2 


. fo much-was d 


| age and To Factor. e ee 
b 7 % . ig. dor Y RACE 


| receive Ee owes 


ane 


for his Service \ c will recei So oe t 1 


ho - 
A 
—_ 


San; the Queltioh 58 70 


Gain of — the 

vice Was valued at. 

. *Add the MetHint's and Fay! oY 914 
ether, the Sum 7 why '68'f, * FS la. 5 8 

| Then ſay, as 3 to 1 8 * 3 


10 Val ve of F | 


Gods | 2 2 a Mu Kino, 1 ity am 80 


C320 t 25 | 
hant hat 170 f 


wech che ters 


Sed. 2 2 o . erly f 


no more than to give o | 0 
ne thing fo 4 
— therefore the ſame With, 3 12 3 
— 1 riß it Comm LEED ae 
: * % Ws 34, bor 7 IF ] 8 * 


wer per, 27 n 
Se n drder A 
Coins 


e oh 


e de 
the e Git of 25 


1 ect Ty 


"A dove ſana 8 GY: ch of de, =_ 


Leto >. * n 
Bano move” 


Queſtion is catly = 
K O7 s 918 + io 1 45 9 ect.” Che if 


, 3 
% 


rin, Wal Hall 
e r 


* 
16 Bl 1 52 8 4 44 


Gelder — 2 45 "whe hal 
be? Auf. 14731. 1524. 


y 4 Wu“ At; 48 85 3 Nie FE AT - 
* Fk alla London 375 l. une 
teceide at An 5 aer for 


ep, 21. 94. 
"—_ Pound. 1 how F 
/ FEccive arme fo! bebe 
3757 Kit ing theft nh bios [tk 


Nt EE 205. giv 21 f. 22 "phat ſhall 


| 1. ling. 1711 
15 Ta Q eſtions. ac chaſe; where there 
n on made between divers forts 
the Firſt is compared to a 
to a Third; and that tao a2 
Are two Vaxieties. . How 
f the firſt Coin are equal to a 
ex of pieces of Coin of the laſt 
How many * the laſt pieces 
| r of f — = 


2 


: 
1 

> +. 
; =. 

4 | , 

VE 2 * 

3 : 
DOS 2 
— 2 
N * * 
* N 


- W u * 1 
e 
wb _ L 


— 


+ * Th 2:53 Calan; 
i Front Sth me 


. N 
E 


75 73 „ 27 


| of 2 in 2 


n e 05 both 1 23 
2 2 ee 4 * "19412 3 


— 


Am 2 


= ontr ary 1 7 fo al 7 | 8 1 75 
097: 5 . LIES 


een 


—— Faul * 


ar . wi SIT a 
— dnn mg 8 


| BY Kt 


Uh be {io 
e 8 


Yam W Ew 


\ Wea ij 
equal to. 


175 "4" 0 5 


- a 


43: 5 


of he ul on wa, 
eatures, Where there os a welten 
6 


7 . 
j 
. »” * 
ut . 4 { 
* 125 * 
7 $>% * 
foes « 
0 as CLE 
5, 2 
5 0 
0 2 —ñ — * 


3 


« 255 55 Ee * 


See. 3: Lofs and Gait; Is 2 Rule 
: that toachugts how, when Goods are bought 


at one Rate, to Retail them our ſo as to 
gain or loſe a certain Sum by the Sale 


Rule, 


As the 1 ory of — 2 
To the Total of the Sum given for the Goods 


and what you woulZ Sein,! or _ 24 


EIN. 
So is any part of the . 


To, 7 73 Number, for which H you «Sell the 


d part,” 


1 will Gain 2 Lof ſe the Sum mentioned WM | q 


the Sale 85 fe whole. Ne. Gs 
«Abies. *. A Medchans bönnbt n+ Ell 


of Holland, which coſt 1 156 J. o, he 
propoſes to Gain by the Sale "of the whole 


98 J. how much muſt he ſell it for àn Ell. 


Say, as 2196 is to 12541, 10:5, fo. is 
1 Ell to 11 5. 4 4 as che Anfw. N 540 50 Fn 


e 84 0. weight of 3 which 5 


colt 386 J. 12 * but ſome Damage hap- 


monks to the Sugar, I loſt by the Sale of wh 
the whole 60 J. The Queſtion is how it Was 


Sold per Pound. 


Say, as 84 C. weight 0 46 is : 


"Vit 


11 JOEY Wine Anſw. "3 FIC + 
Q 


x" 
* 


chereof. For OT yy NR this. 18 che 5 


1 F "> FY 
* a 1 "9% A 
7.3 
82 
. 
Wn. 
3 
* 


= - 


„ 


F 


eee chan would Gain-a a certain 2 
” Sum per Cens. by the Sale of any Commo- = 
&_. - arp. Dorking! |: Th 
1 See what rherurbole ks of your Good; will 
FI : | "Gain, at the propoſed. Rate. And then work 
u rhe frf * gf 


; Eo WT 

I : 3: A Merchanc buz ys 230 C. weight of 

—_ ES which coſt aL demand how he 

a may Sell the ſame — to gain after 

= the Rate of 20 J. per Cent. 

3 II 1007. Gain 200. what ſhall 3204. 

e 

=. Ten 1 230 C. Weiche coſt 384k what 

7... chal eff Anſw. 3 < LS 2 | 
„ If you have Goods at one Price, — Sell 


mem for a bigher to be paid at a time; 
= . _ then to know what you Gain fer Cent fo 
— "An." Do thus, . 3 

1 In the Toinpaund Buleof Three DitcR, 
= Les the price your Goods: (or any. part) coſt you 
3m be the firſt Term, the time you 2 the ſe- 
cond, the Gain for 3 the whole (or any part of) K. 
the third ane dis the port and 
12 Montiu i be fifth ; 2 E According 
to e in the wget Role bs 4 5 
come out the Anſwer. | 


| 3 Suppoſe'® Drug aibays Jos * 
5 Steele, 528 col NO this he "Sells 47 


. | i 2 
"oo / | 
by 2 Dy — — — 2 ö 
EY, — on. Boas a * 1 8 
7 _ — 
# 5 
. % 


f . 2 


* 


01. to be * 8 Months 1 hens; 3 
| Quellidey is e he 


; F P 


— We Pre = rope ies 


- 


* 
7 * 


* 
4 
— 


* 
* 
+ 
5 
— 0 7 3 
j - N * 
1 : * ag? 
j >. 
— 8 
o «> , * 
— ” [4 
11 * . 
* * 8 > ® 
% * * + * 1 
* bY 4 
#7 $ s - 
; * . " i 
* 
* N : a 
— vv — 
2 pe 
#5 * 
* * 
7 *; . Ms F A * 
, 7 * % - 7 4 
% 
* 9 9 
{ LY * \ af is 4 4 Ty 
. * E * * 4 % N 
* 
25 * 
* ＋ 1 
ö . 3 
— 
* $ 
| Kept 8 
OE 
* 4 8 
1 . ; 1. * 
> 
7 8 . 7 
e = = £ 8 5 
— * s - 
& Fg * 
— » P 
* * 
4 „ 
. 
7 N. 
4 * - * 
q 5 ' g FP 3 
F % 
7 ' 
= 
1 = 7 
' f . 
b * ; A 6 
4 4 : c 
s i 
* m 
Þ . 
# I 
2 > 
T Cy — ” 
— +. * 
8 4 > ® 
— rl * 
7 1 
/ . . 
\ 5 | ; : 
: 5 1 8 — 
Lo FE 5 z 
0 7 
, 4 
— * P F 8 
: - 
a . 
* 


1 


Rn 


. 8 þ 


«7 


* 


Softer] zac; 


. 
Ll 


* 


- Wa 


————_— 


n,. a ted 


Fm 
. 
* 
. 
* 
— — * * 
„ = 
. 
* ö 
* 0 
% - Wy 
* * 
8 — * 
Pe 
1 
» 7 * 
2 
2 . 
; e — 4 
AA 
* — * 
0 % * 
£ 4 1 
— : 2 - 
* 
3 = 7 
* o 
% I 
* 
K + 
N * ” 
ſx 2 
5 
— — 
* 


7 +7; 04-5 
. 11 * 

3 . * 
p P 1 ; . 4 4 
F £ 
Ef, 

5 * | 4 


# || Reaſon and Demonſtration 1 


| * | 


1 ET 4 


| 3 8 ; 


1 . . | . yy 3 * 
s | += 
| | | == 
\ | g. : 
, | : LN 
. b * : 


= ap e | 


1 - 
| 3 : A j Fo 
| p * = . , i 


hole Numbers and Fractions, 


7 C * F 


4 . ; ' 


1 


. 
* 
„ 


2 — wad 1 * 


: By William Alingham, Teacher 
„„ Mathematicks, 


' | ; MINE. 
5 XS 
: 
- bd - N 7 e 
* : g 
* 3 - 
> , v 
1 : 4 | % 
| 2 o 
| nted in the Year 1705. 
| If * "I 
7 _ * 
N | 3 
| » * * 
— a — — —— — — d 
» 2 „ 2 2 ; PE, * 
* * * N 5 - r 4 , 
2 mg 
* 2 5 0 
4 Fl 
F 7 1 7 2 i 


a * . I * 
af 5 


l * SH 


x 
* . 
» 
— 
% 
x. N 
— 
* ” 0 1 + . — . 1 Py I 4 
4 bad — F 
«4 * 0 4s " 1 $ > 4 
* - z 
* 
4 ” : 
; - 
1 * d 1 1 2 4 as. gp ter W 
1 Ly . 2 £ £ : * SP. hw a Ry 27 - wa St 4 os © +34 
- * 


* = * 
8 % „ x * * 
e . Ac, 3 5 wn tg 
1 7 PS | by 
i F I5 * ' N 7 
- * 4 , * 9 &- 
”, 3 «4 bs I * * 1 a k 
2 4 - - E - * 
” * x wn * - gs ww \ 
* * 8 ” : 
* — J & 
8 { 3 . * . 
- * «iS * 4 * 
; d 2 « Ra 
5 1 =. 5 ys — i 6 1 
hs p f : * * * 3 mY ie 
Py 4 f * 9 * > 8 * 3 * * — 
* . « a * 4 by * ” » * «: * % * W 
* Ll 2 
* o * $ K = 1 
» 53 = * A * is 
2 5 — = 5 — 2 I * 2 4 6 oa 
i — > 
A * 8 - 5 * a — 3 
l " * 0 ek 83 3 4 2 
* „ V 7 1 £4 * = * $ 6s 


2 8 0 
1 f 4 S & , : . 4 
4 *. & : * : Py # * * 0 0 > l 
— # *r C i - : 4 N Fa y 1 7 1 
wh , 8 * k q 
ew _" * 7 
5 F 4 bs , * 3 1 J | — 
* & © * * * 3 - * - * 5 £ b 
_ * ” "4 * 5 g 
, — I : 4 4 3 * * 7 39323 — 
9 * o 85 «Sg s * 
8 * a: OE: . * 83 
I i a 1 a. a n 2 tn * 3 4 
| 5 4.3 f a 


cf 
4 
” 
4 
7\ 
A 
p# 
% 
* 


Lr 
th ot — nn . * 


* 
* wh 
* 
1 
a. 
ASS 
6 * 
LF 4 . 
5 Aram Wc red. ys eG WS 
= 4 al N N. 
$ 
» 
- 
9 
Ak * HS 4 coo 
TT 
* 
b L u = 
= 


z 
55 . 8 ny * * 3 * 
; Z a | * | | 
ag 8 15 7 
| 3 5 23 ; 
1 by : : >. — 4 » * : 
: i” 6s, ry , * . "I 
| : . ** F — * wy - WF # * ; 
l 7 2 bs s __ * » 2 A 9 85 % — 3 'S 
bY ' ; : * 5 5 7 * ; 8 | X ; 
i + i Ms | ; | 
q 2 5 g _—_— ; N 
. - * * L 3 . 
| 8 2 ; 
1 ' \ * , 
£ . . 4 & 


1 . yer "+ „ x. oo att - ano — l . 
3 40r-2e EY „re A MO Re OA 3 


_ O 
* 


— . S ˙˖˙—˙5 cor >; s en * 
0 x 


, TY „ BIG" 2 
n N. 


* % 


* E E on. is td be ad: 


: 
. 


n 


% 
77 
— 
5 
£2 
; 
2 
= 
5 
* 


, 25 
” 


89 þ N : 
E Þ ae a #1 SM 
2 88 5 \ 
4 7 1 
* ; 1 , 
"Y ks 
* Pe 


* — z » * i 
1 7 
* 17 * 


# 
4 


N orderto the Demonſtration of the 
followin g Operations in Arithmetick, 
the Notation of the followi I. Cha. 


© This fign = placed between two Quan-, 
ties, ſhows them to be equal as A, 
that A is equal to B. 3 
This SE + placed betwixt ty 
tities, denotes them to be added, as. B. 
ſhows that A is to be added 70 B.. Or it de- 
notes the Sum of A and B. «4 
This Character (—) placed between 
rwo-Quamities, thows,that, the latter muſt 
be ſubſtracted from the former; as A—B 
ies that, B muſt be ff ubſtrafed from A, or 
15 denotes the difference betwixt A and B. 


7 1 25 i 
* 
7 by * « 
- 
\ * 3 
- ” 
” Noo - ow 
c : . 
* CS F 
2 EF x 
5 ” 3 #46 
£2 be” 1 Cs. 


0 BA os 
. EF af T 6 w 8 * Fa : 7 * 1 
7 n — aL. : rn : 
£# * iS L &; i 1 Sei NE 
5 8 ; Ps D 
7” LES * 33 1 by 5 3 
" let 4 . * 3. : ' 
4 1 N: 
£ - * Y - * 7 „ 
5 a It * 
„W 1 


"I 232 2 * F 

This Simbol (X) denotes the Quantitie 
on each fide it to be multiplied, as Ax B 
. ſhows that A is to be multiplied by B, or 
it denotes the product of A and B, the 
ſame (that is the product) is alſo denoted 
by the Conjunction of Letters as they are 
ina word, thus CD notes the Want of 
C multiply:d.by D. - 
If two Quantities ſtand one under ano- 


= cher thus? 55 it denotes Diviſion ; that is, 


it ſhows that A is to be divided by B. Or 
more univerſally it denotes the Quote of A 


Aduipided by B. 


©.» This 40 n ( denotes the ſquare Root 
. of the Quantity ollowing it, as B denotes 
the ſquare Root of B, and E denotes 
the quare Root of the Sum o B and C, 


allo /BC BC the ſquare Root of the 9 
of BC. 


If the N amber 3 ſtands Ladies he: radical 


Sign, i it Fgnific the Cube Root, as 5 — 
denotes the Cube Root of the difference 
5 berwixr Band D. | 


"Theſe ' four Points (:: ; 5 Placed be- 
tween four Quantities, is the Note of Pro- 
portion; as if the four Quantities ſtand in 
this Qrder, A: B*: C:D they are 8 
2 — 22 2 . 1 to B, as Cis to D. 


| Den 


Definitions, C lee, Aeg and : | 
4 2 —_— for the. * oF 


n Ws 


, | N 
3 3 b h yp A, * W. T7 <0 #2 3. * 2 . 8 or 
Z - 7 þ 5 * 
** D 4 Ws 
F : 


Who arg tn, 0 bo. 


; . 
: . 05 
0 7 


Ane, is hab Habitude or 3 thas 
one number hath to another. 


: 2. In all Ratio's there is. only Iwo Nom 
bers, the Number Which is refertf d is cal. 


led the Antecedent, and the other to which 0 


it is referr'd is called the Conſegquent. As i 
che Compariſon of 8 to 2, the Antecedent 
18 8 8, and the Conſequent is 2. | 


The Quantity of any Ratio is found by 


dividing. the Antecedent by. the Conſe- 


quent, as the Ratio of 8 to 2 js 15 and the 
Katio of 2 to 8 is 3 they axe e pI 
ction wile thus 5, and thus 3. 


; Corollary 1. Hence ariſes a more clear 


Pefinition of Ratio, Which is this, Ratts 
is the Times, Time or part of a Time, that one 


eſt Fra 8 


Number contains another; thus the Ratio of 


6 compar d to 2 is 3, but the Ratio of X 
| compar d to 6 is 3. 80 that a great Num- 


ber compar'd to à little Number hath a 
great Ratio, and alittle Number to a great, 


[has (tho bur ſmall yet) ſome Ratio: © For 


i 


tho the leaſt Number contains. nor the 
w one time, yet it Contains it ſome 


44 


* * 4 bo 
i * * N 
RE ; 
Wi * 
* 


1 85 


* 


"10000000000 Not one time, yet it contains 
it ſome part of a time, vix. One Ten Thou- 
„Ken Millionth part, whence tis Evident all 
0 © Numbers have a Ratio one to another. 


Def. From the preceding Cirolary it 


1 = ratar nee 4 to the Denominator. 


| Quote of 12 divided by 3, then are 8, 2, 


yore 224 I 3. 


N 1 
7 

w 3 
#7 


* LY 
NS: . 


of 6 divided by 2. The reafon is plain, 


. 


—_— .- pan of a time as in the Compariſon of 2 
= x0 20000000080 here, though 1 contains | 


= "Def. 7 If the Quantity of one Ratio 8 
_ equal to the Quantity of another, then are 
F  _ - thoſe Ratios alike, and the n are 

: * Called Proportional | Numbers. As if 'the 
Quote of 8 divided by 2, be gt the 


os or. 2. ee to able gabi & K R 10 
| is Ma to double, treble, &c. the Antecedent 
of ſuch Ratio. Exam. The Quantity of the 
ati of 6 to 2 is 3, now to dauble this 
_ | Ratio, I double 6 the Antecedenr it makes 
Oh this 12 divided by 2 the Conſequent 
gives 6, which is double the former Quote 


lor two Numbers, one double, to the other 
divided by the lame Number will haye 


— a 


5s manifeſt, that the value of a Hactios is 
= only che ggantity of the Ratio of the Nume- 


F 4 


12 and 3 proportional Numbers, 7 theres F 


* | 4 Ml : 4 . 
[ ef, ; : * 
ST" 8 
. "== + pi 2 « 3 : 
WE - A N iz + 7 
5 1 p 7 = 
4 - * * _ 


* 
* 
rr en ———— TV 


double the Quore, and ene the 


G The Ratio is 11100 Touble arable 
ec. by "bhubuing; thirding, &c. the conſe- 
quent of the Ratio as before in the Ratio 
< 6 to 2, here if I divide the Antecedent 
1, Which is bur half of the Conſequeng 
. vote 6 is doubled to 3, the Quote of 


* 6 del by 2. For 6 muſt needs contain 
1 double, the Number of timesit doth Ac „ TS 


Cor. +: hs contrary of theſe tho Co- 
1 44 the reaſon of them is alſo Evi- 


any Ratio. Tis but helving, thirding, GC. 
the Antecedent of ſuch Ratio, thus the 
Quantity of the Ratio of 12 to 3, or 5, is 


when halved but 5, the later _ being / 7 


| Ry half the former. 


2 trebling, &c. the n wo the 
Ratio, as in the Ratio of 12 to 3, or is 


when balved after this method 5 . 


is . e bur half the TI Gore 4 
5 12 by 3. 


N 


Def. 6. c n is Fe 0-0 . 
res Term betwixt the firſt and laſt 
taken twice, 2 27 4. LE £4 26 are in con- 


35 tinual 


Ratio - N | 1 1 


dent, vix. that if you would Halve,Third,&c, 


8 5. The Rune is allo au No 


A 


3M 


ual 1 for 2 is 10 . * 18 0. 
1 foi 15.8 to 16. a e 


A. 


P Fa We 4 4 > r 4 
. ( ) 88 
. : i 4 X1 M S, a 83 f POOR 
* * . . * * 


. 


al one to another. 
2. If to equal Numbers or Luantities, you 
add equal Numbers or Quantities, the wholes 
ſhall be equal. eg 
3. Af from equal Quantities, you tale; A- 
a wii equal Quantities, the Remainder ſhalf | 
be equal. 
| 4 Equal Numbers or N Multi lied 
1 8 by {qual Numbers or Quantities, will ave 
Equal Products. = 
5. Equal Quantities, divided by "a 
Se, Will have equal Quotes. 


PROPOSITIONS. 


7 
& 
5 


nal, the product of the Means ſhall be equal 
1 the Product of the Extreams. 3 
* Damonſraties: Let the Numbers be 8 

E:: 4 :3then (p. def. 4. 5) = =? alſo * 4 = 


4 (p. ax. 4) and 8X3 = Th (Lak. 4) 
hich Was to be Demonſtrated. | "REN 


43 L235 
#14 
4 


After the fame” manner it Ae 5 
'F 3 Numbrts are in continual Fro OSS. 


4 


4 


| at 
OY 


3 _ * 
. —— oe . 7  wliabt 
— NN — — — 0 


pigs equal to the fare Third, are 8 


*. Tis 


Prop. 1. If four Numbers are * 


4 
4 N 


7 437 
the product of the firſt and third is $ qual 
to * e of the {econd.” 


2. Ratio 8 which are TY 10 * 
a are alſo equal one to another-. 2p 


"Dt ' Admit 2, and =2 2 hen 1 


8 == For 1 —. therefore = 


. Ax. 1 M which was to be Demonſtrated. 


8 Prop. 3. If a Number Multiply two Nun. | 


| bers, the Products ſhall have the fame Ra- 


tio to each iS, a8 the Numbers them | 


ſelves had. 


; 4 
9585 a gf a f = %. af 


"Dem. Sur 3 6 8 82 are dle n 


to be multiplied, and 3 the Multiplior, by | 


Ratio of 6 to 81 is 8. then Multiplyi ng oy 
2, twill give z, which is equal to; 


to double the Antecedent of the Rath, 82 5 
bles the Ratio; but to double the Conſe- 


quent halve's the Ratio. Now to double i 


firſt, and then to half it, ſtill keeps the NA. 
tio the fame,” therefore: the Ratio of 6 
to 8 is equal to chat of 12 to 16. which was 


to be Demonſtrated. 


Upon this Propoſition depends the De- 
monſtration of moſt Opetations' in Fra· 


» 2 * » 
1 ». 1 Fe 
* = 
Y . n 


5 p 7 * 4 : 

C * % 

. x 
® 8 9 N £ [ Pe 
* + £33 . — 
of 1 , d 
. „ „ * J £ 3-4 
2 W.. -S F F 1 $ 4 4 


. N ESE >» 8 


* 4 - : e 8 
p . : 4 1 5 4 
5 *. 
- * : " 
3 0 
a F 
A 4 . 


of Number, nth its Naa, 


fue is nothing elſe but the I | 
tude of any ſort of Things. 

Notation of Numbers, vulgarly called | 

K is that which teaches to expreſs 


Numbers by Words and Charatlers. . 


One, or an Unit, is the leaſt of all Cha- 5 


_ xacters, for Number is only a Collection of 


Units; and therefore, if 5 2 Unit be ad- 
died another Unit, it makes another Num- 
* and if to this ſecond Number be ad- 
ded another Unit, it makes a third Num- 
der differing from the former, ſo that by. 
the comingal adding of Unity, there will 
ariſe an infinice variety of Numbers for the 
Spreſog of which were there requir d. 


the like Variety of Cbaraßters 'r would be 
extream diffcult; but this difficulty is re- 


moved by a very "eaſt e Method of placing 


_  - them), Which for its excellency; and uſe- 
flulneſs may deſervedly be ageounted a- 
1 1 the moſt noted Inventions of Man- 


ind, and as the learned Br. Wallis ſays, 


I duly conſidered, may Teeny to $01 more 
Bo than bare Humaine caVengy (1 


"The Characters by hien N 


'Fepreſt, as I have hinted before are ten, 
one of which, viz. (o) ſignifies nothing of 
it ſelf, the others have nor only fingle Va- 
hues of * but have other Values 

| * 


7 


Tuaditiom tells us, is owing to the Arahians, 
and if you will believe Ariſtotle, the reaſon 1 


the ſecond place, and one hundred Times 


accordig gly * L * Hh hich chey, ac 
5 from the Denory Nnender of our king. 


ſtandingſgniſies only its own Single-value, - - 
of Tens, and denotes ten Times its on 


it ſtood in the firſt Place. The third Figure 


ing ten Times as much as if it ſtood in the 


"3 place before it, Fat * in the next horn to 
the Right- hand. 


follow thele Conloguraem: - 122 1 Hig 


yy I Je - ks - * w 
91 ö i 2 
5 


cidentially Poſts. | 
The Invention of theſe Ebern den ad 


of our uſing neither more nor leſs than 10 


In all Numbers, eue Figure. hath a - 
place. 8 > _— 
The firſt Place next che in n is the =_— 
place of Units, and any Number there 


the Figure in the ſecond Place, is the place 
Value; that is, tis ten Times as much as if 
is alſo ten Times as much as if xn ſtood in 


as much as if it ſtood in the firſt Place, ane 9 by : l 
ſo ir goes on increaſing every Figure, be- _ 


From the oni Explanation will 


S $:2% 


fin, Thar every Figure hack t two Va- 
ue vix. its own, and another, according 
ten the 1 ſtands in. 2 „*** 


2 $4 3 8 . A 2. 5 7 
1 15 * #2 9 3 N * : 28 . 5 Len. 25 7 . % 


5 much as the FIC * 


. AY That ifo one 1 15 Jackd 


; hw any Number, the value of that 


Number is encreaſed ten Times; % 
TVo, à hundred Times; if Three, a Thou- 
fand, and ſo on, in a Told Proportion. 


5 75 the Number 456 be propoſed, then if 


lace 5 before it every Fi 1 thereof is 
A pug a place higher, O that's ſtandeth 


in the ſecond, 3 in the third, and 4 in the 


fourth place, . e the Value of every 
Figure is encreaſed ten I imes as much, and 


eonſequently the value of the Whole is ten 


Times as much as twas before. beſide the 
value of the Figure added; if two Figures, 


ſuppoſe 57 be ſeg before the Number 436, 
every. Figure aſcendes two places higher, 


and therefore the. value of each 


Figure, and conſequently the va- it, 


hae of the whole is one hundred 2 43 217 


_  Fimesas much. See the Tone”: 
Ws 


* 


Mah, That if my: two "© He | 
up AR and 8 be placed an equal Num- 
ber of Oy oben then are [thoſe Numbers 
increaſed an equal Number of Times, for 


one Cypher ſet before two Numbers makes 


them ten Times as much, and another be. 
fore that makes it ten Times as much as the 
jaſt, and therefore an hundred Times as 


\ 


 Fourthly, 


192 


C 


Nines, and if to 2.00 put c 


| Diviſion will be Axiomatically E 
ä therefore 1 fb — 75 n 


1 5 oh 3 {1 ; * * T $4 , 8 8 * : ba , 
4 Ly 0 28 33 R Th 7 FTIK$ 25 
"* . 4 
75 Oy : Rs 1 
das 15 * D (07 T2 6 WL + 8 5 | 


* 
% * 


9 
4 2 5 


— —— 


aa» 


© Fourtbly Ot two W that is, at 
greateſt that hath moſt Figures i in it, for i 
a' Cypher be put on the Right- hand of t 
it makes it ten, Which. is bigger than PE; 
Number noted by a lingle Figure. 


4-33 


n {0 Si 27 | 
 Fifibly, That of Number a. an 


equal Number of Figures; that is, = 


greateſt which hath — laſt Fi 
This is Evident; from the fit ee 
Co pſequent, Where, if to gu. ꝓut two 


the rwo.,with .( Cyphers i Pe Ba ban 


% LY I 


1 with two nines, '> e 19. net 0 wok 


This manner of Notarion being well con- 


ered, the f ręaſon of the Operations in 
Addition, - Subftraftien, Mu e And h 


rhaſe.that-are — * 0 805 begin 


Wh the Rule of Three. 0 % „ 


Bit * 1015 "+ 545 # 70 BWwink 23 clad Hing 


>] 16.54 3 3 NM 100 1 Di * 3 5 3 
* 18 806 er 3 v lich! das 0 ts £77 10" Daho kt 


--- 


+ 1 | \ 
9 7 FE . N 1 1 —＋* 7 "I * 2 q 
— 1 a S748 4 : be 
vu 46 * — + a 4 © Tub: 1 34 . = &S 4 


- 
3 


A : * 5 
. M3533 id "#1 2 IIA. 


Eyphers, 
the 


. 1 3 
firſt 


4 * 
4-9 E 5 
RY > 
. = 4 3 * 
r "A 
Fs 7 ;» ts 3 * 


* 7 
Fo 28 18 + * 1 1 83 * 0 5 
AR Zain 28 CLEFT 10167 5 
. 


ah 2: Aal A e er up 


K * p 2 4 2 
- * 8 IF 8 " 
CA © Op OE x I SY" 2 „ 
* 
4. &* 
1 0 AE 


8 1071 by . 2 - - 
5 1 
CEC Led. 
— pe : a * 
- "+. 6 - 4 * © I 
: $754 14 : 
A 


$$ 


FN de Bule f Tlitte Dire, "where 
F< three Numbers are ſen to find a 
ourth in dire Proportion, the Rule is, 


Arie z te ſecond Nane, by the bird e 


 MividetheProdutby the faſt, the Ne the 
5 fourth Term or Anſwer. | e r 


Fot Ea, if 8 Pound buy 4 Sheep, 
any will 2 Pounds buy? * 3s, 
oo 53 Number, ſuppoſe 


rt al. 4 Ard ver. 
4 a e fourth 


X — — or * by the aforeſaid 


Rule is evident. For fince (by ee 
product of the ſecond and third, 155 ** — 5 


the product of the firſt and fourth. If 


therefore 1 divide Be product of ſecond 


5 > third by the firſt Term, the quote will 


be ſuch a Number as will Multiply the firſt, 


2 and * that product to that of the 


Lag 


+ Io 7 * 
ond * third, as is Evi ent - 
2 and thetefore is the fourth Proporti-· 
W ne 2095) 500 one 

| YE! 3 0+ Semi Tha) 20 


1 


Ext 
l 


* * : * ” "wv : 4 
36d Hiw RR 
N * * * * 
* 
bl = 

— 9 

1 1 ö 1 

> 

= 
= 

» 

0 

- "5 

* 


"Houfe in 10 Days, in how many r , 


*** 


15 Men build che ſaid Houſe? 
_ * The:Queſtian fared a £6 the'# 
Beal Rule, (which ape, That" the fir ond 'J 
: rbird Number muſt be of one Name, 6x.) wil 9 


822 


| Rule the pen will be bur 5, "Which 5 Wt 4 
B . 30 Men require 10 ᷑ 


* 


5 ing to the oe DiceBlon: 
A 85 Fr, 3 4 8 Soqque” -, 


47. 8. Deyn pong ol 


4 
cs — — "yy 


i n b * as v8 3 En, 1770 1 


r f you compare 


them Reciprocaliy; 
- wiz. the ſecond Time tothe firſt Men, and 
the firſt Time to the ſecond Men, the Pro- 
rtion will be direct; that is, if you will 

ut che fr Term i in third Place, and the 
A ae in —— - Place, you 2 
erſe to a direct Proportion, then 

the Demonſtration will be ee. W 
_ For changing it Will tand thus, 15. 
A then * 1 . 2175 = 


e 


4 | Ne TA 
Exam. ö Uppoſe 109 l. in 12 Months 


261. Incexeſt, Leben _ "oy 1. 
gain in 24 Months ' E 
399! ths ve, rhe fin 5 faul. 


"43% COT a Mon,—6 e hk ehen 


£ - + +47 rf 8 5 Þ *% 25 0 
0 * 1 * 'S * A I „„ 1 75 * ah N. 4 


Here 


. 
r 


lere „„ nt wes Fl 
on given in chis Rule, the Auſwer wiltbe,--= 


WR SES Herd off otter © ol 


1 


J. vi 5 Exqooxag g.. r egef 
#1 W . 100 K12 | * apron 
But Queſtions int \ Compane 4 Rule of 


Three may be ſolv d, by the Single Rule of ß 
Three at two Operations. | ied 52! * A 


Thus, Say as x eee 3 % 4 : 
SURE 4 05 Asſe-Hef A 
- Thos, If 2004 755 40 1 = 
) Gagan ( — Gro Anſwer, Which - 
2 * . ys Three di-. 
red it ee nur ee e thy e af wat Bo 

| | 7 "A p 8105 Fat Off * 21 TS. \ | | Wh 


* F - 

. . 2 p 

, . j # £ 

* F 4 # 4 
— — — a — 0 — 7 
0 ” $ : f & 9 : 1 
* 4 4 - = F 7 4 * 5 : 
. — 1 7 


* wal * 
e AE * EY _— 


The Demonſtration of the 
Compound Rule Rec 


HE, Compound Rule Reverſe ſc a 
alſo be ſolv d by two Operation 1 
the Single Rule of Three, only LYN . * 
df Via, ang the other * EO 
Asi A \ this” Ea mole, If It 28 5 
2 * hom winy By 2 


NR * un glg 


CTA 


rating in this Rule, the Aae — 
2 15 e e . 


; 0 8 9 
s! VE. 
* 6 wi N * ” — — % 


* 1 


For , y che Single Rule ſs ia 


—. 


- 


9% "bh is 2 5 >» #4 | 


if 20Am———3203— 30 a 
. ee, oy 


K vb »; 45% E) : - hy 
3 2rN — SG ING 


oy 


e 


** p 
: * . 
** ** * 


Secondly, By | the Single Rule of Three 
| Reverſe. Brant! e whit ee e 


2 ——— 2 5 N 
— — * EE —— 
_ * N * 
2 - 7 " l . 
"FS 5 Nd 2 
3 Fa ©7 
* 
an 


— 


/ 


br 


— 


P 
* . 
al 
*. 1 
4 
7 as 
— 
** 


4 


"TP, 


9 
Wik * 


EF That is 5 2 — and che ching to. FD 
by 1 : ing 


: 
: 45 
? 
* * ad * 8 . * . < ; « i 
* * * * | We” N A * Nn N "Ing * * 2 » . * 


* 


* 


— 19 > I ner, 
8 15 e 3 — 


\ * * 2 a 3 5 "SS, * 
: * - « - * 2 »* Y WE 4 ar 
* , * - * + r 
* n 1 + CE 4 4 > 
% 4 a 


iy 
SIS | 
* 


iple Intereſt tele 4 


5 be confidered. F rf. he Pepe or | 
8 Money put out. Seco ondly, The Rar twas 
lent at: Thirdly, "The Te it lay. And 
f F 7 ;_thas is the Princi- 
* ben 1855 4 gon . 
wee auge of in., 


* * OP * x ” N 4 n 

e Wb”, as wu aaa * 1 5 
he et CEE On” 

WW 2 7 n 

4 IE l 5 . = 4 

boy * 15 

OE”: 84 * : TM 

2 IH t 3 : l 

Sg 2 


5 
n 
3 2 $0 

9 
30TH 


| three of theſes fre on given to find-the 
fourth. wy * As the more better ſolving | 

Queſtions of this Nature, 1 ſhall'getiore the 
fore- going particulars as followerh. 


Exam. Whar' sthe Intereſt of 2501.1 for 2 
TIO + at 6 der Cent. per An. put P= 250 
al or Sum put out; t. 2 z the 

time of Continuance in Tears or Parts of a 
i g . os the gain of 1 7: in one Tear; 
=" = 374. 10's. the Amount; bat is, _ 


Sane" f Pr Inoue _ err 


This Hei premiſe, Note. 8 1 fe 


MW Tr 1755 ear: gest: tg | the? leren br - | 
ok for the ol ed 80 that tg 
l ts amount for the time propo- 
e. 


And chen ds 1 J. into itt amo for any 
time, fo is all —— 8 F 0 its a- 


5 mount for the . n 4 
That is 1: 1 p le 
which is the genera Te, "for eg 5 


Queſtions of this Nature. 


For ſidce p pig icreſord p a 
which is the Cannon or Rule fur Rebate. 5 


So alſo g g which fipds. the Rate * 
flea 
it * 1 


. * 


5 Gi per Ann. Simple Intereſſ. 


t the time off 


E bene pain of 1 U for a Tear. 
N 3 IS 4. near, ogg of proſe 


x "at Simple dur. 


As 


JHE Buſineſs . e * — 
of Annuities, or Penſſons, according to 


Simple intereſt at any Rate per Cent. der An. 


is what may be worth oùr Enquiry; tho* 


not of ſuch Importance as that which finds 


their value according to Compound Inte- 
reſt, the reaſon of which is Evident, be- 
cauſe at Sim 1 Intereſt an Eſtate may be 
computed: to be worth 200 Years Purchaſe, 
which is a great deal more than any Eftare ; 

will ever ſell for here in England. 

This being Fn Take this Example, 


Suppoſe an Amuity of 200 l. per Ann. to con- 


_ 4 Years. to. be fold, :whgt i is it north in 
eady Money, allowing the. Purchaſer 6 L. per 


The things to be. coniidered and noted 
for the Solution of this, e b lake | 


tions, are as followetb. f to honor” 


2==200 L tha Annuity or Annual Income. 
:ontinuanc bene 


Parts of a Year. 


N : 
\ 2 : : b 75 F 
| - w . 1 
, 2 p . 
2 * . A »* . % c : F : ; + * Fog 4 
” 5 ..« 54 Wh is T7 8 323 b 
N ""— * WP l ; \ N e 


45 | Thethings thus noted aper : TP an... . 
5 ſo chat ga is che Intereſt off for one _ 
17%4«wä»‚ vhomup Kio tk: me gi 
Then tis evident, that at the end of iht 
| firſt year, I ought'roreccive a0, che ans? 
nuity only, at the end of the ſecond Year 
200. wun the en won Eras in the 
; 7 | fan . e Ae | Mags" 
= _n. Ooh e COR nf N 5755 = | 
4 Firſt wed: | n "oY" 
0 4175 Second! Faw, VF 
. 2g third Year: / FAR | 1 07 | e vs 9 | 
3 385 Fourth Year. ain INRA. _ = 


Which tend is wail r0241g8—gawhich, 5 
is generated by Multiplying ga by t-. 
Ci Now the Sum of all; thoſe- Annual Re 
B 4e is the Whole forhearance or amount | 
= Annuny; e 40 Simple e ĩð 
reſt, which Sum is gotten; by; — ig 7 „ 
the Sum of the firſt jet ta Terms, by EE 
the Number of Terms; the 770 pr 
is the Whole forbearance of the E510 
Annuity. . 4 
Then 1 — Segen: gg git ws 
gives the Theorem for finding the price or 
preſent worth. And, becauſe ==== p 
therefore 2ta-+ trga — tga= 2p + 2rgp, 
which is the general Theorem from 
Which all others may be rais d for ſolving 
all Queſtions of fl Narggery” 0] 


122 Fs 5 ty Tor. 


y —— — 
l . Ne 
WS © hs) * 
F of # e * 
1 - N : f 2 xl y 
. = 2 n * — "a 
l 9 - a 
. F 3 5 * 
6 N 


For if n S then zWrrttga—tga 
==2p-+-tgp, and therefore ttga—tga—izp 
Dip ita, and-conlequently g 4 
which r 

i Ann. the purchaſe Was made OT TOR, UNC 
—_ . od renten g the firſt Lee . 
mlranſpoſing the Terms you will find- that 
1 | = a= 15 Which * the Annuity or pen- 


. 
4 


. : 7 ; © . 


. 


_— Lach. To find the Time any prop 0 


—_ Annuity ought to continue to ſatief 
given Fund. Let the firſt Theorem, viz, 
=: _ 2ta+ttga—tga=2p--:zpgr:be again reaſ. 
_— ==b, and 24—ga—2pg=x; 
WL >. chen tr4==Fandt= TA which 
lad the Time in which any propoſed An- 
nuity will ; Pay off any Fund or Loan with. 
” In its reach, computing it at any Rate, and 


— IR RT EEIIIrY 
* 


; | 1 
: PA. | 42-4 4 * 3 EC my F. 
1 on Fe ER Oe 3 1. a 8 2 3 4 


| | k | 122 Interel. 1 IE 00 28 Fo 5g 


— 


e 
2 
* 


— oe A — — >: 
1 — 
— fone W 
- 
& 
* 
9 
* 
* 
* 
1 
* * 
8 
; 
#3 
. 
* 
+. 
0 
y 
4 3, : ©, , 
* 
A 
a>. 
— 
- 
! 
\ 
Pm | 
ot 
* +, 
py 
N 
a 


- 

* 

* 
1 
* 
* 
* 
1 

F 4 
i 

N 
8 
* 
te 

„ 


N 


2 0. . + 3 725 


* 
= 
: 


Pa Ca 


or Sum fotborn; Secoridly, the Rate — 4 f 1 
lent at; Thirdiy; the Time it lay; and W " 
Fourth ly, the Amount; tba it, che Cas 20 

2 and Intereſt both together. 


ways 2 of theſe four - patticulars given to 
find the fourth; which particulars, for che 


Nature, 1 mall denote i193 the following 
1 men . * IDE * . * e e 


%s out at Intereſt for 6 Tears at 6. fer | 


OO WO. wt De "TR, is A 2 


* * e : * 8 . 
* ö 
y IT; WE 2-9 
x), Wt. 
| 2 | ws Fj " 
/ 2 8 75 Ge 
„ 1 8 2 - | , 
4 n on 5 
| x 5 3 | 2 
> 5 al 
6 Comp pound 7 | WE 
2 — 1 0 | FY '*; 
| * £ L vw} ” We AR, 
of x +1 BY . Q 4 4 
#2 44 # A EW, e 1 ö 97 


CN 8 ET theſe 3 Thing 
are to be confidered, Fiplt, he Princip 


n 


And are when 4 Queſtion is pro- 72M 
poſed in Compound Intereſt; there is al- 


more ready expreſſing! the ſeveral Parts; | 
both given and ſought in Queſtions of this 


44 * 
aan Whar! 8 wb amount t of 323 bes put 


1 Ann. Compound: intereſt. T3 eahe. 6 
— 25 #464; * Fe 2 
p=325 Principal, or So 2 * 
t=6 im in Years, or parts of 4 Fear. BY 
r=r.06' Rate, or amount of 14. for one 
Tear. 1 
461 l. 01. 44.3 Aden 6K tad prin- 
"pa 5 the giver Tiine ae Rates: 


[ g 1 is 7 o „ * > 
— : * * I. £ Sh 4 * 1 
77 can; oy 2 CA 7 013.6 
: 1 Y # | 1 
f 7 $49 $ * 1 "wy P $7 
- , 7 1 1 * In. 2 Ky X 4 "7 3 A 1 ; ? . 
s 4 x % p 3 ; 


pls amo oven: 


| F mY '7 _” TION? TY p * * 
= | This being n * e As li rrrrzt 
1 © qezerr; rr: T rrr, Oc. which is, 48 1 l. 
= + *roits amount, ſo is that amount to the a- 
mount of 1]. at 2 Tears, two half Fears, 
—_—— or two Quarters end, en as the Pay- 
| * 2x4 ments Are made. ee I i. 
3 Then, as 12 x::p; 4 hes ae 
—_ | which 3 is, as 1 J. to its amount for any 
1 time; ſo is any given DOT to its wes 
* mount for the lame time. FT TOES 
=_ ae That t is the index 5 — power of 
1 r, and ſhows how oft r, is to be involv' d in 
14 it ſelf, being php to the number of. Pay- 
| 3 ments. 4 
= From the two foregoing. Proportions, 
10 By the general Theorem, ix. PI Da is rai- 
_ fed, and from it tis eaſie to conceive Wow” | 
3d by having any three of theſe. Members gi 
yen, the fourth may be found. 
BY For Firf pri=a- finds the amount ; Se- 
11 ao becauſe DA en * 52 54 ls finds 


Ep the principal. 5 
3 Again, becauſe . a chen = ;and 


5 conſequently r 1 =o GN finds: the Rate 


4 — — 
Vos” < * 9 
. !A ⁵.ꝗĩ—ũ———— — 
7.544445 
Ly * * = Y 2 


was lent at. 


Leah, To find 39's Tims, ale prt= 
aa ç chen 1 =. That is, di vide the Cones 
= by the Principal, the Quote is ſome pow · 

_ er a r, to find which Uivide he 10 Cote 


n 


„ 


% 
- ff 


3 +1 7th 399 © 25 
continually by r, till the-Quore"is\ f, dir 
| Number of ſuch Diviſions will be t. the 
time in Tears, Halves, or Quarters, accotd. 
I wg. as. the Payments Were. Bree $659 "Fe | | 


= A 
1 1 T4 j * 2 2 
ind. Hig * Cy & 4 * W * 7. 5 8 R * 5 oC 4 * x & * $i h 8 {4 N 
1 1 ; 5 * A * 44 2 
31 4 7 


+ 


; 8 4 2 

2 < — . 4 = þ ” - 
A * 0. ? * A 5 1 5 43" 2 * K 7 
1 1 r * 3 * 3: 4 TE 


MP 1» 7 K * * - 1 1 1 7 * * 4 £ 2 * %» * - 
2 by : þ F * I . 4 Y 
W - * 


; *\þ A "A as 2641's 8 

3 >. TW 2. 6:00 9 
1 7 

4 * * 


# ” * a . # 28 0 N 75 
2 0 * e W . 
1 chak F331 
ry 


99 Tg ann Revorjon, . 
; © cording: ts G 7 ph,“ Inte- 


, | 12 


4 = 1 
* 7 | e * 722 £ EY; 
$ ö 5 . * 1 * 
E, 4 i 1 "a. 
a | N 8 : 
7 3 8 "frog 1 "" 41-5 A. * + 71 Yi IS 8 3: 77 5 bs 4 


4 — ap this manner; depends penn 
" what preſent Money-ſhould bead 1 
tor any Sum of Mon: be: 12 or more " 
Tears hence. ee 4 
"et 8515 xls Sat tant MY 
For Inſtance, ſapeſt an 2 to con- 
tinue 2 Tears, tis evident, did it continue 
but 1 Tear the preſent worth of it would be 
fo much, as if put out for a Fear, would 
amount to one Year's Rent, and that the 
preſent worth of the Rent received at the 
end of the ſecond Vear is ſo much Money, Ab 
Which if put out will in two Tears time 
6 reckoning Compound: Intereſt): amount:to' 
"ONS ** s Rent, the Sum of theſe two 4 


= N * - > 
F * F 4 * v N F oy 8 * * * n 
% 1 38 * 0 - , ' 5 0 N N 
, F N = 0 e i x Jars . N #7 * 1 * NW 5 1 
5 RF, Ik et ' , 2 + x. 1 2 | 
> | Net OG 4 ny N ES 1 2 ; : R 
* 7 1 7 « ? : * 9 1 7 - * 
* » * A ** 1 1 7 4 5 N 
. 4 . a _ 8 N - v * / % * 7 4 x of * oy 
i * - : * o -$p. 7 _ - >» de 
> we 1 4 * „ , on f * 
* 3 92 r * „ 8 17 ee — * k 
He "0 N 8 , . EW. . . 
— . As . . * - I - * 1 4 * » 
— 4 - by 5 * . * 8 ., * * * 0 1 
* 1 * * 
, * : We . * K 
* 22 I 7 . % 
7 0 * 1 
= 
* 1 * * 1 2 
n 1 


39 


pound Intere 
1 worth but 


. * 
N 
* A . x 
x * 5 " 3 — 
5 * ” Fe * 
* 
7 F — 
1 


TY 10 474 5 4 | 
25 worths i the real and true Value of the 
Amnuity ; bar in tis the price or preſent 
worth of it. Therefore tlie preſent worrh 


of the ſecond Years Penſion, is only the 


preſent worth of the firſt Years Penſions ; 
for 1067. to two Years hence, is of 
the ſame value with 100 J. to de paid one 
Tear hence 8 ehating according to Com- 
) and 100 J. ne Fear hence 
: t 06 5. near. And 106 J. 
one Year henee is worth but 100 7. pre- 
ſent; ſo chat an Annuity of 106 J. to con- 
tinue 2 Tears, is n in * —83—4 
. W 7 
Hence the Solu tion of Queſtions of this 
Nature; upon the finding of a 


depends 
Tank of Numbers in a decreafing-- Geometrick 


n, whole firſt and 
the 1 or Fenſon. 


This bein g promiſed, rhe part 3 are ane | 
W 955 7 ps 4 ni abs Inno 


eareſt Term s 
14 FT. Nite VIV. . 


7 
A 514 


WW a 4 7 s . 1 28 45 8 27571 7 NN 


10 Beese What's the prefers! worth of an 

. of 350 l. *$2yable Yearly; to con- 

. Yearsat 6). gn er Ann. com- | 
1 Ms 5 85 = | 


i e 


sse — Goal Yea y r. Pen- 


408; andthe 


kerl or E Ferm. 


77 He . f "36 e 


! - F 
2 8 4 t=7 


t= The time by. 1 Years, 


or parts of a Fear, and is the Number of all | 


220 | 


the Terms. een eee 
l '66 Tho be of Þ for one Your, 


(hate Lear, t.) and 1 18 the common Ratio 


of all che Terms: - I 1 


29531. Sie 84. the Sum of all the 
e r or e worth of 


Terms, and i 


This; Sec 3 e p 22 "AY 
Fr = the aftof which will be = — . 
* Hence arifes this continued Geometrick 


Progreſſion,” is." p : f. . e 
An the Sum of which Terms, encept p 


the e l is the preſent worth of the Annui- 


To ſind which twill hold, as one An- 


- Satan to its Conſequent, ſo is the Sum 
of all the Anecedents, to the gum of all the 


Conſequents; that i, a8 p: % roms f 2 
; therefore 2p— =2.— then Mulciplying 
all by a twill be zpa —pp pF and 


E. —— both ſides of the mas 
7 1 Zapf Hich 
double Tranſpofirion — At 2 


*this divided by a. —1 gives 2 7%. or 18. 
1 i „ SEE 5 128 An - 
Heng. & to one entire Eraction, ir makes 


t Z. Which is the general Theorem 


a of wn en ee ee 


olyipgall Queſtions of this. Nature, and 
10 0 price Dx, e worth the An- 


. 
ark 1 ney peg 


— —— — 


„ ———————ů—— — ͤ— dJ 
. = 


„ * © 
3 


mainder divide the. forenoted Ake, 1 


| orem, vix. r 


„ 


2 Y 25 Sr *  9rcei3 5G b of! — 
12 * words hus, Multiply, cht amount of ane 
Pound for the time propoſed by the Penſion, and 


from the Product ate the Penſion; and note-the 
Remainder... Then Multiply the-amount of ws 


for the time hy the rate, — from, the Py 
tale the ee 8 vl. for the time, by 5 Re- 


| ene Wi 
Secondly, R Reaſlurin 8 bows Sara, The- 


and Dr che penn as; 3 Þ — £ e 


which. finds the Ain An en 


1<2n:wordsthis.:127/ mu : 
Mulriply the amount of 1 l. for the time pro- 
poſed, by the Rate 1, and tbit laſt. produs 
the purchaſe: Money j this renn Nds 4. 
2 155 * eee of 1 I. fer zi time be 
- The Quote i: the: WEED Qs 


; os 51 3 — — gg 8101 . 


8 To fd: he time ne 05 Condinta. 


ance, let the foregoing Theprem; viz. PLP z 
be again reaſſumed, then pat —'p==zaat-— 
| 2a: then pat - Mata pcand: . 
. and conſequently T | 


which finds the time of Continuance. 
In words khus, To' the Penn ad 18 

Ne: worth and from that Sum take” the 

Product of the preſent worth by the- arge 

1 J. for a Nar, ane divide the Penſon by thi 

. the — is * fo * amount 


of 


dual to t the tine. 


_ 3. , 4 | . 1 | 
RE - Fourthly, For the Theorem where à the 
TX Rate of Intereſt is requir'd, it amounts to 


- ow LY ES 
Io + 


7 ES l OE = 8 
e 3 % ; Ps 4 . aA . 4 es,” 
* 3 DAS, : x o . F 8 \ I G g 
Ws \ * — ** 
4 * 2 
Py EE >, 

* 

7 n 
1 ( 2 d] ' 
Y * ? 7 ; 


* 


I of x 1, for. the time propoſed.” , Then divide-this _ 
Able continually Jo often, by 4, il et Jeff the 


Quote be Sa, | the Number of thoſe more 1 is 


= f | 
4. 1 2 „ 
4 * 


a Compound Equation of thee: Terms, 


Vhereof the firſt contains a power of the 
unknown un whole Index is equal 
to the Num 

The ſecond a Power of the unknown Quan- 
tity, whoſe Index is equal to the Number 
of Years; the third an abſolute known 


r. of Years increaſed by 1. 


Quantity. Now though the common Me- 


thods of ſolving Equations by Approximari- - 


ons might ſolve this, yet conſidering how. 


| Laborious the work would be, I forbear 
giving any particular inſtance of it, which 
I do the rather, becauſe I am inform d, that 


Dr. Hally, Afronomy Profeſſor at Oxford, and 


Mr. D. Moivre, Fellows of the Royal Society, 
have ſeperately conſidered this Caſe, and 


are ready to publiſh what they have done 
in this Matter. Now the value I have for 
Pele is ſuch, that I-ſhould think it a Pre- 
umption to meddle with that they have 
undertaken, and of which the Publick will 
receive the benefit. in a ſhort time. 


- 


The reaſon why Annuities in Fee-ſimple 
are worth 20 Years Purchaſe,” laying out 


"314; 
From 


your Money at 5 J. per Cent. per Ann. 


* way ) | 
en bt befote Ras been faid A Evi 
dent, that when a Fee-ſi mple; that is, an 
Annuity to be purchaſed 'for ever, the 
Terms of the Progreſſion are in finite, be- 
cauſe t which denotes their Number is in- 
finite; and in an infinite Progreſſion, the 
tft orlealt Term is nothing. 'From which 
Suppoſition i it will follow, that the Sum of 
an infinite Progreſſion will be 2 finire 
Wand 
For rppoſe 4vt. Annuity to continue 
for ever be to be ſold, what f is it worth in 
ready Money. aft 


In this "Example; 1 ſhall denote the par- 
e a followeth; . 


= 1 the firſt or Sg Term. 
e the laſt and leaſt Term. * 
x the Sum of all the Term. 


3 1 1 the Ratio not Terms. 


This premis d, it is north chat as cone 
es er is to its Conſequent, (or the 


Ratio to Unity) as the Sum of all the An- 
tecedents, to the Sum of all "We Conſe- 
{toe SES 

But, diene the ane is Infinite 
the laſt, or kaſt term, M's POE: 
eee 8 1 


3 


e 


5 $4 4 22 2 18 — 3 | - | | 
4 a ** | 4 a 7 9 * ; 
% x _ * 3 e Ys PIR 
1 1 1 3 5 85 * 9 ” ; Fob 7 5 3 
\ 5 . 8 : 5 W a r 
5 then % = 24 — = | | _ "= 
g ; ERR 
n . 1 
> chat is 2a ee FS = 
, 3 
e 2 | I: | 25 E 
— 4 1 34 * * t 4 z * J a. : * — 
ty rbat i is — 80 r 
8 ' : 


+ M# FF 
* = 
mY * 


e 
| 
= But 850 11 is equal to 20 titties dns ant 
233 Rent of che Annuity, lay ing out your 2 bo 
2 ney at 51 per Cent. 8's: _ 
From this Theorem kale Con- „ 
Y Legen will. follow. 88 1 
Firſt, That in giving 20 Years Purchaſe - Z 
for any Annuity for eyer, you have 1 burs 38 
teen for your Money. = 
Secondly, . If you give abave. 400 Yours 
£ 2 you have not 5 5 05 lor your 
Money. 
Tb, I you would lay. out your Mo- 
Hey e 6 ger Cent. for it, you ar? give 
har I Trans af abqut £5 Months. Par= 


rom \ this aforeſaid Theotem you | 
ap Loth, Fi une a Table, that will how 
ou the preſent. worth of any Fee: ſimple 

te. Provided-you would 2 out e 
dure at Fg Rare of 3 


ks hos #5 
* — oo 8 7 f „ 
4 Þ 25 | - f », £ 


4 „ Os B 4 N . 1 1 5 g 7 5 2 
* "ad! 4 £ : * * F wa 
- . 
- On Fa 
has * * 4 4 
© BAR | x - 
- % « * : 
3-4 * . a 
” * 
2 * : = 


11 — 
n 


k N 2 
14 * * 
= . 
k G : 244 2 
+ 5 "* 
\, ey 
— 
q * 
9 1 
=. 
CS | 4 
? . 
= —- 
. 4 1 
3 * 
je 
— 
i 
2 
ö 1 ; 
* d 
—1 8 
_— \ 
© J * 
4 * 
2 k 
N ; 
«of. 
d 
t {A 
8 4 
$5 4 * 
1 
q o 
19 
F 
" * 5 
_ 
- 
11 
. 
A 
wi 
* 
7 * 
*- 
+ 
14 
1 
$ 
. 
4 
E * 
1:Y 
N 4 
1 1 
7 A 
17 A 2 
_ . 
n ; 
, 
4 3 
F 7 
= 
1 N 
x 
. 
38 
4 
» 
. 
1 
y 1 
17 
* 
x 
„ 
N 
197 F 
: , 
1 LY. 
11 
749 . 
1 ö 
14 F 
r 
0 4 
* 
F 1 
4 38 . 
r 
48 
- SY 
134] ; 
1 
$308 
* Is = 
. 
1 5 
95 
41 . 
. 1 44 
47 8 
[4 - * 
7 2% 
LN 
14 
13 
5 # = 
F \ 
4 4 1M l 
q . Lf 
„ 
15 4 
by > 
== 
- +» 
34 
it 
* 
9 


Is 
” 
hs 
1 
. 
a 
2 


EY 
_— * 


The Demon ak on. Dif Elin. 
1 . Tine © 


"H E Deorftraticn ers Sin 11 Kale 
I. i elf Evident, For as — whole 

See to the whole gain or loſs, fo is any 
Part of the Stock, ſuppoſe 3. 3. E to _ 
like part of the gain or loſs... 

Admit by Trading with: ARS p Stock: 
we. gain 100 l. then tis Evident, he chat 
put in 5087. which is Half the Stock, muſt 

ave 507. which is halt the gain. And he 
pen put in 2504, which is one Quarter of 
the Stock, muſt have 127; 103. Which is 
of the gain, and ſo whatever ſhare of 25 | 
Stock you put in, ſuch like part of t 
_ gain muſt, be received, And this part of 
gain or loſs is obtain d by working the 
Queſtion according to the Rule of Thitee 
G1 "wh kl Wb , Om” 


1 


4 4-3 
&.-% 


E a 
* 1 
2 F 
5 
— SA 


2 


o » . 
. . $5 35 5 E e 
1 . * * * * 4 * N . F " 7 
5 ; 
, 1 5 #7 . 
— * * . l go * : wo N 7 OR 
— 1 4 l * * L a 
k * — 


he e of 


* „ 


N | N 4 . 
8 * N . 4 þ | 8 ; Y * FM NV. 
+ 7 1 8 a * 1 


8 N chis Rue we are to prove, thi at 5 


4 " 


„ 


tion as the Sum of Intereſt Money, i, 
might have been gain'd at any Rate 


Cent. Simple Intereſt, by each of tir FT 


Stacks 1 in their reſpective S e 


Take this Example 4: and j trade toge - 


ther, A put in 100 J. for 4 Months, B put 
in 594, for 16 Months, they 


particular gain or Joſs is in ſuch Propor- 


= 
# 
5 


jo” 


what muſt each Man have of Te Yair) 1 
1 G77 N EOS 4 x T We top 


bern 1 * 5 tf 
300 


22920 (+: 57 7 


* 
T 
£30571 
* 
* 2 - 
Re - 5 8 


WO, 4 
. 
* 
5 
A 
* 
2 9 4 
Y 
as 
$ E 
* 
» 
5% 
>; 
= 
r 
— 
0 
L % 
%. 
. 
9 
N 
* 4 
: «6 wy 
. _ 
Lad _- 
* = 1 
* # 
. 
N 
F F 
Cel I 1 
; EY 
1 * * 
\ 4 
* 
. "Id 
'Y 
2 > 
- 
2 
3 . # N 
* - 
* 
I J 
— 4 
VS 7 
* F! 
"* 
- 
*15 
Li 
* 
- 


1 188 . 1 
3 we F SA, by * 5 G. - >. » ** © 4. * 1 


o 1 8 
% 2 Wert 
In : w To 
PA 5 YL, 
© 20S ) 7 
ty — . A * 1 
3 * 1 4 8 2 ne 

3 4 4 4. k 

. 1 


ts 4 * . © 
— Ly 
Fx. % ws, 1 » 1 * 0 — 
. 61 8 72 4 * e Ot 3 Wes Me "_ 

n 2 n 1 

* e ie 08020 pate. 
ta that o . — 
e . 3 1 122 +8 


h 4 . "2.4 2 * 
— wy. o i = * 
EN C | \ 6; 4 k 
* 4 ty, \ : 87 1. — * 8 : RY Yu 
: \ 2 ** | * 0 8 1 


oe 
* 


1 | This row ſed, 1 am now 10 prove that 
doe LS ck, Multiplicd iro his Time, is td! 
—_ he others Stock Multi * HY into his time," 


kk 


N 3 1 i 3 
ther. . 
®; & 5 * Ts. - | 2 "mY 7 


4% 14 


bee 496: 40 d 818 
fore 460: Boo: 10 26 
„ 2 tis Evident, that if I prove, 
iat their re ſpective _Ifrereſts arc to each 
ö other, as the 2 5 one Stock. and 
Time, to the Product of the other Stock 
and Time; I prove What's required. Be- 
| cauſe each Stock Multiplied Ei met is 
4s their true Shares. 
In order to this, ſuppoſe the Intereſt 7 
_ . for 4 Months tg be 3 7. then the Inte- 
* \ reſt of 530 l. för the fame time is 123* Now 
—_— #0 get the Intereſt of 30 J. for 16 Months, 
= y, If 4 Months give what will” 1 
13 Wende give ? abe, Wee. 


—————— — 
. > = — * 7 
KK r 
8 _ * = Ss * 
q * * 7. 


——*—*ꝛ 


— ů 


_ „ 
VO —— U — 7 ˙ 


WE 


— 


—— ON ms 
—_— 


_ a 
8 4 
ed ere — r are 4 ogy + ooo Hr Aon vs L 
= EP 8 * T = 
- 
£4 * 8 
2 n F 
* * * 
. % 2 


1 hare of one, to PE un, wW 


9 of + 7 45 12 « . 2 * : = l y + 7 1 4 I 0 8 4 Fl * SY " T1 N I; © © 
2 4 2 3 * 5 4 5 23 4 3 "IK. #s Py * 25 Go. a z * » 8 4 4 ? Jy * * 
5 
MN * ; 4 1 F * * 


e 


oY 4 ) : 9 
Hence A Intereſt; is to Es Intereſt} 989 
3 to , and therefore, if L — > oa_g 
X 45 0 K* 16 as 3 to r the 
ching is done; becauſe their Shares are in 
ſuch proportion as their Stocks  Multipli 
by their reſpective times. * 
To do this, Multiply: both Terms by 
100 X 4, then will their Products, viz. 
1099.X4 X3. be. in the ſame Proportion as 
* e 5 hut 3 is. A;comman 
Multiplior, therefore expunge it in both 
Terms, and the remaining Quantities. willy = 
be in the ſame Proportion, that is the 
| ſhare of A, is to the Share of B, as N 


— wy eee Wake ems rnb ty 


„ 


1HE 88 557 a 8 | 
dial, is but little more than the De- 
Re of the Rule of Three DixeR.- 
For e e Þ 9 Galen 
ak: 3. per mixed .W n 
of . at 95. Gallon,” hats the 5 : 
. Price of a Gallon of this Mixtur | 
. [Tis, Evident firſt, that the 50. 3 
N Will a e re 130 Shillings, and the 
ry. to 270 Shillings; 
n the Whole 80 e Gallons will "OE yy 
to 420 cy ak <q „ 


1 £4 


UE: S 4 Then 


AC (264) 35 
Then, if 80 Ballons coſt 420 Shilliogs, 
hin ſhall one Gallon coſt ?' Therefore 48 
the "on of one: mewn on 8 Mixture. I 


A 


The bee, of 5 la 1 


His Rule of bg, Ker is of 
vaſt Extent, and will ſolve variety of 
tions: but yet, as tis delivered by moſt 
Writers of Arithmetick, tis very A 
for the following Reaſons. | , 


* Firſt; It gives various Solutions to feve- 5 

ral Queſtions. * as 1 Mw. 
Secondy, I 2 Apen Sotuont © 
that is, ſuch a as do not anſwer the preſent 

_ Occaſion.” | Sol dba 8 j 1 : Is 5 1 ; 


Thirdly; 10 ere Catesit it will give EY 
than one Solution to 4 Queſtion; and yet 
mot all 9 l nor nenn 

En id 10 Ag an 630-2313 % 

„And dere I ſhall not inſiſt upon, a 
Arik Demiobſtration of rhis Rule, in all its 
Applications, Limitations and Anſwers, but 
only in Relation to the common Queſtions 
r * enen 


8 * 


Example, ſuppoſe would mingle Wheat at 
12 5. the Buſhel, with Rye of 3-5. the Buſſel. 
ſo chat Light ſella Buſhel 0 the Meſt- 


pe mixture, as if each Quantity was fold | 
at its un price, the Queſtion is, how ma- 


this nn w ee eee en 


1 "a 1 ; 1 * 4 > Fg - 
4 +3646 Y - TH FA.” "LS% in PAN 180 4 


_ : v8 55 1 2. (Dirt 15 (2220! I: "7% 514 1 * 8 | 
rh e da ny 3Hqq ads u vo gin 


| comes to 24 at 1A , the Buſhel, and 2 | 


mean Price comes to 45.5. as before. d 


qual to the Sum of. thoſe; e Mut: 


„* 


| i 9 5 


This being Won wks the following = 


4 


ling for . and make as much Money of 


ny Buſhels ot each ſorti of Corn 2 be in 


12 


* 


1227 
21480 
— 


D A . IN = A W 7 442117 


— "Aaf eds; 2 Buſhels of- Wheat, — 2 


Buſhels of Nye, ihich eomes to 2 4 at 3 


the Buſhel; the Sum of which is 46 . Now., 


the Suni Off the Buſhels cof Mheet and Rye. 
make 9 Buffels, Which a6 3 a Buſhel, te 


Whence you ſee, that the Propoſition 


Aerion Alternate requires tc he Demon- 
ſtrated, is this) clue ot backs ee 


70 There are 3 Numbers, * the grearclt; 


the mean, R the leaſt; if the difference 


betwixt the ne and greaten be multipli-. 


ed by the laſſer, and the UG wes betwixt 


the mean and leſſer be Multiplied by the 
greater, the: Sum of 'rhefe. Products ſhall: 


eee Hee ed. 


JI | | ME: "Mean — 

OY 2 , q N 2 3 

5 | 3 - 
- 5 " 

a | 


* 


5 AR 10 te Buſhelb of When, | 


ich if Multiplied by V the price ol a 


Buſhel of Wheat, will give 1 A R the 
rice of thoſe Buſhels of Wheat; ſo alſo 
—M is the Buſhels of Rye, which if Mul- 

riphied by R the price of of Buſhel of Rye 


Will give W RM R the price ot - thoſe | 


be ſam, of choſe: Pro- 
dvds, wiz.” "HE Men RAW R MR or 


-M R (for R is deſtroy d) wilt be 


equal to the Sum of the Differences, vix. 
MR + W—Mzyor WR Multiply'd by 
A, which waer e N the ſame Ws: 
before. © To HRERS, han TUNES 95:r 8 2 
0 * 2011 1 N 5 

erhe reaſon Why the Bine are Al | 
* rernately plac'd is, becauſe they are to be 
Mul ply'd by the contrary: Number; hae 
3s, the differente betwixt A and & i is to be 
Multiply diby: and the difference you 
i W and M' 5 be r R. 

7 * het Dl. deen 
Therefore -R is the Number of Buſh- 
els of Wheat, And 8 reed of 


| the Meſtling. . 


8 The Book 8 more 2 3 


3 
* 


C 467 iy, | 

uf there be ſeveral Things of n 
prices given to be mixt as aforeſaid, the 
Demonſtration will be more perplex, but. 
not different from the former; - I hall 
therefore omit proceeding further in this, 
not only for the. perplexity of it, but be- 
cauſe both the Solution and Demonſtration 
of Queſtions of this Nature are eaſiet done, 


and clearer ſeen, Son's an Algebraick 0 
VVV 


"8 


Suey 


12 


4 _ + 


I. ſhall omit the Demonſtration of the Rule. 
of Falſe, otherwiſe I muſt leave out ſome 
hat will be more uſeſul and ee in 
1 = Reads without: 0 we ac 
2 in Algebra, the Pæmonſtr ian fen 
be ſomething MC to LN o „ $665 


Win cet org r ict 22 of b 


"Y 7 3 3 25 
ot oor ie Es 25k 


ee een ed oh org”; 
1 7 2 8 - 
c — Pre RN 
her gailloiqed * Born 51 


£ 


2 
25 #2 2 


* 


hed Fg * : 54% 1 . WH "de" % F 
| 1 : * * * 1 * F : * | 2 4 * * * . 
ako 645, hag wb + fed et 1 wt 136 99 7 
LARS SIR 1 2 NS. CL 1 1 > * 4 ; 
FR : - ** 2 


Hh 


* 


by 
754 
2 


"> | tay 


my 


* 
3 | 
* 
A 
* 
Af 
FN 
WM 
_ 
. 
' a 8 
1 — 
A 
— 2 
= 
Co 
_— 
1 
Is 
- + . 
Fe 8 ; 


my 1 * Y 
2 * 
ELLE — 27 N 
1 * 


* © 


s VERB ge n Went e et 15 5 2 7 HF 
_—_ 


PEAS e ano 


4 


+ a 


I 
A 
* 
or 
 - 
$4 
7 : wer" 
- 
=” 


6268) 


1 20 RH! F. 


bl | 


„ RENT x 
— Ly b 

if In 4 4 1 A «SH n 4 SF. * 
= 

* 

+ 


er W 0 lake *. 


. Ffallion. ze e e 


SG 


2 — 


: #"% oF) * Id 1 2 Ls &. A 
ene adore 


# * + 


N ordes 10 the more clear Wpieben 
ding the Pemorſtration hereoſ, I muſt 
make a ſhort e of what has been 
: already laid. 2 | 
2 ee 1122 ot 7a u oo H 
6%. That. Fract 05 sa pat ot — 
of iſfome'Diviſible! leger, and 8 fepreſen- 
ted by two Numbers, the One above, the 
other beneath 4 1180 U thus z. a DOS 
he Numbertplaced below the Eine * 
called the Denominarer,” And Thows What 
parts the Unit is broke into. © 

The Number above the Line is called the 
Numerator, and ſhows how many of we 
parts are to be taken in the Fraction; as 
the Fraction 3; denotes dees ſuch parts, 2s 
the Integer contains 5. 
From this Method of N Fracti- 
om, theſe nee * 


1 * ka 
1 *t$« . 


Firſt, Every Ftastlon, is to its * an 


e : 5 3 


Second, 
** $3". 4 
4 - 

; | 2 *% 10 
2 * 
* — — 5 5 N 
Þ * ES De 
1 3 


Mute, as the Numerator 18 to o the Denomi- | 


3 


4 


Sp r e 


c 


#$ © as 


equal then the, 
r 


5 reatery 
Second That if (5 earery 5 


the Numerator be 


1 Denominator. The Fraction i 18 3 
greater, equal ox -lefs, than its whole an 
Unite. The firſt and ſecond of theſe kinds 


are called improper” es: &; lat are 


2nd 


” Thirdly That Frattions 2 are fot to 9 55 3 
— by the greatneſs of their Num- 
bers by which they are expreſs d, but by 


1 che Fropor tion the N umerator FIGS ro 92 0 | 
Denpminaroras: 1 


. That F e whoſe 2 None” 


N rators to the Denominators > che fame” 
5 Proportion, are n as 35 2 25 EL YVES” 


* 
. 
ON 


Fifthh, That every FraStionis the Qu G. | 


of the Numerator, divided by the Deno- 


Ns this Sante 1 ſhall ra wha 
Keul the Fir. 


+. © 8917 


This 1 is fo Clear 4 5 ann 1 than. 


ner of Expreſſin g a Fraction, as alſo from 


the firſt ue that it Wen, no . | 


ther Demonſiration./: Tarn 


: +4 * 


* 
! 2 * * 4 þ : 8. 
+3 aa + $4£ 3 
U 5 Z N 5 I 5 
. * a 7 * & > © F . 1 
: 12 2 N * . op Wn CITY 7 is 
” ; 
_—_— U 
. 


1 
65 > TE * * fx 4 0 4 
b y 2 L | * 
| 5 * 
; 3 
. : „ - 


1 2 of Multiplication, and — 1 re- 


viding both Numerator and Denominator 
hen a Remainder. + 


bh $ "7 
5 = 
- 82 N — 
8 n 
r 
r ( „ 
— 
- 


- 185 ſuppoſe 3 to be reduced to its loweſt 


| -Denominarions, to one Denomination ha- 


common Denominator, and each Nume- 
own, for a Numerator. 


5 duced. 


(470 * 


- ies the * * | 
The Proof of he is a conſequent fins 


fer it to that place.” 


 Reduftion os Third. | 
Teaches to abbreviate a Fraftion, by a 


This is Evident from the id Pro opoſition, 


Terms, here dividing 9 by 3, and 12 by 
Hef ariſes 3 and 4, which 3 has to 4 

ſame Proportion that 9 has to 1 Ay 
_ therefore by the fourth Conlequent = =; 
vbieb was to be Demonſtrated. | 


 Redubtion the Fourth; | 
Tesche to reduce Frations. < diets 
ving the ſame Value; for me of which, 
the o 
Multiply all the Wenn en bot 2 
rator into all the Denominators, rr its 


Suppoſe + * 5 were * to be Res 


r ; 


* 


* 1 c 


ee N 2 PIO. ib 3 * 
cording to he Rule they will ſtand thus, 


3 mor. Ss that i is, _- 28. 2 which — * 
: ions a are by the 3d Propoſition, and 4th 
Conſequent, equal to thoſe given.” 


| Reduction the Fifth 1 IO 


This is proved in reducing A R 
Fraction to a wn 


_— 


Han ons „ Demiſe 2 


"HE Prafions, wha cem 0 Dilſe- 
rence is required, muſt be reduced to 


And then according to the Rule, che 


{Diterence dof. the Numer ators placed 
| over the common Denom 


IDiference g e 30 the kractions requir . 


(inks; What's the wan and Difference | 
, The" 


of {and 10 


Ws 


actions © of the ſame Denomination.” 


ator, * the 


* 9 


3 ns DN. <: 272 HS. Wu OT 
The Fractions reduced to the ſame Deno- 
| mination, are g and '33 conſequently *';;* 


= Sum He 
| e. of the Fractions; FA 
F BY, 1 oh Difference 
3 is, the Sans 18 3 the CER 255 which 
bY 1 Was require . e 4 „„ 
. 4 Eg. * — a —— — — — 1 — 


. 2 = Pf 5 ＋ 8 
= " Denmſtrared. 


. 10 R fnding the Product of any rwo 
2 Fractions, this is the Rule. 


| Shaw. the Numerators together, for a 
new Numerator, and the Denominators 
f together for a new Denominator; the Fra- 

| 0 thus: produced i is the Prada. 


- aſs 8 given to be Mol: | 
= by, the Product is 2}= &=3.'.... 
The reaſon of this is evident, for by he 
5th Conſequent, I conſider theſe Fractions 
as the Quotes of their Nùmerators, divided 
by their Denominators, and ſo if I Multi- 
piy 7 by 2, it gives , for to double any 
Quote is to double the Dividend; but 
now, ſince I have Multiplied by 2, When | 
fuld have ITE” by of 2, there: 
E rote 


K — . - K 
* * 7 
* | 


: : # T G 
i ? 1 F i 3 
e b 3 "A 
N : oj * 
vol. 4 } 
— N . 
* * k . 
s * by 
( 73 ) — 


fore 3 of this Produ i is the truth, which 1 


effeck by cripling the Diviſor 4, therefore 


22 (i) is the product of ; by 2. 


"Hence the Product of two Fractions is 


evidently leſs than either of them. 


And hence, alſo, the reducing of Com N 
pound Fractions to Simple ones is very 
clear. For to take the ;; of ; is no more 


than to Multiply thoſe-t two Fractions to- 
gether. 


Diviſ on 6. 1 De. 
nonſtratel. 3 


F OR working of Diviſion the Rule . 
Multiply the Denominator of the 
Diviſor, into the Numerator of the Divi- 


dend for a new Numerator; and the Nu- 


merator of the Diviſor, into the Denomi- 


nator of the Dividend for a new Denomi- 


nator, the Fraction thus formed: Is the 


Quote. | | 8 


ee 30 be divided y! 


9G lan. > 


Tm | Here. 


1 ES 
p Ho " 
A 


— 


= _ = 
CS eo aa. . — Lennded — 
— — . — — — 


„„ 
9 8 
* — 4 
ET 12 
SITE 


EC] ͤ II 
. 22 — 


— Re 


EY . 
44 
47 
_ = 
ry 4 
1 
vB | 
4 2 
3 , 4 
't 1 
11 # 
1 
TJ 
{TY 
3 
5 3 
1 
[ is | 
is 4 
\ 
- 1 
4 8 
4 
7 1 
1 3 
£ W- + - 
. * * 
i 2 
+ 
* 
7 : * 
Ll 
| 
Ig 
"= 
v2 
1 
R 
= 7 4 
n 
- z f 
14 
„ 
4 \ 
7 
4 
[$4 
il = 
{ * 
4 | D 
- Wo” 
=. 3 
1 
1 
4 
4 - 
4 
1 
N 
5 
U 
. 
33) 
4 
| 
7 
1 ; 
15 
% 
x - Fl 
1 > 
$2 a 2 8 
i . 
«| { 5 
; I 
x S 
1 8 
_- 
+: VN i 
Y 
* 
, * 
1 


ö ; 


BY puting Cyphers before che ſignifica 


pF. FEI j JT . 


; . br 9 J 
_ oa " Ix . . 
6 * * 
2 ) . 4 
. 1 * 7 


Here, as before, I take the Fractions as 
Quotients; ſo that if the Example had 
been, how many ; is in 32 The Anſwer 
would be ſo that is only Quadrupling 
the Numerator, there being 4 times as 
many Quarters as there are Units; but 
ſince my Diviſor is 3, tis evident the for- 
mer Quote is 3 times too much, wherefore 
I rake 3; of it by tripling the Diviſor, and 
then it ſtands as above. . 


1 — 


1 
* 1 5 


Decimal - Fractions Demon- 


„„ ſtrated. 2 
Ecimal Fractions, (as I have before 
noted) are only Fractions, whoſe De- 
nominators are an Unit with Cyphers, as 
185 1855 1888, 788885 Oc. are Decimals, and are 
conveniently writ without their Denomi- 
nators, with a point before them thus .7 
135 284.0036, Cc. | 


So where the places of the Numerator, 
are not equal to the Cyphers in the Deno- 
minator; ſuch defect muſt be ſupply'd by 

nt Fi- 
. gures 


Decimals, is the place of Tenths; 


ff 
* 4 * Pg 4 
by =o „„ os 


. 
gures of ſuch Naumerator, as 888, 18855 
s are thus written o 400003 | 


.000437- 


= #*. { k 
a. * 


From this. and the manner of Notation 


of Decimals, it will plainly appear that 


22 is equal 0 18 70 ns. For gg = r= 


— — 234 the Sum by Conſe 


Narr the third. 


80 chat the firſt place, Ander the point in 
the fe- 
cond. of Hundreds; rhe third of Thou- 
ſands, Oc. decreaſing i in a ſubdecuple Pro- 


portion, from Unity towards the Right- 
hand, as the whole Numbers Increaſe from 


Unity towards the Left in a decuple Pro- 
Portion. 


The Reoſo of 8 a” Vulgar nau, to. a 


Decimal, 


9 as the Denominator of the given 


Fraction, to its Numer ator; fo is 10. 100. 
1000, &. that is, an Unite with as many 


Cyphers as I intend my Decimal ſhall have 
places, to the ane os At en 
Ae to it. | 


+ 


— — 
— — 


a 


. 

That — — — — 

» 83 — 7 
2 = 


- - 
— RT OO — = — wy _— n — — — — > 
. — — Pp 5 = — ry 2 "yy ne in3.4% ON * [2 1 " 
— r — . Vo as * - — — ä n 7 — — 
== ** . 4 W — * 1 0 
— — m * 4 2 ,” S n r ae warts 5 => & „ da cn be — | Oo — * 
9 * * W 9 * OY Ee C F I ap 1/1 p * 7 r * 
; as e - f D 
vw, * 
* = 
4 


4 
* — 
7 2 
- 
of > $ - 


1 b 


ſuch Fraftions as had 10, 100, &c. for 
their Denominators. 


the Deeimals, place Units under Units, 


02760 


Exam. of :into a Decimal of t two 
places. 


EY} 3:4 200 -.” 
3 


4)zoo(75 


So that g or 75 is equal to the propo- _ 
{ed Fraction, by the third Conſequent. 

The 5th Redustion is here alſo prov'd, 
this along the ſame with that, Only then, 
we knew not the Name of Decimals for 


* 39 


n * 8 8 | 
Decimalt Demonſtrated. 


\ 


Lace Tenths under Tenths, e 
under Hundredths, Thouſandths un- 
er Thouſandths, & c. 


"If there be whole Numbers join'd: with 


Tens under Tens, &c. and in the Deci- 
mal part place Tenths under Tenths , 
+ Himaredths under Hubaredtbs, &c. . 

4 


”. — * 3 * On a ; 
5 a 8 ; 


+ 277 * 
add or ſubſtraft: as if they were whole Num- 


bers. 
. Example i in p "1:5: mag 
6o $545 4 x06 WO 
298. 23 that 1 298. 230 
43.171 43.171 
—— 347.801 
| Example ; in Swhfrertnn.; 1 
From 5. 45 | "Ra 5. 46. 
Take 2.9 that ts Take 2. 90 | 


bs - 56 Rem: . 2.56 Re 


— DI In 


Demonſtrated. 115 


Ultiply tbe and Declinate? toge- 
ther, as if all were Integers, and 
then cut off as many Places from the Pro- 
duct towards your Right-hand, as is the 
Number of Decimal places in both Mul. 
riplicand and Multiplior. | 5 


* . | Exams, 


— 


* 1 


* 


Multiplication of Dicimals g 


* 


079 


Exam. Mutiply 23-4.. .0023 a 
' N 6 | 09 


= | | 141944 Prod. 1 tt 
_ „ 


prod. 24624 5 


Bere 32.4 is f and 7.6 is © which two 
Fractions Mulriplied by the Rule given, 
for Multiplication of Vulgar Fractions pro- 
duceth *# or 256 24 FR lame holds in All 
other. 


MH Divi 2 of Decimals De- 
35 monſtrated. 


zz I Nlvide the Dividend by che Diviſor in 
1 all reſpects, as in whole Numbers, 
1 enly obſerve, that ſo many Decimal Places 
__ - as are in the Dividend, more than in the 
_— - Diviſor, fo mary maſt be cur off from the 
= - | to the 8 for e 


; 4 Y oy : 4 ; 
J 7 * 7 * —o» 4 E - * . att 43 a N . 

9 93 #52 - EY 
_ Ta 4 q 2 < A Ss 
4 ; d x | 2 . | 


lt; ; 3 5 P 5 , p 2 
. 


1 d "> 
| — +" 
f ] ; ; : By 
= 1 ww | 6 Wo 
, , I'S 


Exam, Divide 7 9 by 34-3. 10 1 
"Np 34 37 7.90930 N 4 


5 5 47:5 a_ 


ES op 5 1 


— 


\ 
o 

4 + 4 Wo 

N > 9 "7 
5 - 
1 1 O * 
1 N = 
s 
* 2 * 7 4 
; — —4 5 


— 
”. 


For 34: 3 = 2 and Te 9 —= 2 = 18. N i 4 


* 
. 
7 x 
o 


| 2 10 9902 = . 230 . i 3 4 


The reaſon of which is evident from 1 


x ulg I Fractions | ; . f 
, - : | i 
7 4 _ l 
_ 2 * —» 4 , A f p 5 I I 
” | = 
* { 
f a 1 
7 a 
DH 
. % - « 
e — 
- 
* , 
- 4 7 
2 — — ws j 2 % 
8 
e 8 : 
os - 


= 
# 

f 7 
- in 
o x 2 ** A 

IJ — 
F 
% 
7 A "4 
; $. - * * 


42 
? > 
1 


* 
* * 
% 
A 
— — — 
* 
- 
1 
* 
th 
= 
2 - 
* 
F 2 — 
Wt * | 
gh: We 
* ** 
* 
5 - 
7 
2 + P 5 * 
* 4 
S 


8 


Majeſtys Revenue. 


| 


Containing the 


Ute and Applicaion 


In the Several 


OFFICES 


"OF WEE 1 


WITH 7 Dots 


+ "WE the Wathematicks. 


8 wh 


'LO NDO N: 


Printed in the Year 170g. 


PART III PP 


By ran am Alin ghe am, "ins 


ARITHMETICK; | 


| Collection of Queſtions. 


a 1 


W 


? 
% 


N 


„ 


„ 


ws, 


— — — 


> HP .. # 


— 


IN THE: 


alen and kale, 


Arithmetick more Univerſal, 
immediately Uſeful, 1 ſhall here give a 
Taſt of it in the preſent Practice of ſeveral 
of her Majeſty” s Offices of Revenue. | 


Firſt, in the 1 and . 
chere is need of being skill'd in Arithmetick, 
both in whole Numbers- and Fractions, 


for the making of Dividends and Proporti- | 


ons; as alſo, for the Caſting up the Intereſt 


of any Sum of Money for any Rate and 
Time, with ſeveral other things of this Na- 


| ture. 
For doing of which, ſeveral practical 


Rules are uſed different from the common 
Road. 


I ſhall give an Inſtance of to or three 
that are * nn and ä 


FY 7 $ 5 — 


H AT 1 might: nd chis "TE; of 
| and 


One 


i 
28 


(/ 284) 

One of them is this, Diviſion being the 
moſt difficulr and troubleſome of the firſt 
four Rules of Arithmetick, eſpecially when 
the Divifor conſiſts of many Places, tis then 
the beſt and ſureſt way to make a Table of 
Diviſors, b.; Multiply your Diviſor by 
every one of the nine Digits, making a 
Table of the Products by ſetting them one 
under another as followeth: From which 
Table you may immediately ſee whether 
the Diviſor can be taken Once, Twice, Thrice, 
Ce. in the Dividend. For Example, ſup- 
poſe 6587945 79828754 to be divided by 
1748692583647, Here I multiply the Divi- 
for by the 9 Digits, and Tabulate them as 
...... WE ROE AT he 


1748692583647 8 
33497385 767294 2 
3246077750 13}. 
3594770334688 4 
874346291823351750 
1049215550188 2 6 
12240848085529 7 
13989546669 176 814 
2 


13738233252823 


7 


FY OD ae bates” adi. „ a> *® N Dd + ok +» AAR . — 8 — 


| ; The 


J!. PTT 


1e 


( 285 ) 


The Table thus prepared, place your Di- 
viſor and Dividend in the following Order. 


1748692583647)658794579823754(376 / 
e 


134186804 3465 | 
12240848085529 _ 


te ena 1 


1778323879364 
1049215550188 


1286168377482 


— 9 


Firſt, Seek how many times the Diviſor 
is contain'd in the firſt thirteen Figures of 


the Dividend, which by the preceding Ta- 


ble you'll find thrice, ſo I ſet the produck 
of the Diviſor by 3 under the firſt 1 3 Fi- 


gures of the Dividend, and Subſtract, bring- 


ing down to the Remainder, the Figure; 
in the Dividend. Then I ſeek how oft 
this Diviſor is contain'd in the Remainder, 
and the Figure brought down, Which by 
the Table of Diviſors I find to be 7, where- 
fore I ſet down the Product of the Diviſor 
by 7, under the Remainder and Figure 
brought down, and Subſtract there from, 
bringing the other Figure in the Dividend 
down to the Remainder, and then ſeeking 
again as before. wrt 1: ap 3/288 
4 - This 


(886) 


7 


This night 8 0b dividing by A ; Table, is 
of great and excellent ule 1 in hers, Di- 
Won 


Secondly, In Bravching of the Overplus of 
à Revenue to others, which are Deficient, 

there is often required ſeveral very large 
Proportions to be made, which may be 
contracted as followeth. 

For Inſtance, ſuppoſe the Sum of 62317 /. 
103. be ordered to pay off a proportional 
Part of the following Deficiencies, the 
Queſtion is what muſt be paid upon each 
Deticiency, | 


uf. 45. Aid —— — — 36356=18=3 


ff. 38. Aid ———— — $24099=16= 
Poll Tax ———————— 60278=14=9 ' 


Additional Impoſitions — 25 x96==1 5=6 
| Births and Burials — 37684=17=; 
Tonnage an Poundage—28G01 5=06==0 
88 5 on rer — 16. o 


* 55 eee 


hi 8 
1 . * 
nc bf *% 4 


According to che common way of Work 
ing this Queſtion, there ought to oy 4 dit- 
- ferent Statings, 

For as the whole Deficiency, to the 
| whole Money allotted to pay, fo i is any par- 
ticular 


* r - 
* Feen 1 
- , 
- of X , „ — ee 3, 
# 7 


E 
ch | 


| 0 287 + 
ticular Branch of the De ficiency, to: a pro: 
tional part to pay that Branch. 


- But the method I adviſe to in 9 Caſes, 
is this, reduce the Shillings, Pence and 


- Farthings, of all the Sums into. Decimals, 


and annex them: to the whole Numbers, and 
to the Money allotted to pay off, add 6. 8. 
10 Or more Decimals it need require. Then 
divide this Sum by the whole Deficiency 

and Multiply the Quote of each — 
Branch of it, the Product is the Money chat 
muſt pay off ſuch of it. 


If 870748 1. 425 parts give $230 17. So 
What ſhall any one of the Branches? 


Here, enen to the preceding Rule, 
I add 10 Cyphers to the ſecond Term, and 
then divide 5 the firſt, which Sives the fol- 
lowing Quote. | Foes | 


P 425) 62317, 50059596056 f ern 
This Quote .07156774 Multiply” E by | 


each of theſe particular Branches, Sie 
cad of their agen | 


r * * es os 


C 288 ) 


The odd Money in each Branch, reduc'd 
to Decimals, ſtands thus. N 


e 


V 
1 f. 3 6. Aid — 424099.8 

Poll Tax————— 60278.7375 
Additional Impoſtions——— 25 196.77 
Births and Burials———— 37684.8625 
Tonnage and Poundage —— 286015. 


Duty on Leather — — 1116.037s | 
: "1M." . — | 

870748. 4250 
157 a | a IN ents L 
The Queſtion being ſtated and operated 

according to the preceding Directions, 
there will come out part of the Overplus 
Money, that muſt be paidto each Branch; a 
that is, Deficient, as is expreſt in the fol-Æ ; 
lowing Table. EY ; 
iff. 45. Aid —— 2601=z19=7 | 

If. 35s. Aid ——— 30351=17=3;z 

Poll Tax ———- — 43 145=002=3 7 f 
Additional Impoſitions——18503==052=6 7 f 
3 Births and Burials . 26975=00Z=4 7 "I 
= Tonnage and Poundage — 20469==09==4 7 F 
Duty on Leather 7917 7 f 
| — np— 1 

62317—09g9=tl 

But 


But here note, that there iꝭ a Deficienty 
of one penny to make up the compleat 
Sum of 623 17e; · which Deficiency is up- 
on the account oſ che Decimals, that is o- 
mitted in the Product of their Exp | 
ODS + © non 

I shall conclude this, anich givir 

y. conciſe Rule, which I ee 92 
my loving Friend Mr. Ralpb Snow, Writing. 
Maſter in Morefields, © 

This Role ſuppoſes firſt, that all Sums be 15 1 a * | 
calculated for 5:4 per Cent. and when tis fo » 
dane tis caly W reduce ie copier rate FO * 

For admking debe 2t f Jogid Cent. per. e 
Ann. tis but adding 3 of the rate at 5 per — | 
Anm. T it, and it Bios it.ars J. fer Cent. 1 __ 
| * Anz. So alſo, if you add q, it gives it are 

Aer der Ann. and contrary,” if you A = 
* of the Intereſt at 3 l. Nr Cent. per” _ "= 
Ann. — —— it at 44, per Cent. pe per Anm &c. — 

Boe b 644 . Hence there. 
fore, if the Intereſt of any Sum of Money —_ 
for any time be gziven at 5/4, pe Een "tis *. 
_caſily redued to àny other rate. Fer . | 

ample, The Intereſt of 2.50 l. at g Lp Cn, 
for two Years is 25.1. What is the Intereſt of: : 
it at END a 4 


þ 3 * * : % yo 
. v oO BT; ; : ; \ — * 
b PM: "> - "I , | 2 ; 


_ Ki. 


8 . r 4 
: N Wo + 4 


4.44 — ky * * 473 —_— 


— — pb: the Intereſt 
ngo 7 800 Years N an per 
Ann. * * 5 Vale * r "1 N 


7 * 


* 


+ my 5% 
344. 7: . Hence dds ak © ta mand this geben dle 


{ob Gan 


Multiply i rbe given Printipal by. the Number of 


Lupe ; the Prod divide by 7 . 4 + el . 0 


Cent. per Ann. be 07 
4 Rt | 


* 
1 21 
. 634% TY 4 "oO 5 4 


"I TH't3 * 3 


gehe 
„ +. oo. 2 Is 14 N 72 1134943" Mts: 


No 
Or 450 o 


A wer. 


n if on 
„Noe, The given Princip al : as hed 


duced imo FS. which is, on boy 
Mullriply.by 4 . To ae 


* 


3 915 21 p * "uv . 7 #15 Wo 17 CV; 
3 5 15111 9h i N. 4 7 5 — * 9 — 9 5 10 


N W « Ad 


5 
— 


\ | 0 ps be BY Abb Wo 9 
24 5 N A he Ws BR * vg 


1 


FP — 2 7 2 3 FX HS 0 


i eee eee pſy NEVE 0 | 
45 2 5 Mei 9K; N55 3 i\>irl or 8 r 46 


a I 
ES: n * 100845 et ont td 


See M1 70 
c $ TOM- 9 E - 


Rirhnjtich 15 of g great be in moſt of... 
the aiftin Offices In His Palce, and 
therefore both Cl 95 a Ole 
ought to be well 22 ſt," in the * ; 
Ciel Rulez hereto: III 1. NN : 
But pre and prindifally' ſu > 3 
caſt up the nn the Landywaizers, t 
at the Warer-ſide which 1 BoPaG * 
ported and link Orte. From. whicty 6 5 
tory, or Account this taken” 181 Caſt u 
the ſettled Rate, _ the Cuſtom of 4 


Quant 1155 51 of C ill, amount 


to, m , C Ter 7 — 7 
Tan” as 18 95 '& e for part e 
lar COT 3 1 1 in 


22 . the ee Au 2 now 

uſed at the Cuſtom: Honſe, | g up 
tha Taye of ſcycral Comt 7 e Lact) | 
fi 00 + A es + 7 l * : . X 


88 


* 


3 


| "© 292 ) ö 
Firſt 4 dedusting of Tare, Multiply „ 
Number of C, weig bt Groſs, by the pounds Tare 
to be allow'd per rol weight, the Product divide 
by 112, the Quote gives the whole Tare, which 


| ſubſtratted from the Groſs leaves the Net 
weight, for ens Cuſtom is to be paid. 


| Exams. 14G weldht of Raiſons, the Tere 
bs 141 87 ; how —_— Net: 


2 SV) 4 6 2 * 5 : 
: hs %,. v ; 1 g 1 2 * : bs % $ 
3 3 3 5 
4 5 N 
2 . 


55 I 2 31 tec alen Thr / 


=} 11. if there had been 32 C. . 
25 che Tare' would have been 7 B. more; 
hat in the half of " 1; then a quarter 


"ir ie Tre had been at 14 W. 1 0f 
5 A 157. C. Et, then you 4 "have 
en 1 Or 10. 32, ant added to oi former 


K #4 
Fart. 1 * 


We 1 + 75 8 116% : 38. . | * . 4 40 "Eb 37 


If the 74% ho 4. 400 Ae the 
7 weight by i 6, and the uote 
* the C. weight Tare; the 125 >” The. 


caulc 7.1 5 ou . 144 T A er 
giz bly. If 11 1 
2.2 4899), 


| 8 wie 5 


Ped 


2 


* 


n 


. 
— 


a 
Vx 
2 


: 495 4 divide by 8. 100 the Quot 
che l 0h: 


Warrants, for he (th r 


a PP»: TD Tg 


| of it, after which they give ſuch ac 


8 "IE TY * 
* 


IN 
[8 


ce 293 Y r | , % 
er thigh 4. 
thly.. "of che Tare be at... 16 - 


e, for 1410114. 1 5 


* 


405 If the Tare be at 16 e 
weight, divide by 7: and the 415 3 
C. weight Tare, for 161 is 7 1137. ee 


Taft of the Buſineſs, 


1 ſhall next mention e ar of the, | 


Land-waiter's Buſineſs, and : mer 
theix Entries at the Res. 
The Land. waiters baying receiv A Ba 


aking an Acc ount of ſuch 
and ſuch partic lar Comm ities As. Axe ta 


. * the 


be en and 1 —.— they At conve- 


nient times attend the Ship from which they 
are taken out, or into. which they are car- 


ried, and write down the Commodity, 
with the number, Weight, or Meaſure gf i Ws 


alſo, the allowance for Tare, as is Cyſtgme- 
ry and Uſual, with the Adark and Number 
nt 


into the proper Office in the. Cuſtom: 


for Oy up the Cuſt m that is duc. 5 
on it. 2 i 1 


This is the principal boknek; of 1 his 0 


ficer, and therefore he Ak endeavo! + 


ö . 


More Examples of this Nature 3 be Fr 
given, but theſe are ſufficient to give yoqa 7 


bd * ; 


"54 


getting of fuch Employment, ought'to have 
10 PROT: * in Arithme- 


mich 1 hall n now is co to how you 
| th Practi Rule or e of. OY . 


The Sate Rale ed up FORT Keys Yor 
c TY Wie *. Oi Car, 4 


* «> C45 7 R 1 6 "Be 
is thus; Es £ 4 nv 


Ale the Dice, 4 ; Cai TP 47 Rong nd 

Head within the ack, 2 as "alſo. the length 
of he Cack within the Heads, 1nd Jet oy * = | 
Hows Jeve/ally. * > 
"By theft Diamiibrs find our *the Area® of 
the Circles to them belonging Thus, .. "mg 
5 1 Of the Diamerer by. Zt, e | and the 
roles thereof. by I. " The Quote divide 1 

| Lo "gives the e Area of th chat. (Circle. 


ate the, Arta of 1 the. Balg and Ha FL 
belly: por after, this manney ; *, Maltiply the 
Bang: Ares 25 4 divide” 53. it 1 
the Area of the Bun Diameter; £2 this, add. 
255 i 7 75 of #1 1 "Hi 14 Diapither, fon 44, 


e 7 74 De - Sault * — 2 | 


ask; "this. mean ea mullip l : 5 | 5 5 
2 =] wok the Cask 1552 the Taka Hivi- 
. 28 157605 bick. Hehe: p ec 
5 3048 1015 Y DN Se the 
| — 0 : e 


286": 788 Del ingot a0 "Fo ox 


” 8 : * A 
- * *. 5 £ 12 


allon ty he 


1 
4 
* 
— 
= 
vo 
a 
2 
* 
5 


— 


8 5 2 N 


fror Example, Let the a of a 
Cask be as ollowerh. "AY 


z *» 4 


| Bung Diameter 36 Inch. 
| | Head Diameter 30 Inch: 9 
; 5 _ Long 50 Inch; | 

1 0 3 MAIS * 73% 8 V deln 


- 
— oe 5 ee my * 
W a &% , 1 
N 4. 2 o 
A c 1 / 
e p y 
3 : 
N þ 33 
x © . , 
fo *. —. Ern 
_ * 8 %. 
: * 
„ 2 f 4 
, ak F 3 * 5 * x 
: . ; 3 A 8 75 a j 
——— 
140142560 1018 Area B. 1 : 
- * f * 
65 * * wy by . G 
4 5 L " 5, 1 1 FX * * ry o 
OMP -. 
3 * = - 
4 a I Ga TC” : 
4 " : - . . a - ” 3 
» 9 I . ; 3 { 
F + 7. SQY * £ e 
42 — : " 
A * . : . Os N _ — S (64 1 2 
" * 
678 3, . of i it. ; | 
Y 3 # 
——— a ; | 
. = Y * - - . 
F 8 * Bs . 
* | 
1 3 3 , : 
* 4 * * A 
. „ 5 A N oy 4 ; 


„ be at der yg ee aft . 
ee od dere s 

ac der ON. 121d eee 

3 0 n dei 1 i Held it 


* n * 1 1 5 
% 5% 7 * * 8 4 
* 2 # pl 7 
", og 3 * 
1 „ 
: ' ö 
* 
2 1 
9 
2 | 
* *. * 7 
* 
0 * 
* 13 E « 1 2 
8 jk 6.4. % 


C 
e bo 
| #47 3 ? 4 ö f 
Wr . 
0 (0 Area H. Diameter. 


o 


23533 Zone rd H. Ws 
678 7 two thirds B. 


* f ; * $ 
— — bf 2 


- 


50 
45716 : contains in Cub. Inc, 


. 


2370760 Gallons] - 5 


Ss 


* 
* 4. x 
, E 45 
4 n 66 e N 1 l 
4 
— p * ow 
D F ; 4 * F 
. 8. R | 1 ; 
- "4. * , 1 
\ S : 
22 n — * eee ee . 
* 5 * . N 
* f 1 
209 | 
. 99 ; 
». 6 — — 
1 Xs i 
8 
* £ 4 ** 
” * a 
» 8 \ | ' 


= This Remainder of 209 multiplied by 4. 
2 ud divided by 230 31 will give 3 Quarts, and 
=” _ fomething better, ſo that the content of 
this Cask is 1 97 Gallons 3 Quarts, near. 


1 1 
3” - F i * 


— 8 . 1 ; 0 4 
£ 1 a 4 8 * 
1 85 | Note 
. 0 h 9 


* , *. $ 5 ” : 


pe 
| 
| 


O97) 


U 


Note, 1 che Remainder, es 1 


| divide by 14 as inlignificant, it ban r 


enough in common ice. 
But if you would Work it to a Nicety, 


or if the "Dimenſions of the Diameters, or 


length, have parts of Inches in them, reduce 


them to Decimals, and that will make the 


Work ſhort and eaſy. 
I ſhall end this * Gauging 2 Cask, with 
2 you the 
ng up the Net weight G 
But fir 


tis to be noted, that 7 th. and; 
** Oil is 2 Gallon; and for Oil in uncertain 


Sanne allowed 18 b. far _ 


ry C. for T-. 


" hah therfore alva 5 Tare allew'd 5 
by the Remainder, mul- 
double the Product, and © 


from the Groſs C. and. 
tiply the Groſs weight, 
it brings it into balf Pounds, which divide by 
135, (the balf Pounds contain d in a'Gallon und 

the Meute Su — _ —_— * the 


. e 2 5 N 8 5 


1 s ** 2 $7) W: 1 4 


Badu, duppoſe Fa S wage 


vellet;of Ol be 30 C. oy N n 


12. 4 oo C3353 FAS 0 8 


* * > 4 4 ; 1 75 " 
EL 5 "iS KC * R N W 1 
f 1 55 oF; : ' 
3 : ” +. / g N » "of 
a ? . 8 N 1 8 


* 


Coſtom- Houſe Rule, for 


J oy f ky 85 


. 
T 


* >.> 


_ 1 i « 1 0 94 . 8 1 7 TEES. 
A 0 by Lec. e oct . 
= N — m — IS 
li 3 Tr ates 5 _ arch 2820 Pounds Pen. 
Y 5 5 | a — Dn 3:t 1 * ot 
. ff 8 tet bene 
; Then he Tare of Fs 18 2, vhich taken 
from 28 leaves 235 this added to 28205. 
gives 2843 3 "which, doubled" makes 3687 
half N and then divided by 15, 8 Wes 
379 x the Number of Gallons, bie. 
4 the Nett content of the Veſſel 1 ny 
1 5 Wenne — N. en bn 
=. To-find.the Tonnage of 4 Ship; chat 1 15 0 
1 5 N N TIS 8 16. . N Ra! £20 5 
| * Men ee Rt LIL » WE. WG 
XNuule, Meaſure the Length of Reel, alſo 
ite tengek of the Midſbip Beam within- 
=. fide, alſo the Depth of he Hold; hat is, 
. from the Plank n me Kelſey, to the 
under part of the Upper Deck Plank; 


Lan From. 12. Bas * 


— — — —ñ4I4Hi ae "mand 
"Ye . * 8 4 
FA, aer # * 
« 4 - 7 ar 
. N . 4 
* 


N 
— —— — — 
en rh rv eat ee rr 
f _ ö * * * 
* A 2 
8 = [& * 
TH 
1 
CY 
- 


. 


2 


* B—— , 
* 3 * * AY 
* 2 * mY * Fan 
** * = 


then multiply theſe 3 Produits together 


A 4 "1 continually one into another, and divide 
* the laſt Product by 9% the bag will 
_— oe? her Tonnage. — Ok 


i olf a Ship be * Foot; che Breadth ' or 


- Exam. Suppoſe che Length of the Keel 


„ £CÞ% 


1 i 
Length of the Midfhip Beam 24 Foot, and +" 
the Depth 15 Foot, What's her Tonnage? 
Multiply 72 by 24, it gives 1728, this —_— 
product multiply by 15, the Depth it gives 
25920, this Product divide by 94, it gives 
275 p near, Which is the Tonnage, or Num-. 
ber ot Tuns; that is, the Ships Burthen. 


The general Rule uſed at the Cuſtom-Houſe =_—_ 
E "JM Meaſuring of 7 imber. 


1 Timber imported hete * none W 3 4 
Square; har in four ſided, except Maſts for 
Ships, and their Duty is Jo much a piece. yu 3g q 
TI ſhall therefore only give you the _= I 
Rule for Meaſuring of our-lided: Timber, | _ 
whether the ac be, Ne Square, or of 
unequal Sides. 


A 
* a 


| Fa Pot bis -q rg 2 
9 6 2 
Rule, Take Ad 8 25 on the F1 


3 25 * K* 2 
. 


ko alſo on the other, (if it be 15 tun 7 j 


Square) juſt in the middle gf the piece: an 
_ multiply the ons by the MI 200 6 

Produ again by the þ L pgth;. and yes: - 
e contents, N A . 
"Exams, Suppoſe” c one fle 8 1 * 1 
4 ber b be x, Foot 2 Inch 885 "the. r 
1 Ft 4 Inches, the 5 7 
A Pat's ihe Pa. 


85 
. 
7 
l 
1 * 


FE 
* 
* 
F 8 
f by a 
8 9 
pe "7 "Eff * 
1 0 E 2 
1 = 
. 320 
Ne as 
** wy a 
. * 
2 
4 *% 


A 2 #* i p £ 998 


N e 
„ SEP 5 1 36 3 A A 1 3041 of 
SS). 91, 2.43 mon? Tt 36 5¹⁴ digg 


"1 WS. N - l 2 . 
— 1 * 8 
1 | 


30 4 
2 
* — b 


ap the Operation, ; Fo — 


NB 


* 
1 As E 7 : 

*K My 8 i 4 + N. 4 me — 
ms, 4 - * 9 I” : rind : . 


yep. < Wy 
—— 


; * 
— — p l — 
5 I pn ny wo Pay — — —y— — — wa} 
CRT NT NT Oe re CT SE ITN 6. t& 
> Ck ? F = l 4 * 25 * E 
A a * 2 


— — 


=_ 


+6, 8 3 22 
25 . * 1 20 Length. Act 


\ 


yg 


(Om 455 ee, ä * 1 N content. 
2 4 i. 


| 22 8 is 18 he Waal! practical way, Gor 
2 firſt I multiply. x Foot 4 n x {Foot 
._ 2 Inches, it gives 1 Fogt 6 Inches 8 parts; 
this I multiply by 20 Foot the Length, it 
gives 31 Foot 1 Inch 4 parts, che Content | 
7 F d e 3 = = 
The Inches and Parts above the 31 Foot, 
may be neglected as ere 1 | 
Ne, This way of taking che Dimenſions 
pf the Thickne( and Breadth of the 75 | 
| 5 im the middle of th pc 3s falſe, 
= plece be Tapering, as 1 haye ſhown in m —4 
i = | Epitome of Geametry, where I have prov'd 
= that thoſe Dimenſions ought to be taken, 
=_ in this Calc, at near from the Sreater end. 


4.4 wg 


* 
„* 4 * 


+ 4 '' N . 
" * * * 
"=; = * 7 
, $ * . 
1 . by * 
— 4 ' 
2 * 8 9 
| | 
* ' * _ 
” 
- 


n MOR rs: 5 


nene. OFFICE: 55 


HE and e . PE. Praftice of 


_ Arithunetick is great Uſe, particu- 

1 Adtition, Subſtrattion,. Multiplication 

and meer, in whole Numbers and Fracti- 

ons, both Yulgar and Decimal ; as likewiſe, 
the Rule of Three and Prattice. 

With the aſſiſtance of theſe a Perſon may 


be Capable of Officiating a Clerk's place, p 


In the Accomptants or Receivers Office. 


Moreover, before any of thoſe that de- 


Gon themſelves for Officers, or Gaugers in the 
Exciſe, can have an Order for there practi- 


miſſioners for that purpoſe, (ot elſe by a 


Surveyor) Whether they Underſtand, or can 


Work the firſt four Rules of Arithmetick; 
as alſo, the Rule of Three and Practice, and 
upon Certificate brought from the Exami- 
nent, or Sur . to the Commiſſioners, =. 
WE they 


1 
9144 
* 


cal Inſtruction, they muſt be Examined ei- 5 
ther by Examinants appointed by the C- 


1 
9 Th . 
3 


F 5 *h : 75 Fg | (182 5 
—_— they arc MM with the aforeſaid Rules; ; 
| then if the Commiſſioners think fit, they give 
them an Order to a Surveyor for their further 
Inſtruction in the practical way of Gauging, 
by raking their Walks with the Surveyor, 


EE and ſeeing the Officer take the Dimenſions, 

both of Backs and Coolers; as allo, the 

method of ſetting down thoſe Dimenſ! tons, | 
and caſting them up, and this Iniſtruction is 
to be given them both for the Brewry and 
. 


* Wt | "the 8 N Ale the {18 
me & Polite that * is perfect of the fame ; 

EX then he writes. a. Certificate, that after 
= long Inſtructions from him, he finds you 
ficly qualify'd for a Gauger's place when an 
rtunity preſents, and the Abi oners 


. r 


| „ 8 the Ss 7 Deyn 0 jATS ſuch as theſe. ng 32 


ih Veg Of * 25 1 N 


i 8 ns "fa 1 — Ae 45 upon 
= - 6lnchss, 48 Gallons, 6. Trains, War: _ 
=_ rms ago. one Inch. | Fate 


75 D N I 4 "> 1 2 


ve the igt of ==> 


* 
3 . 

4 25 

x 1 

214 5 75 12 . * 
1 - r we 2.146 
$372 $: For x os a "A 2 4 mo 8 1 9 1 
i © * : / 4 

7 . 
1 „ ; -1 ; 0 4 pt f 

— 2 - f _ \ > 32 EF: * Ns 

; 4 0 7 89 ; x * 7 8 

1 L F a + "Mp 1 . 4 * *. * 4 N 

3 ** Fi * 
1 


= 2 | . 
; 94" Hons % . This 


bh ok ft co g beſtow 3 it Hoy Ws - 0 
8 0 f the things. you are Bac in 


A 


% 


K * 
** ** 


nm : 8 1 wh * * Rold: 


may know What it holds N ADJ Nam. ; 
ber . Inches deep. 12 5 


1 155 by: 


„ MW FI. 


mY wu 9 — F n a a os A 5 1 ORR 
< \ p 3 Via CBI» mayo 4” TY l \ 
. 72 0 8 3 ITS * 23% 
* ö 8 A f 1 
x 75 72 * * r L 2 1 y uu 
* * * „ 
* * * 4 — =" 
Py - y | F = * 4 = 4 * *2 
. _ : g — RY 
4 * + «= 
- 5 
* | * 
"I L ys 24 . * * 
4 Y e " : * K 
— ET 5 
ds U hon, I | f : 
% + 
1 5 4 - 7 
1 f 
2 of 


three Inches. F mT 
After this mai Wu Log ants - 
Veſſel holds any Number of Gallons upon 


any Number of Inches Deep, What it holds 
upon one Inch deep; and if you-know * 


What it holde upon one Inch deep, you 


8 "4 | > | 
Exam. 2. Suppoſe A 1 or 2 _— 
Tun, holds 165. Gallons, upon 7; Inches 
deep; What doth ic hold upon one Inch - | * 
depaolit) gaj' 1444 bitgye 09447 108. 
| Reduce: the Wei nne e gie 
this's5* divide. x65, arbe. Quote ii w;, 
which is what it holds upon. half an Iarb grep, 


this doubled gives ( 22) what it holds upon one 1 

Inch deep, tripled, i, what ache olds Aan 

Inch and half died. e „ 
Again, ſuppoſe 1 would t urn Gallons of 

Ale or Beer, to Gallons of Wine, and con- 7 


ary ; that in, to turn Wine Gallons to Beer © 
or Ale Gallons. 5 5 
Rule, Multi * . the, "a 
282, and didi. Progutr 
is Wine Gallant, _ + 4 


= IE 


Glas gives S 5 
LE W 


- 


| | | > 17 - Example 1. 1 72 Ale . how ma- 
1 WP Wine Gallons? Anſwer, 87 53 Gal- 


1 4 | ns: . 97 * a 
=. | i a” l 
bt L. . — 3 4 Iv 7 ? 2 —— » 
; AS. 7 * 4 = 5 5 . : N (7 ” * 6 £ Nn * 4 * 
0 6 F 05 3 . 6 * < - , 


i} & WO. - . n 
| | | 


* by % wt 
: 5 +: \ wa vi, 
* 8.4 * *X 89 2 4 A > 0 - . 
T7; N | * a F A * 
5 : ” * * n * 1 by 
. 3 1 * * - * 
q . . ; ; 
4 . 9 FLY 
1 5 = N * 4 
. -Y . 
_— - * 
. 3 
f k xo 
* 
"4 - 
- % A * 
1 TT 
X * * N 
ö ö f 
þ F . * F . , 
; 7 1 2 5 + W, 
! * ; 
2 * * 
A 1 N * on 
* 4 1% 4 
6 — e 
8 
* ry ; * * % * 2 * ; 72 
* 3 OS oY a 52 8 1 * R 4 
> — 1 - » - * 
. £ 4 1 4 . * 3 
1 F , ; , : O * 
3 ? - 8 1 * 5 2 ; l 
x [ - * 4 * f 


» ; 4 


* . ** $ ö \ 1 1 Y 0 5 E, pd = 3 5 
Na . , 4 th A 7 . 5 * * 


But if you would turn Wine Gallons to 


how. ma- 


p Lin a * * 


4 „„ . in roa Wine Gallons, 
ms ny Ale Gallons ? Anſw. 8: 85 


, : 1 
3 S 3 » FAS 6 q * Ko. Fe bs a "Us. I 9 
n 3 . rie 


* . z *47 


. 2 
Wo 


ö 5 


( 


4. 


4 


3 . „ 55 FE 
As to the Gauging, or finding — quan- 
tity of any kind of Tun ot Veſſel, any 
Number of Inches deep, you. may fad ir 
amply taught both Aritbmetically and Iuſtru—- 
mentally, by a ſliding Rule in a Book called 


Steręometry, or the Art. of  Gaygins: newly. 
| ſer foxth oy Ty One, Eſq: ard 8 5 
miſſioner of the Exeiſe; in which: 
has fully ſhown the whole Buſineſs of 
| ing, both by Arithmetick, *andiatfliding 
Rule of his own Contrivance, which me- 


Jar 

in Little Britain. 

fey in Little Britain n 

CCG ity! by On 
- 4 o 

iin 


ad ” 


; 5 . n 1 X 2 WF 
* * * ene at * 8 44 4 


1 g * = 
us 1 5 1 7 * T 3 7 
8 8 4 


„ 
. 


4. ” 4 1 Ws — 

W : 41S % 

„ „„ PN OKNR N 

& 3 * : 1 i : ; . 
1 N «ut 2 1804 $7 Eats — of 3 
+ 75 - 2 Gy) mM, «5 «3 
. BY 142 £* LIE &: $5 7531 
a Fo » 1 Ps SS. Fond *,+S 9 1 a 


I £5 3 * ” 2 7 wy * 7 
. 5 


. * y 
88 


225 222 8 
nn 3 


_ & ag. 

i 4 1 
-_ 45 LT: af 
1 5 2 1 


. we Wh 3 5 $ [ 5 OY F ; 3 * & 7 : 
3 ; 4 1 $f : * 2 — "OS | bY t 
F vs * © . 2 4 — 5 * = * ze. f 
WP.” - g a 4 
2 . 0 ; 3 GG . . 
8 ti yelating to the Com- 
ow. 155 1 I 
} ; : * A 
; N k G9. + 4 Ge. 2 ; . 1 | 85 1 : 
= 333 „ — i 2 4 : a : E 5 
dum of Soldiers and Sea- 
N 7 "© Boa ; 


Het 0 
h - 
* * 1 
= A = 4 
72 * 
2 
0 * 3 
—_— { * 
/ 4 A % 
2 S 25 33 "> 
* 8 


4 
* 


+» : 
* 1 4 k - 
3 * 4 * 19 2 * : 
1 . 
7 * 
— . — 8 * 
=, E = * . a * 
, + - 
. * 4. . » 


- 4a 


1-6 


N the Pay- Offices of the Army, the firf 
four Rules of Arithmetick; as alſo, the 
3 Kule of Three, Practice and Fractions, are 
= highly Neceffary , for computing the A- 
1 mount of any Number of Men at ſo much 
zer Man; but before I give you the Uſe and 
Practice of Arithmetick in theſe kind of 
Accounts, it will be requiſite to give an 
Explanation of ſome Terms relating to the 

Eſtabliſhment of a Regiment. | 
The Eſtabliſhment of a Regiment, is the 
1 3 b IROEny per day, of all the Of. 
13 s and Soldiers e er N 
S8 Subſiftance-Money, is the Money paid pre- 
1 ſent to each Officer and Soldier in * 4 
giment, and is to ſupply their preſent Exi- 


51 1 


re 


r e A -» 


"= Regu- 


* 
« «5 a to. 


ng; Een Een 
KEI | OI * 
9 


77 is hat & 
- Fs. neceſſary, for the preſent,” upoti 
- BE fome- Extraordinary Occaſion; and there- 
fore may be a greater or leſſer part of the 
Full Pay per Day, as neceſſity requires, and 9 
- & fo is renew'd from time to time 
© Off-Reckonings, is what is deducted 5 
of each Man's Pay per Day, for Cloaths. _ 
Poundage, is an Allowance to the Pay- 
Maſter- General of 12 4. per Pound, out of 
all Moneys he pays for the Uſe of the 
i Real Hoſpital, is a Deduction of one © 
1c Days Pay in à Year; from both Officers and 
re Soldiers, and is ſtopt by the Pay-Maſter- 
VV Eo nant as 
An Agent of a Regiment, is an Officer 
put in by the Government, and by Virtue 
of a Letter of Attorney is to tranſa all 
Matters as relate to the ſaid Regiment. 
And according to the Ef abliſpment, Muſter. 
Rolls, &c. to Account with che Pay-Maſter- 
| General of her Majeſty's Forces, fot all Mo- 
ney iſſued out of the Pay- Office, whether .- 
on account of Pay, Siub/ftance, Off. Reckon- 
e- is, N &c. Receipts Or Arquit> -y 
e- ances to give for the ſame, or any part 
t- thereof; and according to the Articles or 
Tenure of the ſaid Account, ſhall truly de- 
— * 2 each — 5 or their juſt / 
and equal Proportion for himſelf, ers =_— 
nnd Stare a to Creditor — Date = 


4 


- Or, accqunt With the ſaid Pay- Maſter- Gene. 


7 * 
* * . 


zos ) 


art of his 1 and that as often, if 
— 5 'd, or needful, as he ſhall ſo receive 


ral. ONS ; 
Agency, is an Allowance of 2 4 per pound, 
out of all the Money receiv'd by the Apens 5 
from the Pæy- Maſter- General Over and a- ( 
bove which, he has the et of one G 
Man in a Company. L 
Reſpits, are thoſe Sho dre nat ut eg 
neral Aae or Call, of the Rolls, and fo are M 
prick'd two Months by the Commiſary, C 
which Deficiency falls to the Queen; except Ml 
one Days Pay, which goes 1 to the Com C 
fary. | , 


n are accidental Charges 
that may happen to an Jy in a Aan, 
or in Heres, . 8 


hs add 


Suppoſe the Aſtabliftment of a Regiment 0 
a 4 ORS E, as hag Th ſ 


3] Sta and. Till cers e eee 

9 11 Fo Mfc — 164833 
...r. 

Colonel as 3 G 12 


3 


tenant. Nee e 1 435. 0 


Lieutenant: Colonel, as oe? 3 > 
50 


Chaplain — — — — 3 


Tee — 528 2 | >) 
Kettle Drum — 0 — —. Teal £ _— 


„ 


8 4 3 — ͤ—ͤ— —— — 2 Ae. | 


O5 * i I —— WIG 
EC 2 | Ee + EEE 


2 353339 1 


85 8 2 this TROOP. 7 


Captain 10 4. and 2 Horſes, - 
uo omen 8 d e 


* tn e 


ieutenant 64. and 2 55 — 85 * NY 
Cornet 5 Fe and ROE — oy. 


Wi Maſter, 4:3. RAP! 1 Horſe; 10 4 , f 2 


rumpetcrs, 24:84. each N11 
Three Corporals, 3 5. cach- 90 aan 


59 nene Men, 25.6 4. each — 7 7 6 


| — — 
Fe 1 N 10 o 10 


— — 


X 3 Reg a- 


"y 4 ; 


£ * 
f Y 
* : 
* 
2 _ 
„„ 

2 > 

. 8 
* 4 


"X'S 


, 


1 * 
SID 


ale. 


: = - — N — . . = 
2 — — — — = RES, — — 1 
. 2 OS II NE — PSs I ns mags ̃ OR 
: ns 8 4 - 2 , - l 2 > 
__ - — N 5. — * 8 5 9 er e 4 N a — * — 8 * =_ 
5 > . . 3 < 4 — 
n Freer —— 5 —— 3 5 1 1 —— | "wm mm — ns n " 
\ a6 wh * 2 T ends des, * P > my TY SE + ooh 1 nnn FIR? "$a N * 
* LF? 18 * 6 © 3 
F * 1 4 D L c 
* 2 * 8 be. , ; — 
L - * — 7 R 0 ? = . 
7 = 
[ bn, TW 2% va. | 
: — 


Os 


— ae neg Oo et 2 rn tans 
5 — " " — —_ 
, x 
e 
"I 8 
* SD OF 2 
TRI 
c EIN tr 
: * 
- 
, 


un Bd 
LEY 


— — o—o—_ys —— r 


— — 1 


— 
* — — 


—— Ay I. * 
x " Pe on * * n 
2 * 8 


— — 
—ů—— 
hq 


5 


: . l 

—_ — — 
ä . 

— — — ES 


* 
— ————— K— rw 
— en oe o 


— ney oy ge — 
= + - Py = _— 


— — — . 
E r 
* ö R 0 

* % - A * Ps 
i £ * 
2 q 


— 


6 Lieutenants, each 5 . 1 16 
6 Cornets, each 4 6 4.—— 1 Dr 


Chirurgeon 


* 


. - 
Pl 232 ” 
( ; Yip ) * 
R * 


3 1. 
Colonel and «ky „ 13 


s 


Lieutenant - Colonel and Captain © 11 


Major — — 10 
4 Captains, each 7 5, — 83 


_— 


6 — cach 2 4.— © 18 
Chaplain q —— 0 5 
Adjitant—— 0 4 
— 0 4 
Corporals 18, n 9 
EG — — 
Trumpeters 12, each 25.— 3 
354 Men, 4 —y 
4 wg r 
is! EN 
The pay, of 5 ern more to .compleat. 
this Regiment at the ſame Rates and Num- 
bers, as in the Troop above, comes to 507. 
45. 24. ſo that the Tora NE of this Re 


1 2 22 


2 


2 1 C 4 : | Fi: 92 9 * 5 - 
— « J 5 o | © he 1 N 4 * 5 42 te 4 * 1 : 75 25 
N — 5 ö 8 : 


+ 


* 


4 


— 


2 — 


| 0 3 THY 
"i 2 A ˙A ²˙²˙⅛'lL . 
The manner of Computing the — 


By the full Off rec lonings of 18 Corporals, 
and 354 9 all 372 Men, at 64 
Diem, each from the firſt of April, 1700, 
to the laſt of December, 1793, 
included, is 1371 days, Whi ch at 9h. 67. 
per day, comes to 1 ä 


Fun this {s to be DA | : 


n 4. „ 
22755 '£ offall pay (being 5 7 4 j IF % * | ET | 
227 Heſpz 4 


x all 2 ; 127 


4 gar 1151 9 nt 
- This 3 931 T 3 a ſabfrated from 


1 1270 l-. leaves 88 19 l. 2. 5 l. 


10 Nett 1 3 thus-rq 


* 

4 2h * 
— GE 2 
© — % e 


pp < Tru rs [9 N their Servants Okkreckon. 


Auna 2 
44 


| which Remains bein 8 taken trom the Net 


00 | 


f 


85 7s Om”. F 


- 


Sh #554 0 
4 „ TIT 


e 
25 [ 2449 COT) K 5 ; 6 
6 Con 0 


* 198 : ® 7 0 * k 
— 12 CENT OR e 


*6 Quart tes 6 G0 e A 
1 2 1 8 i 2 


IM 19 4 iſp 4 * 14 * Ns 1 


30 thin thete l 18 51 I Sexyapts, v which at 
6 d; per Diem, Port Man, 2 or I3 + Gays 


; "Pg to Cod We 70 * 
: W e N 1 NO 


. 417 
* b by 
: * k £ 
p ; 6 — Hs wet — -- Nins 
5 ” 
% 


2 is to k ue. 
SE er Ee ee 
ee 7 . 
Poundage o all n x 
cn By ge acc fend; Mager Ain * 
4 — * 


In 1 555 5 15 7 [ 


This 51 15 6. 7 4 | ſubſtraied from 
1748 J. 05. 6d. leaves 1214 J. 4 5. 10 d.; 


\.- 11 
x | *- uw 


* 
- 


* 


* * Tm, 


117 


nnn , TD ww 


Off-reckoni ings before 


Note, That Poundage and R 
is ſtopt hy not 7 Te. 


ound, Vie. 88 
2.5, 5 d. leaves 7604 l. 17 5. 64. 


aſp 1 
4 ; and 


3 


1 * 
* * 
*® 
> 
* $ 
% 
+4 * * 6 


** 0 * . 15 . nec i 
. k * Þ * 2 0 *1 * * + * 
| : 


- + 5 
* „ 9 
Agency * U ef — I "I 
: OP * 
J ® Fg * ry „ . * * - * 
— * F - 
; ow 
4 * a Rue * * % Do 4 
* * .- * 4 5 : 
. . Mg we 
* * « * 4 s ba 
"= #£ 4% 4 WL 3 i 
x 0 * 1 
— by * hats * ; 
* 2 i pt 
+ ; 
> TR N 3 TL IS 1 
933 : * | . 
3% - a. — 2 5 N 
* ” - 1 * k + 
by ” y : ” "_= ” 
N . of pt 1 g 9 : 9 at N 1 + 
2 > , ob 473% * F 
; * * e * * % 2 Ex M 
* : att - 
1 * * o . 3 % i » 
5 ot B . — « , - AER: a — 4 — k [ \ FE. Ka 3 4 
4 4 . " 1 — 
* 2 4 0 ” % 
- ab 
STD] OUR ROY * — 2 — — 23 a 
as, o ph bay | 2 11 * „ f ” 
- kd E 14 — . 
% . w * 
K — + HS 0% % 3 2 
* 
* * 
f %UL $4 
7 
: 
* 1 , 
4A 
[3 ”— 4 0 
* o CA Tx * * - 4 MU FI Y 7 * a * 1 4 4 1 
a 1 — 2 1 * * * CIA * ad 3 — „ Ss * % - 3 
* 3 4 . . 1 4 1 * : * 
q " EIN JOEY . 
* z ; - LL „. reer | * N 1 o ec 
4 5 . * : 
ST L 1 
11 
: , 23 * n W 1 —— THY n+ Re ES "8. * $4 - 2 x” 0 > 
ep ys " % : : 2 
— 4 * * * 
* 2 Ee 5 4 * 501 
F * 
"a 1 * * % p] os . 
+ : , a KA 
. = £. = N * * * ” . 


BS 

l f 
». >| 
by i © = 
7Y 
B 
149 
19 
1 
| J 
i 1 
2 

7 
5 
Nh . 

. 
L 
* % 
41 WT 
Y * 
» 
be 
> 1 
xy 
3 

gs © - 

} . 

: —_ 
4 2 

(# 
. * 

Y * 
1 

f i : 4 
47 Ex 
= P IJ 
4 1 . 
< | - 

9 * b E 

RTF 

4+: ++ ks 
; * 2 

Tt 1 
- * >; 

0 Y 3 
' : . 
: 2 
, - g 
5 : . 
* 1 
1 A 
1 el 
8 [> 
Z 
% : 
1 
* U 4 
J * 
141 
4 + 
Gs - 3 
+$ 
, ba. 
, ? * 
7 
_—. 
U 1 
1 
.. 31 
— 4 
8 „ 
17H 
. 

8 iy 
ll 
n = p * 
4 « 

* a 
4 wed 

r 
5 

4 3 
bs] aq 
* 1 1 

- . 
. 5 bo 
4 { * 
F F- N * 
1 N. 
N 
C . 
A 1 4 
et. 6 
of 
4 
U 1 | 
£ 
. 
1 = 
| | 
IE 5 
1 
= 
" * * 
£ i 
n 


* CCI — 
— ny — 


— — — — ̃ — — 
P ot a ITS TREE * ah 
th Cn” a þ 
; . 


. — —— — 

= FE — — — * _ 2 
PP nn Ss qr er ce 

— — —„— — ä— 

2 * 


. 


— — 


— 


To 1514 days Subſß ben 4 


| 38 Royal 


To 683 days Subſeftance at) 


\ or ' Colonels Account. ” 
a CH , 

10 Pamndige of his full: 
pay, being 1968 J. 4 ally * 15 
To the Royal pa 5 7 
To Agency 


at 135. per Diem. I 


”—— 


To account of his — 
ARE — 


To Arrears paid 76 13 


pi 17 


To WS — 9592 2 


3 
x 
2 
X 


142 


— a 6) a wy cat. 


* Captains Account. 


To . 
pos tal = 
To Agency— 
To 413 days — at} 


12 f. per Day, according 
10 Regulation — — 


| 135, 6 d. per Diem. c- 
 Cording to Regulation — 
To. account' © Servants, 47 


Off-reckonings —— 
125 ae 350 


5 


rent 


— 


„ Ot, me 


A 


2 
19 4 


Colonel Account: - 


* 


FO 


By 1514 days Pay,as c- 
lonel and 5 Captain, from the 


219th. of January 1693. ˖0 
7 12th of a 1 697. At 


4 | | 
* | 
. 
S 5 
- 
a * * A 8 


mentioned time. 


| * 
: a 

| - 4 > | | 

* 4 : 


K © 4 a 


4 ** 
4 ef * 12 * „„ oder 2.44 
9 7 
. ' 4 
* r en A rt f | 
+, 28 
; 8 
ai 3 2 
- * - | | - 
#8 - K 2 y 5 8: 4 
% — © "= & 
: =—_ 
* * „ r - — 22a £ | | 3 
; * 
? — 
4 "= 
4 : | 
0 | 
+ * 
* *, 4 o 7 . " $ % . S. * 2 * 2 5 
s 1 * * *r 2 1 „ % 8 7 Mx - * ” 3 1 ; 
x 0 * | | - 
7 | 
4 | | ; 
C3 4 ; 
q 8 | 4 | | | 
; 5644 ; 


By his Pay, as Captain, and 
three Servants, from the firſt of 
day 1694. ito the laſt of April 
= both days inchided, 
at 1 J. 1. 6 2 


_—— 4. Fe e N —— a» ae pda 
5 


= 0369 
, Abu TOA 0.3 
Cornets Account. 


. 8 
ſ &, d b 242. 2 
Poundage Eu. 0 15 as lis. 
70 „ erke e as _ 18 iO. 8 E. 
To Agency — — 1 1 2 1 ner 5 2 + F 
To416 days Su ſFance, at $I og Hog id i! 
Ti. 64, per Diem, — 8 
To account of Saane ed 262 e 
© mare 71 23 H1010$15 OS if 
To account of lg reckonings 277 Dane 
Fo Ban. — 5, 1 8 
F „ 
e A TR 1 0- 


Sf, & £:% Fw . SR 
be Traz "IT 2 K oy x 


r00ps 4 cedunt. 


Dr. 0 "ods 
i 
— 7 6 
11 43 7:9 6 I's 
(portation..; 72001 6. TD 2 
AK — ane 2 


} 


8 
pe 
- 


1 


565 | 2080 10 © 


EI ——_—_— 
— 2 1 * * 


Cornet 


* 
J 4 ' A to ** 


q 1 - + "Y | a 
* * 5 : , 
(37 e 
ö | 9632 * 
— e. —— 
984 oy * 1 
7 


ru Fre 7 


2 Dei 


* 
24 * * ” 


% 
— 
82 
* 
W 
<3 


2A "2 Cormets Abtount i ls 


A ME is th 9G ur 2013. TONE * TO1 -, 109 

ce. N bus A : 16 21005 
lig Bet wen, Ming dogs 

By his Pay, a8 ; Cornet, and}. aw vs, _ 

two Sexyants from the qi i117 ft 

Fae 4 ta the 4th of F 

+ ly 1696. 

ing 731 days, at 14 % perilf}. > 

Diem, ac e s 10 


e TAE 


* F 5 

bliſhment..... +> > „ 34 AIM IRC (ISOs 
in 3X o« $ 

22898 1 


k & - N 
ah 4 "1 . 4 Pro * 1 «. A + #5 : 
4 N < oy 
* bh 14 1 * * S + N 2 £m _—_ 4, 
* * * 1 6 k * 
—_— 


The 2 Account? 
1 : ; * — 5 2 "a ; * 1 HP _ er., 1 77 7 x4 * 
g . Er. 4 . ** 4 « 2 FTA? 3 . j f , { ki 4s 
| - . | 


By the e ande of 1 Ket. { 
the Drum at 2 5..6 d. 2 Dum. 
pers each 2 5. 3 Corporals each 
2.5. 64. and 50 private Men 
each 2 s. from the firſt of 
April 1696. to the laſt of 
March 1697. being 365 days. | 
at £4. 27 5, per Diem. ] 


i * * 
1 * * 
: , - C 
w* A * 


Feb included, be of at 14 de 


SS 


7 
J. 
—_— 
l 7 3 
1 . 
1 8 
i 7 * 


g 

f 
% 9 — 
Un ? j 
«> 


any Sam © 


98) er ao 
This little AbſtraR will, 1 hope, give 
ſome light into the nature of theſe Ac- 
counts, for after this manner are the Ac- 
counts of a Regiment and Troop, and of 


eaeh particular Officer ſtated and kept by 
the 4 gent 


I fall conclude chisAccdunt with giving 


the 0 Rules, for caſting up 
Rojat Hoſpital, and Agency of 

Loney. ._ 

What's the Poundape, Royal Hoſpital, and 


Agency of 354 Men, at 2 5. 6 d. per day, for 
186 ys ? 


B)354(440. 3 per day: 


„ 
. 
2 


4 


— 


Then, What comes 80 days 5, at 440 
$ «. per day? 5 
K 


186 dayvar 44 þ 37. e 


7 


4 
TV * 
* * - 
9 » o * 4 
4 
F + 
5 A _ A 9 
* * 4 
. I 
J * wo f * 
N 5 ” 
- — * f 1 * TE + 2 . 
* F : 8 A 
n e | W=. 
8184 F 
= h 
n ERS 
— — kd P 
"> . . : 
bf! 
85 220 10 \ 
\ 
* 
* A 
wa - x ö 3 2? 
| 8⁰ 
x 
. 


N 


* Hl * kJ a 
_ AYE W 12 
6 

* 9 


„ 8 8 
PPP 5 5 
FEE 
o ö ä 
oy — 64 * * % 
4 3 "oy . 
"I 2 E „ 


So that the Pay of 3 54 Men for 186 days, 
at 24. 6d. per day, amounts. to 8230 U 
707 n TE” 
The Poundage of which is thus gotten; 
Conſider, that every Pound pays a Shilling, 
vhence tis fo many Shillings as there are 
pounds, and therefore divide any number 
of Pounds by 20, and the Quote is the 
Poundage; but dividing by 20 is practical- 
ly performed, by cutting off the laſt Figure 
next the Right-hand, and halving the Re- 


mainder. gn" # 
For Example; What's the Pounds 4 ge of 
of 8230 J. 10 d. at 12 d. per Pound. 


: 8 c : 38 * 
* 4 0 2 1 b 
23 | © | «1 
1 | ; 


: = 
* 


6 ae — a —ü— anne 8 * e 7 2 
411. 1010 the Po „ , 
4 » 0 * n s 85 * 
: \ 
” x ! : Z . 
A FEY — ; " : iz ©» 7 VF 
'F YZ — 28 1 * * * * I \ F ** 4 * 6 


| The Poundage of any oddsbillings is com- 

puted, by ſaying, If 20 s. give 12 d. what 

_ ſhall any other number of Shillings give, 
according to which Rule the Poundage of 

10. will be 6 d. and 5 s. will be 3 d. 8 5 
Next for computiting the Ropal Hoſp#- 

tal Money, which is one Days Pay of each 

Man in a Tear; ti done thut. 


Fr : 
* V4 . 
* oy 
* 
* — " 
. * 
0 4 


| . 15 
A? L 2 | J ( 
8 5 7 3 3 a 
e : a 
* = | Y ' 
. 7 * 5 * 
5 % 1 5 2 0 . 
Or” : 4 © . . 
: * . | 
* * * 4 1 * 
. A * 7 7 5 . Av | oy 
* . * "i U 7 
A „ 
1 1 l 2 $ 
* 


SS. 
7 ob 4 
, 1 3 
LAs + 749 
. 
* , 
os 7 


* 


— Es "yy 8 g . ; ; 4 — * 7 
: | 


Y — 


Exam. What Money is due to the Roya! 


1 # * | Rp : | - TO 
= Hoſpital, from 354 Men for 186 days, at 


25. ö d. per day 0 | —_ 
354 Men at 2 6 d. en Man! 


| U 
* wy G k ? , 35 hy . 4 


708 
n 


886 


82 * \ | * 


From this Calculation tis evident, that 
if the time were 365 days, che Money due 
to the Royal Hoſpital for 354 Men at 2 5. 64. 
pier Man, would be 44 J. 5 s. But ſince the 
number of days are leſs than 365. Make 
nnn no notes, 


- 
8 * ; ; 
* 4 LS 


Fe TS... 


em). N 
1265 days give 444 $5.4 whg will 186 6, days 


Dre: £24 425 22 18511 +: 24111 14 Tb . 


207 346035 40811. Sadr an 


W 930 464Y 310 101 27 ID 


3 29951, . A 9 z 1 
: 2 


F itt: 
20 Ran If 1 HS ori "$93 ) Ta kg 
104 85 


11 5: 101 bert 39 f 


AQ da Ir alma 164 
+ URS eh de 10 yonolM 


if n 


Ju maltichag dig third mam IO 
ſecond, I do 25 Ptactieally 
ply the days by aps y the Pou 
Shillings above;che 
2 theh 1 in oe 


2 e 
leſs than 3 Decimal —4 


0h RSaeu WE Io ge 
1 Ing VACALON, in 

Tak „ 
18 22 


* eig \d £13v3 N bagoiw 
65 V 


SY 


n 9: 3 10 ener f 


i, . the k 
e . 


8 


1489 


ek Þ ir che Ums be more tan 36 
days, the like Proportion muſt, be made; 
— bf: 1 Ts be Jalt 2 3 or more 
Tens, for then tis but Dag: a PS. 
Ce. the Süm for one Tear. | 


| Note +3 The Officers, cho bey have the 
— of days, y et, becauſe, their 


is differences ere muſt be 2 
portnt Gy Shade for each Officer. 


For Example, What's The. Royal Hoſpital 
ty for 186 * 21 : 


ee iir 5. An 
_ wendest A 35 


* . 
„ : 9 & 
« * 
a * 
* 
. * 
Th 4 


1 


P N | ane 


. — u Peng; e e 5 
t che 
whole Sum. T1 fob omen env 1 | 


U 


8 * 


0323 ) 
to the Agent, and therefore divide any num · 
ber of Pounds by 6, it gives the number 
of Shntlings the Agency amounts to. 
7.4. $7 Ax, Ei 5 W 7 128 


an e bar che re. a 
4860 771 kh 1 


 rhax balk; 1371 1 9 4 
' Qr, 68-144 99.qbe 


che ire, 


2 1 29 ono A 


4.of 2 Shilling, which is 84. and the 


9 d. or 68 J. 113. 9 d. the Agency 


*. ks. pk 1 e d nc 155 ow 1: 

ore, Th «1 Hap 1 im ſmall guns 
is nearly of che — as in the preced-= 
ing Cafe, Which is, a large Sum, it differs 
not 20 5. and therefore in ſmall Caſes, as in 


| horror orga e take 5 


of -{gepcy.t0ri Raa | at; CD of 51 GE 0 


h 52884 1 Wes 30) 161) ei ogg wor bee } 


r. bh © Ws. 


-+qx3_ 08 261 ba: 5010 26 iop0y1 1-124 A 


* 8 "£3 4 4 7s 4 4 , 3 
EN 21 + $A. 407 448 


0 cee 5111 2"; * 


. PLES 15200 comes to —4 


Is r* 1 (Que- | 


E 
* "+ 
—— 


* 


a hs... 
# * , 
; X ® 


A VEST ATI DN; rv s of 2 


= | | Wiſts jltn to Aden 0 
1 Soldiers and Seamens Wages : 
bo 4 5 8 oſt I "Computation of Subſtance, up- 
= en * e Occalione. 


— 


T. pay 0 one . 8 d. per day, 
hat's that for 48dοο Men? SO 
1 $455, 320000 d. Or 1333 (. "64. 8 4. 
#4 . 5 92 Ade paß ol one Sanity be 13 Fof on 
. S Month, "6r 18 Days; how much is chat r 
i 2PM (go fs 3600862} * | ir, #:0068 2 7 
1 n eee A 
* 885 hat 8 doth that Ay c 
off which hath 856 Men in 54 
FH ue d, e 
Dopa 27 BY 28 N © > 30 3 een: 
exHdid ii rue -By Div wdw 10) aur 
r bis x os ot 
« = -:Suppoſe there beiotderedrfor 2 Rufe 
/ of 38 pieces of Ordinance,” 1824: 

4 | TH how. much is that for each Piece 
—_ Anſwer, pound. 

Wn > I 35227 be ordered for an Expe- 
dition of 180 25 t's the PR of 


0” ATI 


\ of; | on 
A 


{ 


n 


% 


. 


fb 


4) 
4 
i 

Us 
7 
* 


5 c 325) | 
Admit there is ordered for the Soban⸗ 


ance of 1265 Men, 4832 4. 10 . what 18 


e 1 71 162 For 


"He a Battery of 4 ee was ere 
Qed before @ Town, from the firſt Was 
diſcharged 2 Bombs each hour, from = 
Fg 3 Bombs, from the third 
| from the fourth 5. *Tis gar? re, how. 
many hours they will all re 658 


bombs? 4H 47 Hurt. $2 Ye 


4 ar | 
rig * lun, 5185 2 7 


þ FR 43 


. ere is * FR 1 „ 0b 


ſiſtance of a Company, conſiſting of 60 
Men, 1501 the Queſtion is how many 


days it will ſerve them, and what each © 


Man muſt have of it CONS ®c fol- 
_ lowing Allowance... + 3 Vos 


2 Captain 36 pence 

A Lieutenant 24 pence 
An Enſigu 20 pence 

A Serjeant 12 ay 

A Corporal 8 pence 

8 e Soldier 6 pence 


N YO 


gives the number of days it will ſerve #hem; 


if then you Multiply his —_ of days by 


* Y 3 Py” each 


IT e K in 13910. 55 . 3 * all 
ſe wages per day,reduced imra-Pence,the Quote 


i 
: 
* * 
* 6 
of 
* 
. 75 7 
2 1 
77 
S's 3 
4 - © 
2 
L211 
1 0 
4 
7 1 
- * J 
3 
I 
_—— 
_— 
a 4 
©" 
- ER 
: 


2 * Man 2 per {oy _— Siue you. the 
Money each Perſon muſt receive, | 


Proceed thus, and you. will find e 


will ſerve the foregoing Company of Men 


83 days, and that the Captain, will re- 


"Wi ceive for his ſhare 12 J. 91. the Lieutenant 
8. 6. Euſign 6 l. 18 . 4d. Serj eant 41. 
35. Corporal 2 J. 15 5. 4 d. and each private 
Aua 2 1. 1 6. 6 d. beſide 1 l. 5 . 10d. left, 
— which will not give cach of them one days 
* | | pay More. 45 * N 
2 Suppoſe, for a Battery of 4. pieces of Or- 
dinance, there is, appointed 12 C. weight 


ee 3 each 8 carries: at a Shot as 


; 4 F "= 
3 Ful 14 4 ponad, Fe W e 
1 3 Second 1 2 pound, * 75 A 
8 ; bf 25 ; +, | ; * | 
R$ Te 2 0 
a Fourth 6 pound. 1 n Vt 


5 How many times will the ſaid Powder 
diſcharge theſe Pieces, and what. 
allowed to each Piece? 

This is done juſt after the fame manner 
the former, and the number of times 12 C. 
= weight will diſcharge the ſaid Pieces is 33, 
* auf the fi firſt ſpends * the ſecond 96Þ 
= eb 2644. He fourth 198 1B. ef. 


int 4 i 


9 1 "2 2 9 1 2 5 n bs x i”, 
c £1 0 OE TT BK, 
Y þ Fr 5 ; 80 p 1 2 4 s 5 #5; 
. 1 : - 
mids . 5 
9 


mos. 751 


was "os 0m: wm" "MO le 
Round, | | 


ing of 1150 Men coſt 496: 
that for * Man 7 b 116050009 I. 


(3270 


R yy 4; 105 4 & N 2 re 75 2 «A —_ 20 nf * | 


ad Rule of Threti-29 =— * 


nie "$4 J 


os r of 890 U Men for one, day be 


361. 175 A hat onen days? 

As 890: 3607 6 $ 4:26 3 

3 near, 2 N EN R 15 
Suppoſe 35 15 l. 195 be be ufficiens to pay 


2 Garriſon of tag Men a certain time but 


there is occaſion to reinforce the ſaid Gar- 


riſen to 3000; how much Money muſt be 
ordered on fuch an Occaſion ? Sayy ari25904 
* fx _ 


3515 J. 5537 zoo 84374, 


/ wer. 


Admit; a Garriſon bas gag Men in ir, 
out of which a Detachment is made « 
2126 Men, the. Subſiſtance for it at fi 


was 966 J. 13s. what ought it o he now > ; 
Say, 85 ae 5 : 740745 $35/ . 3 5, | 


8 4. Anſwer. | 

The Yearly pay of 1960p FARES FARE 
17 5. bur Money 
allow'd but 1101 561. 14 how Jap of 
theſe muſt be disbanded to make the ſaĩd 


4 Sy 


; 22 72344 


3 5. 4202. A thy ein) 


"4, 5 W 


1 che he Coating of a Pan, "aan t- 


Ant 1140 * 8. G . ks who "TY > 


1 bY N.. 


* N: , 77 20 91 14 2 922 


8 e T3. Sog 


? 


ſhort there can be 


Allowance ſerve 7 Sep, 4 18260. 1% . 


* . 


11 5. what 3s 


if 
4 
NN 
. 7 
ov 
. 
pf 
„ : 
5 2 
1 
* i, 
«4 ” 
. 
«| $-4 
| 1 
* 2 * * 
| 
1 
G ;£ 
$1 
i 
' n 
! * 


8 — 
n 


r wa 


„ 

Suppoſe part of 2 Regiment are ordered 
on an Expedition, the humber of which, 
9 their Subſiſtance, being as followeth. 


| b 910 i nr des EE 015 254 
as One captain at y. whine) day. 1 Ea | 
N Lieuteriant at 6% 4, d por day. | 


An Enfign at 47. 7 d. per day: ns 

bs Seren ut r 5. 4.4; each ptr ay; Je 
1 4 y 4. each per Gaye” Was 

: 37 BA 1 111 601 . 

ow wack/ Money Will ſoffice -theſe 

Men for 270 days p. A, 1 tothe Sum of all 


e day: 270: 1369 J. 9 'tbe 
K Sone; receives ſor 3 Montbs 2 Skye 


pay 6 l. gs. what 1 His pay! rofor 4 
; Fear ?“ Say, 4. 86 564. * i"; : 365% wed 


12 . 1-04 near; Anſw 
alle hah 8 


* Cinumiſſory. of — 
to give for the Carriage o 


Ammunition 170 J. 10's. how much muſt 
he give f6rthe'Carri 


10 CN? J. 70 / 1266 2 
bY 1 5 Ne 4 0 * 73 K 
e often for e 
2 of Sali Peter; 6 15. of 9 abs 
ONES = 
Gel 6 ions W t 
of Powder. 2 Nd 10 2771 7 34 pit 
Ne Chief nr took with them 
a ſmall Body of Men, the firſt 600,7 the fe 


E 550, and * 1 _ w 


9 
* 


720 C. 0 
of 1260 C. r * 


each harty? Say; as the Sum all a Men 
to => whole* Booty, ſo it each Party, to the 
Booty. Proceed thus; and yok ll 


(329) 


| take a Booty of 1200 l. the Diviſion is co be 


made according to the number of Men each 
of them had; what muſt be the ſhare 


the- 


frſ 6 Neo NE the ſecond 181. 7d 
third Goal. ane +50 ONS 1 29 12 


= 3 As. * * N j- „ 
* 1 „ TS 1 
2 ? tu © 4 „ S 
4 


1 5 
: 4 : b 4 
* 8 14 . * 1 
n 1 1 
— "7 Peck oh 
y s, 
9 ; 14 4 7 ** 


Six ere 25 e «@ 


Army 
by: by the aſſigned Men in Rank (or File) the 
Quote (72,) is che e N. * 11 be in 


" 4x . 
1 1 * F | : 


£2 | * Yor 1 WIN 
C Ma ee Soldiers 

(ſuppòꝭſe 36000): in ſuch ors 

* 12 Butcle, that there ſhall be any aum- 


* ber in Rank or File. Suppoſe 5 o in Rank; 


211 there be in File. 
Divide the whole Number of the 


File (or Rank.) 8 zach 


Prop. Oo Min ca of Sol- 


cer, ſuppoſe e in ſquare Batrs· | 
np Th £51] 57 rd 

_  Extrat the "4 or Rook bf 65536, the © 
number of Men propoſed, {twill give 256, 
the number of Men that muſt be placed 
both in Rank or Flle. Prop. 


* 


330). 


ble ro thoſe in one File. | 

Extract ce ſquare Root of 17956, which 
is half the number of Men propoſed, it 
. 13 
in File, bis dgubled, gives 268, the num- 


numbers multiply'd together, will make 


right; x 


Prop. 4 T6 — any number of Sol- 
dices, ſuppoſe 12996 in a Battail of the 
Sead Hom, Which is in ſuch order, that 
= © the Rank may be four times the File. 
j Extract the ſquare Root of 5, the num 

ber of Men, which is 3249, it gives 57, the 

number that maſt be placed in File, this 57 

multiplied by 4, gives 228 the number to 

be placed in Rank, and che numbers to be 
in Rank and File ene 9885 
| ther will 1 the whole Arm. 


Prop. 5. Any nb of Men ith 


their difkance! in Rank and File, beipg pro- 


Fer Stoned to 35 them! inc 8 _ Bate 
of Ground. 5 


* in a * Battail of N 42mg in ſuch 
| FO TAR e 


0 Ft 
1 n roher any . of Men, 
n 3571 2 im double Battalia, rhat 4, 


bh ſothat the Men in one Raute; may be dou- 


4 the number that muſt be — | 
ber that muſt be placed in Rank; theſe two 
up the whoſe A. bed me * 2 I : 


'S Suppoſe 25000 Soldiers wete to be Mar- 


Wane wits 


. 
TT n at. r LP OY ALBEIT YT 


— — 


divide 48600 


03 
order, that their diſtance in Fe ſhould be 
8 Foot, and Rank 3 Foot; tis required to 
know how many Men muſt be in Rank, 
and how many in 9 \ 
Say, as 8 to 3, ſo is 25000 tog 9375 the 
ſquare Root, N nk num 


ber of hien ic be placed 8 Pie, Then to 
find the number of Men to Be placed in 


Rank, divide 25000 by 96, the Quote 26 
is the number of Men to be placed in PN 7 
beige 40 Men over and ee 


Prop. 6. Any ann of Soldiers pro, 


pounded to order them in Rank and File: | 


es, to the Ratio of "any two num- 


Let 48000 be the number of Men to be 
Martialed in Battail Array in fuch forc, that 


the number of Men in File ro) thoſe in Ranke 


ſhall be as 8 to 20. 


Say, as 8 to 20, fois 48000 to does de 85 
ſquare Root, of Which is 346 Heur the num 
ber of Men to be placed i in Rank, by which 
„it gives x 38 the number of 


Men to be mk in File, bell de bl Mew” 
that are "oe 


* 
5 mY N 
0 : | s a 8 
* 7 . 5 : 4 . * 1 . * 4 & 8 Bid 4 
x WER F | "I, 
TX 


931 
— * 


1 | (433 *. » 
=. ed blyodi * ai Di tied: 280 oe 
OS) 41/063, 1853001 5 ane ins 10 1 
| are q a fi mm, wo: "won 
are 7 O0 r 274 Fe MA | 
@ F — {hal}, not 8 1 3 
0 4 * Nee _ me»: 
| g Hulgarly, Necimally and 
Fact call, = the Cuſtoms uſed by Ar- 
rihrers tor Meaſuring: their ſeveral Works, 
in a Book lately bubliſhed, Eacttaled, An Epi- 
tome of to which I refer the Reader. 
And therefore I ſhall only give ſome ſhort 
practical Rules, neceſſary for ung up he: 
Content of a.picceof. Work. 
Of Meaſures there are three ſorts, Ui 
EE 
e, Which relpects only length; | 
| al, Meaſure, Which. reſpects Superficies, that: 
m, length and breadth ; and. Solid, which: 
reſpects. both bah breadth and thick- - 
neſs, more than N le cbere not in Nu 
El es 120 
. N I hall not run igtg- the, 
Mleaſurement of all forts of Figures; but in 
this place content myſelf with giving you 
the general Rule for all four ſided Figures, 
| whoſe oppoſite ſides are Parallel; hich 
_—— Rule is this. _ 
_=_ * Multiply the length by the breadth, ns the 
=. I - FR * the Content. £8 


r Oo eh ER. on road 


3d 10 2095IGO09 orig * zonal. 


$ Ego Ew 


| e by 12, it ies 17 Foot 4 Inches. 


r 
eee uppoſe Abe dag a! Subor- 7 
Leid be Foot 10 Aneties *g br eadth * 


14 Fo 


Inches, what gi ares : Þ» = 


i 101 Bel Gene Mel 6 10 3 2 brig | 


2 dan d Fuck d d tab 
-ons(Q 120014 312 1 50glq idw lis 
tet 2397Y 1901-30) 245b8 ed anongagt 
100T 


. 364: 05 mack, i 
, * ws ſl 7 * 0 " 


8. 105 
N 
8 29 15 
= 
/ — 1 
7 . & 
* J * i 
. LM Kin 
4 1 Tt > of 1 
s / 3 be. a 15 
g e be 
© «< * 0 3 ly 
p „ Wy { 
"ng | 
. . ” As *Y . 
* + ff 
- : 
* 


Hou? A” gil 32971 
41 303. 8 Parts. 


Q 1 | 1 2 


| The mat Manner of this Operation is \chus. 7 
nrſt. the ſeveral Denominations in the Aalti- 


_ Nicang, ate multiplie& by .the Integers in 
he- ſaid- ſevera 


ine Multiplior, then t | Deno- 


| amine Multi, N y the = 

: A in The preceding — 1 mal 1 
ply 26 Foot by 24 Foot, it 3 4 364 Foot, 
ine 8 * rg Foot it giebt 140 
#5; They cles etel com te 


211: Foor.% Inches; — 
it es 255 Inches, which 1 


* 1 
ply 26 by 8 


h, 


P. 
9 
1 


5 © 334 ) 


* L multiply the 10 Mcbes by 8 In- 
ches, it gives 80, which are parts of In- 


— ——— O 


ches, Bs deing pieces of one Ich lon 

andthe, of an Inch broad, and th — 
Fainide them by x2,1t gives 6 Inches 8 parts, 

all pink place under their proper Deno- 


— theſe added together gives 393 
Finches 8 Parts, the content of 7 


3 12 17 # hs wh 0 4 1 
A ein 
NM 
od — 
2 hene. gore bh 


e 


| 1 B al ; "WW 4 11 E 

n AI 00471 7 win A £2 48 55: 1 

92 8 us Tok : 5s - fs "> i 15 5 * 
1 * ; | | | 


* 


4 ; ps * * ? 27 Fl . e 12 a "Ms 
8 e ES _ "2" "=—_ 
HQ h x 7 = 5 ; ” ; 4 
— CL * af & 
VI — . K 5 
$77 * # Shy 91 15 5 "RAY 7 . * E. 
4 ** r $ 1 'P 8 $ 1 7 4 * wy 199% by 2 If ; * 3 


38. 3 9 iN 5 Be 


bY Ab ir . 150 | nf EY dT 4 5 N 44 A 
38. 11 pr ! 2 > WW £09 | ky 1 
1080. 2.32 # ee e 
251 70 client 7 A 
i ien ig c d wil 
ly, If che works. valued by the 
| Rod, y et ſtill the Dimenſions 18 his G 4 ö 
taken and a 0 in Feet und Inches, nad 
afterwards rede d to Mute Tatds by d-. 
viding by 9, and to ſquare Rods, by di: 
E che 2240 2 35 but moſt Artifcers neg - 

ct the 2, 4 N a1 


Neuen ic 


alued 155 he — are . LR 
2 den 5 * a . 


ee Jo | 
12 


8 8 50 oh 


4 


: OR 
x: NY 


* « 


0 336 * 
into. 12 1 Parts called Seconds; 
each —_ 42 "I Parts called 


Vhirds, &c. 4 1 


5 4 

f » 14 ny 
af 
| 


- 


Fifebly, That Akkrent 
will give different ProdpRs, . „ 
As Feet multiply'd by Fea gies Peet. 
Feet by Inches, gives | nches. 


— ws . * 


— + 12 
. 97 4 1 1 Fs 4 
F . + 


which is Rag Gat ro be fore has be Brick and ha 


chick, ſuch à piece of 


eber or thipner than d halt, 
IS or lels; an a R has 25 N j 


wy vG bagls 8 2 


ee 


4 


9 


muſſ be fed ro ſag 
dane thus. ),. ts : JOE? dz 2 


Ws 


5 


wg 


all the Dimenſions to half a Brick thick, the © 
gum of theſe Dimenſions diude by 3, and thas  _ 
gives the content in ſquare Rodd of Brick ani © «+ 
half thick. : he | b 0 1 


wy 


Exam. Suppoſe the Dimenſions of ſeve- 4 
ral pieces of Brick. work, with their thick. 4 
neſſes as followeth, whar's the Content 


* . 


. +... F 4 , 8 
. M$: - F 4 % *4+ 2% ; 
* 1 + 3 ; 
4 £<v + 4 } 9 , ＋ f PI 
— 4 Wo a ww 4 ia 1 1 ; 


F. I. Pts. BG £4 an 
A : S ? ' 
RY "4 » . = > 


— 


1 8 ; % 


- > — — „ 1 . 14 
ſquare Feet 3416: 11: half Brick thick. 
8 . — — | * 8 5 3 1 5 


4 


” : 44 


109 | 3)341 16 "48 | 


> 
+ 


27201 13804 Rod 5 5 


* 
x * 


oo; 
» 


oot Co 


. 
* 
— 
4 
— 
4 : - 
4 ” * er 
* © __* } 
. 1 
» * 
2 
Py 
of * 
; * 
8 
2 . 4 
, 
" M 
* * 
o 
* A 
: 1 * 
— LES 
* . 
> 
. 
5 * EY =4 " © 
** * . 
50 * 
5 5 
1 
„ - 
a 
bo. _ * 
g o 
: « 
* - 
* 5 ” % 2 
+ . 
0 8 
2 
2 « 
3 
9 1 3 EY 
on * + N 
as \ 
oF : 
: * * * 
. 
. 2 bs 
. * 7 
. 
* 
— bY * o 
by G ” 
<A I” * 2 * * 
E Aa* 
<X 2 
E. 4 fy. * 
bs. 
--* . # 
2 — E 
. * P * 


1 4 * vs * * 
Sz „ y © 
p : ; 7 : 4 : x « 
wi a * wt 7 $ 
* „ 5 . F 1 K 4 » 
I S * N © 
3 — 3 
. . — 3 od e 
- * 1 
* 


. 88 $.5*t Anh * a e 7 4 , 
So that! in thſe Dim Gons there is 4 Rod; 
30 Foot of Byick-work of Brick and har 
5 7. Thick. 1 bo DP . N N. W an 


7 


3 of Solids. 


Mie mode 24; ode 


Foot 2 Inches thick, What's t 


or Solid hath Lernt, mail and 7 ak 
nels. 1081000) S0 21h hr 95 r 
And therefore to Meaſure a Cube or Pa- 
| rallelepipedn. JT. 
, Multipl the fo "gth by. the Breadtb, and 
that Product again by the Thickneſs, the Pro- 
ali i is the ſolid Content,  — = 
By this Meaſure is  miaſticed,: Stone, 


| Timber, and digging of s and Cellars. 


* 


- 


4 - 


Exam. A Block of Stone 15-8 Foot 6 In- 
ches long, 4 Foot 8 Inches broad, and 3 
| e Content in 

ſgqauare Feet? e | 


Pe EE. OE —_— 


jo ne 


. by Fr my, 6-56 "SEL * ry 1 . 1 * * q 
nn 1-406 1ac $551. 55.00 


gw © * . 
: 


| n 
\ „ 
FA * \ = „ 
\ N 32 7 % 
e is 1 = * : , ; " * 
5 MY. / 4 
& < J * 4 a) . i - 
8 | /- JE FSEDLE 1 5 
Ss ane Pp 
4 : — — * 
4 ag” y L 5 
100 o 50H „iter : 
. - N * b 
a , N 8 — * 8 44 1* 4 © 7 1 4 4 - 
5 8 8 * 2 - = * 
W x N 1 * "oy x. < i 5 1 


* 
- 
* 
* 
3 
* 
8 
* 
＋ „ 
& 


- 4 ; » 
: 3 * 5 2 * * 1 
| ; 4 — 
; Fs £3 ot OT : * : ” 
: * " * 4 * 
8 7 IF 8 — bs 5 
8 * & 
55% z 
” * 2 I, x "a * 
. - — * - 
N. 1 * £ . * 473K. , - FS * x d , * \ 
* © % : > Ss. % * 25 a * 
0 * vr , bs . 
d 4 * N * A 5 * \ 8 
4 7 4 * # . * 5 þ 
* "wa q 
: „ N ye. Mend ot 
4 ; 
* * 9 _ 
: 
' 4p 
* * ” x . * 
\ 1 : * F * % * 
7 24 * 
8 x . e 5 
* 2 * 
l | * ; 
— 7 * $ 
e * 
* 
2 : 
4 | 
7 * - . A * 
7 7 n JJ et 
% 6363 7 . 
i 1 ee 3 . 
CI * — Ee" 
8 5 3 a 
8 - * : FEM EY — 


"4 
= 
Fi * 
9 
1 
45 
* 
+ 
43 
% 
* 
— 


_ 
TP 


£ 
7 
* Fa 
s 
* oy 
* 
$2 
Fo 
Fd 


1 * 1 S 1 — A 1 L [ - c & "2 N 27 g g : * * 
- ; 34 & 4 8 8 * EY » 48" 
4 5 * . : 4 ; # 
F * IM 
= - * 
Fo i 7 


„ 5 11. 1 % 
9 3 : 3 ” * 4 oo i - $4 * 5 5 5 - H # > 7 2 4 + . 
. #3 * 4 0 


80 chat the obs of fucis 
Stone 1s. — wha bes, 4 Parts. 7 
Nate, Digging done 55 the ſolid Yar 
and therefore x ben you have brought your 
Dimenſions into ſolid Feet, you: muſt re- 
duce them to ſolict Tards, by dividing the 


ſolid Feet by 2 12 bol 1 in a ſohd 
Land.) 2 tnt gt 1 


Epitome of — 


8934 | * 


# 


Hs 


0 340 N | 
0 n iS ging of one Figure to another. 
N 5 I ſhall . Fare this with giving you the 
I following .ccount of che Dimenſion and 
nf Tale of ſeveral Materials for Building. 
1 A Brick by the Statute ſhould be 9 In- 
* ches long, 4 + Inches broad, 2 3 Inches 
* thick, 500 makes a Load; but are gene- 
4 rally ſold by the 1000, Plain Tyles for co- 
"  - vYering Houſes are 10 ; Inches nds, and 6 I. 
| broad, theſe are alſo. ſold- by the 1000 
which is a Load. Tyles for Paving arc fore 
a Foot ſquare, others 10 Inches, they are 
about an Inch and half thick, and are fold 
by che Hundred. Lime in London is fold 
by the Bag, which ſhould be a Buſhel, 25 
of theſe Bags is a hundigd of Lime. In 
the Country tis ſold by the Load, which 
is about 40 Foot. Lathes are ſold by the 
Hundred. of Which the is bur 5 ſcore 
of thoſe of 5 Foot long,-blit-6 ſcore to the 
Hundred of thoſe of 4 Foot long, their 
DYED is 1 3 Inch, thickneſs ; an Inch. 


Timber is ſold by the ſolid Foot, or elſe 
y the Load, 40 ſolid Foot makes a Tun, 
50 Foot a Load, 324 ſolid Foot; that in, 
18 Foot ſquare, 3 — thick is a floor 
of Timber, 300 Foot ot two Inch Plank, 
200 Foot of 3 loch, 150)of:4. inch blank, 


400 of Inch er Plank, and 6oo of Inch 


=: Plank makes a Load: Deal boards are ſold 
= | bythe thanded, .offanbich 4 8 — 
3 of | Sean NA 27 1 . _—_ 2 

ET 1 bes. „ Sh VP 5 „ 


f 


„ 


a © 


18 0 34 
hen is ſold by the Tun, wich is is 20 oC. 
weighs, or 2240 i. 

„ Lead goes by the Fother, whichls 19 8. 

or 2184 16. 

* Gag is ſold by this e which is 24 
Stone, or 120 fh. New-Caftle Glaſs has 25 
Tables in a Caſe, 5 ſquare Foot is a Table, 
45 Tables malelha Caſe. Nor mandy Glaſs 25 
Tables is a Cafe, which is cut into long 
Squares, the other Diamond Faſhion, - 

If one thouſand of Bricks coſt 15 5. what 
0 35 Load each 5 C. Anſw. 131. 25. 6d. 

A 6 — of plain Tyles at 19 5. 6 d. 
Po: thouſand, what coſt 6 thoufand and a 
quarter ? Anbw. 61. 1 5. 10 d. 5. 8 
If Lime be 5 4. rer Bag or Buſhel, what is 
that per lindred? Anſw. 105. 5 4. per C. 
If a bundle of 'Larhes coſt 1 l. 4 d. what 
wen 3 bundles? Auſib. 3 l. O gd. 
A a: Deal. board be worch 14 d. what is 
| char per C. that is 320 Aſp. Towns 
If Timber be worth ro d. 5. per Foot ſo- 
1 8 is that per Load? Lale. by 


1 5 2 Rod of Brick work) be worth 5 * J 8. 
hae comes 9 Rod 113 Foot to? Ale. 


49 I. 8 5. 7 d. near. 
f the rene nſhip of 2 Rod Br, Brick- 


ork be worth 205. 64. what is 27.2 Rod 
Yun ? e . Nate es only - 


| BB ads 2M 


8 4 


* 8 


1 


* o 


"BAY 


a WO. 
3 ling be worth 24 uare, or 
100 Foot; what is for 8 Square 83 Foot, ? 


Anſw. 101. 11 5. 11 4. 


If Stoping, Waſbing and Whiting be worth 
1 d. i per Yard, what comes 2716 We 
Aren. 14 J. 23. 11 4. 

If out Door. painting be worth 6 4. z ber 
Yard, what will 1486 FW. coft : : Ae. 
40. „„ 

If new Glaſs be worth, "4 < on Foot, 
What comes 634 Fot tor Anfw. 135 

5. 2 4. 
4 All theſe . are "moſt cabily,and 


ſpecdily e d by the Wn in entice 


f The follwi 0 Table is the 8 of 


' . the. Enghith Standard Foot, irh the 


"Srandaed Foot of. ſeveral other Coun- 


try Meaſures: By Mr. John Greaves, 
Profeſſor of e in the Uni: 
_ verſity of Oxford.” 


11 * * 4 
- * 


F the Enghſs. Foot "_ givideds. * | 
into 1000 equal Haris, then of 1009 
* theſe Parts 


The. Roman F00: contains — - 2 — 967 


The Ft of the Locle of Storm, 

kilius in Rome — A 
The Foot of Vill. e TWP go 
from the age of Pan} 9 556 


„ 343 * 
The Greek kot — 1007 
The Perſian Foot ———>————3197 
The Venetian boot 1162 
The Paris Foo: — — 1068 5 5 
Rhinland Foot of Snellius —— — 1033 1 
The greater Turkiſh Plos at Conftan 
tinople ————- N22 200 

Thelcfs Pico 38.10 the greater} 20 3 110 32. 

The Dairy or Cubit, at Cairo in Egypt, 1824 
The Canna at Naples — 6880 
The Braccio at Naples 2100 


The Brarcio at Horence . 19 ] 
The Bractid at ienna fot Link — 1 i 
The Braccio at Sienna for Woolen 1242 „ 
The Genova Palm — 815 
The Vara ee and Gibratter in | 

Spain ft 760 
The Anton, 


* 


: | : . 
a La 
-aa 21 0 20 N GONE 1,2 . 
7 . 4 ha b "XK # * * "— - 
8 f 1715 . 1 „ aSIS.2%5 5 2 $ P IV TE g 
* : oy | a ; 
5 2 * ” | 8 * : . 


** 

£2 

2 

2 
2 pr 
2 .5 


a + 3% R 4 71125415 T7 17 1 . 1 
. N Ol 2 


epa. an p 0 40 Did 20 G1 K 
BE Ye ö 15 ro 34 „ie 5 % 


4.7 


= ® + . —_—— : * ”) 
; ; "=. nr 3 1. Anse 
. NN I 10 A f 3 

4 L's d 4 K 301 05 3 


* * 4 
— 1 3 ; Fd, L 
* 47 53 | $83.2 3©' 212 48 TA F775 * Proc 
b 4 FF . 4 5 N * N 4 8 2 — 4 


133 
C 


| Collection of queſtions 
To Exerciſe moſt of the 1 


Prece 0 nn Rules. 


> + 
£5 8 
- 8 


0 Adina. = Hh 
"Rom the Toning: of 5 World to to he 


Flood is 1656 years; from the Flood 
ling of Abyabom. 366 Tears; from 


= 


ro "he cal 
Abrabam to the giving of Moſes Law 431 ; 


from the giving of the Law to the De- 


ſtruction of Troy 347 ; from the Deſtructi- 


on of Troy, to the Building of Solomon's 


Temple 192 ; from the Buildin of the Tem- 
ple to the firſt Olimpiad 2163 from the firſt 
Olimpiad to the return of the Captivity of 
Babylon 238; from the return of the Capti- 


wity, to the third Charthaginian Conqueſt by 


Scipio Africanus 336; from the ſaid Con- 


queſt, to the Nativity of Feſus Chriſt 202; 


* the 3 of Jeſus Chrif to Conſtan- 
tine 


; - 
* e 2 
2 + £346... 
- F k 44 
— h » f 4 
N 45 


. 
tine the Great 1 2 and from Conſtant ins 


the Great to Charles the Great 488 Years ; 
the Queſtion is the number of Years from 


the Creation to Charles the Great. Aufin. 
4784 
ER Rome. by Auguſtus Ceſar was divided 


into 14 Regions or Wards, in the firſt was 4 
Temples, in the. ſecond 5, 1 the third 2 2; in 


the fourth 10, in the fifth 6, inthe ſixch 1, 


in the ſeventh 4, in the cighth, 21, in the 


ninth 8, in the tenth 10, in the eleventh 
and twelfth none, in the thirteenth 6, and 


in the fouxreemth none; the Queſtion 1 is the 


5 number of all-the Temples. Anſw. 91. 

3. The Moon runneth. thro the Zodiack 
in 354 days, 8 hours, 48 minutes, which 
is the Lunar Year, and is 10 days, 21 hours, 
1 minute ſoohgr than the Sun, What is the 
length of the Solar Year, or Time, in which 
the Sun runs thro? the Zodiachb.  Anſw. 365 
dn hours, 49 minute. 


In Seripture we find mention made of > 


a-Certain King that had the following num- 
ber of Men to wait upon him, under Ad- 


nah 300000, under Febchanan 280980, un- 
der Amariahzo00000, under Eliada 200000, 


under Fehoſhabad 140co0,,, What was the 
whole number he had? Anſw,,i 120000. .- 


7 © 


5. The number of the Inhabitants of Len- 


dom are reckoned 695718, of Paris 488055, 


ber 


of Rome 125 00, What is the Shah num- 


» 1 
N Pe 
* Ai x 4 
. 53 * 


( 346 * 

ber of Inhabitants 51 theſe three Cities ? 
| Anſw 1 308773. AH} 
6. What's the number of Days nd 
betwixt the 27th day of March 1701. and 
the 17th of July 1702. Anſw, 471 days.” 

It is reported by Srow, that Brute, 
who deſcended from e/£nezxs, built the Ci: 
ty of London 1 108 years before the Nativity 


of our Saviour. Ho- many e is aber | 


. fince? Anſw. 28 12 | 
8. The Birth of Feſws Cbriſ was in the 
47 r ath year of the Julian Period, that is, in 

that year of the Julian Period, the Chriſtian 
era began, What year therefore of the 
Fulian Period” is this A man your I IMS Y 

2 bor e 


o Surat Oh 4 E 7 
9. PAO 0 was Born in Wurer ”Y 
the year of our Lord 1664: - - How old {wil 
the be in February 1705,  Anſw. ar. 
10. Prince George of Denmark was Born 
ji April 1653. How old will he be in 4. 
* 1705. -- Anſw. 5 1. aeg ar 
11. By Queſtion, che" firſt: you' 
that the Nativity of Feſ#s Chriſt was In the 
the 398ath year of the World's Creation, arid 
that Charles the Great was in the 4784th 
year of the World's Creation. In what year of 
Chriſt was Charles the Great? Anſw.in the 


Jah year. | 


12. The 


7 


* 


bo 


(3972. 

12. The number of the Inhabitants of 
London are 695718, and thoſe of Paris but 
48805 5, How much doth 1 endon exceed 
Paris? Anſw. 20 7663. 

13. he Buildjag of Rome, ere 0b 
Varron, Was in the 396th year of the Juli- 
an Period, and the Birth of Chriſt in the 

47 14th year ofthe Julian Period, How ma- 
ny years befere Chriſt, according to com- 
mon Companttion," was Rome builr : ? Anse w. 
— 5 4. The namber: of 8 piritual TORE Fl 
— * in King Henry the 8th's Time, 2- 
mounted to 320180 l. 10 fl and in the fame 
King's Reign there was taken from the Po. 
ſeſſion of the Clergy, and Converted to 
Temporal uſe, Promotions to the value of 
161 100l. 9 5. 7 d. What remains now to the 
n Anſw. 159080 I. o 5.5 d. | 

16. In the year 1 174. Henry the 2d. Con- 

er d Freland, and annext it to the Title of 

he Crown of England, how long is it ro. 
— 17056 Auſu. 5g ,ꝭꝙL;. OD 
16. In the year 1296. Soor land Wah Far- 
rendred to Edward 3d, How long is it to 
this preſent year 1705 ? Anſw. 49. 

17. In the year 1431. Henry the 6th was 
Crowned King of France in the City of Pa- 
74s, ans is it tothis prelent year "79 7 

. * | | 


%* 


18. at 


* — Fe 
* . 


* | 


- C40. 


18. Alfred King: of the Weſt: Saxons, laid 
the Foundation of Oxford Univerſity, and of 


the Colledge which beareth that Name, in the 


Fra: of Chriſt 8 * How long is it to this 
preſent year 1 5 2 aer. & 3 3 Wa 


By Multiplication. 8 


19. „ The whale: 'Cirenmferemte: & the 
Eorrb | is 360 Degree, each Degree contain- 


ing near 70 EngliſhMiles, What's the Earths = 
Circumference - in Engliſh * "Miles * Anſw. 


25200. 


20. In the . of the Spaniards i in the 
year 1588, there were 3 2000 Soldiers, for 


whom the neceſſary Expence: amounted 


each Day to 30000. Ducatoons, 'How much 


will the Expence be in 6 Months, at 28 days 
to the Month? Anſ. 4040000 Ducatoomns. 
21. A Thouſand Sail of Ships are employ- 


ed by the Dutch in the Herring Trade, each 
Ship occaſions yearly the breeding of 4 Sea- 
men, how many after this rate willbe 728 d 


in ſeven Years? Anſw. 2800 0. 


11 22. Every Minute of time the Heart of 


an abſolves 75 © Pulſations, How many 
Pulſations is that in one Hour? Anſwer, 
A. 


People within the Bills of Mortality, coun- 


ting: them I 200000, I is moderatcly compu- 


red 


The neceſſoty ape * all the 


3 

98 5 

"0 
fe 


pa, F 345 99 58 | 
ed at 63667 J. per day, ws: is it foro ons 
Year : 2 Anſw. 23238455 * 7 | 


24. The mean Semidiameter of the Earth 


allow'd by the French, is 19615800 Paris. 


Feet, now the Space that Light runerh in 
one Minute of time is 1000 Diameters of 


this Earthly Globe, How many Feet is that | 


in the ſame time? Anſw. 3923 1600000. 
25. The mean diſtance of the San from 
the Earth is 5000 Diameters of the Earth, 


How many Paris Feet 18 that? ? Anſwer,” 


196 "yy 000000. 


3 

95 — nth 
#4 1 
” + 1% 


oy” Div Nn. 


"i 


4 


26. In the. time of een Elirsler, the 
Groyn in the Kingdom of Galicia in Spain, 
was taken by an Ergliſh Army conſiſting of 
1160s Ergliſh-men, and the Booty they 
there found was valued. at 320000 Gold 
Dwatatoon;,” How many will this amount to 
for each Man? Anſw. 992 EVE: 

27. The mean Blanes of the Moon, 
from the Center of the Harth (as has been 


hinted) is 1176948000 Paris Feet, How 


many Miles is that at 5oo0o Feet to the 
Mile? Anſw. 235389 5 Miles. 

28, The Meant Diſtance of the San from 
the Center of the Earth, is esd 
Paris Peet; What's W in Miles? 
peat 0 unn; 


Fe 8 
of 1s Head goloogbiy} nal i . dp 
= J * * * N 8 0 


. N . . 5 , _ . N " * 1 
* n S l * 9 9 A > td. ; r * 7) 
den li n * Wm 6 5 * 1 * 9 * EE : 9 SIN 5 
4 * R 2 ** ory, >= N * "Ws" > 1 - TO 29 
* 0 , 


* 
_— 1 350. 5 ; 
29. If the yearly Value of the. Spiritual 
Promotions be 1590801, as before was no- 
ted, and it were. equally to be divided a- 
mong the Clergy giving them 120 1. a 
Year a piece, how many will it ſerve? 
Anſw. 1325 
3o. Admit there be within 92 Bills of 
| Mortality 1050000 of People as. before has 
been mentioned; now tis commonly re- 
ported, that x ouf of zo dies in a Year, 
What is the ee of People that dies. 
A1. the Bills*0 Mortality in 2 Year ? 
31. What = 3 is that, which if it 
be multiply'd by 87, the Product ſhall be 
283622 Anſwer. 326. Tre A 
32. From this Propoſiti ition may be found 
che length or breadth of any Parallelogram, 
by having che breadth or length with the 
Area given. As how long is a Court or. 
Yard which contains END Feet, and. 
15 18 Foot 8 * Anſw. 194. For tis but 


dividing the given Area by the no” 
breadth, and the Quore is the lengih. - 
3 by G7 4 H Reduction, | 2 Ar 1 2 


© r e 

33: Admit, 1 employ a Carver at 4 veper 
55 a Bricklayer at 25. 8 4 a Carpenter 
at 2 6 d. and Labourer ar 40 d per day, 
How many days work will 20 l. 1. 8 d. 


receive E 


* all theſe Ken (uppoling them all to 


00 351 * 
feceive for the ſame number of days) and 
How much to each Man? 4. 38 days, and 

the Carver muſt have 7 J. 12 5. the Brick- 
layer 5 J. 15. 4 4. the Carpenter 4 1. 155 
and, the Labourer 31 3 5.4.4. _. "4 
33- A Meddaliſt Jays. out PY © 8 d. on 
curious Quoins, VIZ. French Crowns at 6 Fo | 
each, Portugal Cruſadbes at 3 5. 6 d. each; 
Half. Crowns at 24. 6. d. each, Gilders of 
20 d. each, and 12 4. pieces; he buys of 
all a like Number, How many ot each will 
he have for his 4 J. 8's. Anſw.,6. 


By the Rule af Three Dired., 


a 
=. * * 
* 4 % 
< FF 2» 


— 


34 A Gentleman ſpends one day Shs 
another 3 J. 14. and lays up at the Tears 
end 250 J. What is his annual 3 
nſw. 16004,.10 5. 3 

35. If I buy 120 Oranges. for 3 to 
penec, and 120 for 2 tw bence, — then 
ſell them mingled for. 5 4 Groat, w 


do I gain or loſe? Auf. Lip: 8 d. by the 
Bargain, | 


36. What number of Florins (ought Ip 
receive for 94l. 13 46 d. at 3 5. rd. per 
Wee e ie 90 + 1730. 3 

| 37. I by ſelling Wax At, 2.5. ; 1 of 
ic 


Sound, I gain 14 J. per Cent. What di 
colt ready Money? ' Anſw. 25. 4 d. . 
175 25 C47 4 ©$ 


38. A | 


* * * 9 1 4 A * Y 
— A 9 * KI . 3 i 4 
BT — n 1 ; n Fit TW . 2 AS 


OE”. - 7 
38. A Butcher bought an Ox, weighing * 
bende Skin and Legs 868 pound, the Skin 
and Legs he ſells for 21. 6 d. and 15 

Stone z of Tallow at 4 4. x per pound, What 
doth a Stone of Beef ſtand him in, ſuppo- 

fing it coſt him 18 J. 105. Anſw. 25. 10 d. 

39. A Vintner buys 4 Tun of Wine, 

1 which coſt 750 J. to . hefe chanced to 

leał out 112 Gallons, How muſt he ſell it 

by the Gallon, ro be no loſer by the leak- 
age? Anſw. 165. V 

: 480. Tis reported of one that made his 

b- Will with this Condition, that if his Wite 

* (ho was big with, Child) was deliver d 9 

3 of a Son, ſuch Son ſhould have 3 of his | 

Eftare, and the Mother the reſt ; but if ſhe 

3 | was delivered of 4 Daughter, the Mother 4 

8+ was to have 3, and the Daughter ;, now | 

'B ic happened that the Mother brought forth FF | 

2 2'Son and Daughter; how muſt the Eſtate 4 
* Which was worth 5400 l. be divided to | 
7  _ Falfil the Will of the Teftator ?  A»ſw. Son ; 
243400 l. the Mother 18001, and Daugh- 


TW «f 


Kü Att abc. a... 1 PY 


" * 


ter x2001. IJ. 


444. What's a Wedge of Gold worth, 
1 chat weigheth 4 Ounces 16 d. weight, 15 
Grains 2 4. +3: per Outice? Anſwers: 
1 19 J. 11 r 4 1 7 158 L COTTON 
3 ; „ N 7G £6 . | toi WII ; 12 3 


W A. td 


3 Wo | | ; 
- : p 


Bought 0 39 , enn ö 
ug 30 Pieces. o Eloath for 1307. 2 
=, them again for 150 Ul now if they 3 
had coſt 150 J. How muſt they have been 2 
ſold to have gained, after the ſame. rate? 4 


Anſwer, 173 bt = 
43. A. Witt Toy upon Contract with a og 
Fngliſh Lady 175 es Portion, ſettles aa 
Eſtate in Scotland of 800 l. per Am. by Way _ 
of Jointure, ., — upon Scrutiny into ie 
matter they proy d Scotch Pounds; & 3 2 MK 
ſo many fixe Groats, , How, much +. " 
he in Juſtice to e PE ds on, Mo. . © 


3666 J 13 Sis, viel * 'T 8 
N Pact 92 55 1 1 3 Ah "Son. 


£% - 
—Y 


"292. J. What 
ſwer, Firſt 20 


429. J. 3 5. 7 d. f 
Firſt Daughter. 23 


ob.” 


Daughter. 165. I. . ak Re LN (144,521 ON 


8.4. \ | 

An Oilman dee 
1 at 9. d. 3 per DOPE ISA or 1 8 85 _ 
ſtained Damage, he is willing to. hi 4 
10 s, by the dale of. the hols, it What 


price pen a e he ſell it to uſt 

that Sum? Weh at S henne 
A Yeoman, at the irt his] Dau gütef, 

of 4 and de the : 

oy N Nen I 


* | hich, ich, in" 26 | | Tr * yu 
ood o ik Oaks. this he ſells, eite. 

g all Charges, for 314 J. 19 s. Had he 

2 27 Acres with equal Succeſs, What 

would. that have amounted to in w_ fame 


- Tims . 1700 J. 14 : 
2 . 'Heylin tell us in 1 Cofo rography 


nar Es "Thar in the Cuy | Label, 


ed. becauſe they thete once wor- 
8 the Moon F there is 2 Houſe: con- 
1 in each Room is — 
each of which is boiled once a 
—ks Tun of Salt, each Fun being fold 
95 ee ſh Shillings, How much | Sale is 
6 4 5 in one Tear? And vrhat doth it 
mount to in pounds Sterling, at 7 d. per 
Beis lings? Anſw. F73956 Tuns, and 
4 38937. 3. «. Sterling 939 , 
=” 48. Race e d 35 0 Feld at London, to 
= be paid's at Ba 2jon in Spain, for every 65.84. 
© 2 o Mare ders Which I deſire my Factor 
to arg © London, that I may gain 101. 
ey at how many #arveides ought he 
"Ui 9055 7 rerling? Say, as 100: 
BH 915 e the Marveides, he ought 
etui Mane e Sterling at. e 
5 19 Minute the Heart delivers 77 
1 ohe aig to tuns Proportion, 
1 ir deliver in an Hour 2 


7 - 


” 


7 4 *% 
< 


- Th e057 541 * 


that 4 Pune 
Pace f a; 


4355 W 
the Heart Of Man every Faltin, How, 
much is tranſmitted eyery. RIA in 
45 oo Pulſations? Anſwer, 1890 0 1 5 


51. The Proportion botwirt che W 
= Blood of a Dog, is As 20 to 1; that fight | 


the weight of- the Blood is. Body, 
now tis granted it holds 10 f O in 8, te Bo. 
dies, whence, it will follow, that if a Man 
weigh 140 lb. bis Blood will be 7 lb. or 
x12 Ounces. This admitted, in what time 
will the whole Quantity Elood . pats 
through the Heart of Man? Sa a8 oo 
60: 112? Anſmer, 22 Secon- „ near. 
. In one ſecond of time found. 
968 Engliſh Feet, How far will it run in 
285 Minute? Anſwer. 58080 Fot. 
bz. The ſpace heavy Bodies deſcend" in, 
Me 15 ſuch proportion as the ſquares of 
their Times, that 1c, if two Balls deſoend 
from the ſame place, one is ſtopt at the 
end of two Minutes, the other at the end 
of mee 1 8 28 7 An ro 
the ſquare: of 4, ſo is the {p: 
| Deſcent, roche pa Wow Sec 


from. the E wrth's f by. 7 nc 


move 16 Foot in one eg d of time, How 
many Feer will a Body fall in 8 {comb of 
Time 7. aver 1024 Fee. 0 
54. If a Body deſcend 16 Foot in one 
bend“ of "Tims, In what time Will it an 


A 2 2 N © — > 1 
_ g 4 
* „ „ 8 33 7 ES a 
- * * 


wy 


| the lr Robb r rhe Wires rhe Anſwer: 


- Queſtions. 2 to wag . ang { 


Man be Allow the {pace of 3 ſquare Feer, 
chen E ſquare Mile" will contin 9292850 
ion. e e 


| . That the World may endure 10000 


hin the ſpace of 50 Years 1000000000 


36 ) 
20 25 5 5580 Feet! > alu, 

9 2 * « ov, . e 

Divide the#, ance tit 10 fall bs 16, "this 


we. „ ter en QOH RO FG, 


bo! * 1 0 Rule Ui Three Reverſe. ” f 11... 
n&We s 1 lent my rriend 2501. for 5 Morail 
How much muſt he lend me for 9 Months 
to Ballance my Kindneſs? Anſw. 138 J. 5. 
36. Suppoſe my Friend did botrow” of 
BE: 750 J. for 8 Months, and that he lent 
me 8601. How 1 1 muß I keep it it? 91 OE. 
CH Months,” * 


i 1 45 i 


EY 


1 * "#- 2 F 
* 1 8 * 8 * — £ 


- 0 * » 


- 4&7 NA. 


Analiſis ef Powers; that is, to 1 
bei raiſing f ne and COPE, o 
Roots. 3-23 IO ein ene Of 


2 7 * 4 3% 1 
49 "#4. J ? ba | : & 10 3 10 "> 5 4 ey 


©! g5. In an Ew 2 1p Whats Feet, How 


n ic guat er ntained in a ſquare 
Mike ? br 7878400.” Now if every 


443% N $004 C# "s 11 


en With the Tugeniaus Tuc- 


58. Suppoſe che 


Yeats. '"Thar the number of human Kind 
Alive at one time be 10000050000.” And that 


0 


1 357 
to have departed this Life, and in the ſame 
time the like Number to have been born. 
It will then follow that the Number of 
Mankind from the Creation to the end of 
the World will be 200000, 000000. Now. 
if 2 or 3 {quare Feet be aſſigned for each 
perſon it ill be made manifeſt, that 15 0 
{quare Eng liſh Miles will be ſufficient to con- 
rain the whole Multicude of humane Race; 
'ris therefore required, How-many ſquate 
Feet are in 150 ſquare Miles? Anſwer, 
627264000000. But 200000090000 Per- 
ſons poſſeſs no more than 400000000000 
ſquare Feet, if rwa ſquare Feet be allowed 
to every Perſon, and eee 
three: be allowed. 5 A 1 OJ | 0 
4 59. How many Cubical get! is contain- ji 
88 in a Cubical Egli _ 2 Anſwer, ;- * 
1471975 20ꝗ”æ is 6 HO SB 
60. Again, the ute Wee 
dies being '200000000000, and ſuppoſe 
every Man upon the Superficies of the 
Earth to take up two, or three ſquare Feet; 
that is, allowing rach Perſon 6 Foot high; 
the ſpace that each human Body tales aß -- 4 
will be 12 or 18 Cubique Feet, ſo that 
'2 00000000000! humane ''« Bodies, may 
take up the ſpace of 2, 400000, ooo, or 
3. 6060600060000 Cubick Feet, from which 
it's evident, that the whole Maſs of Man- 
kind may be contained im leſs than a Cube, 
vhoſe fide is ö WG the hr” 2 = 
2 VIp W 1 


— 


K 358 y 
_ h is FI, pa IR ſolid Feet. 
*®6x. Suppoſe, 1 would encloſe a ſquare 
Piece of Ground containing 2209 ſquare 
- Perches, How long ought the ſide of ano- 
ther — Field to be 4 times as * 
| 2. The length of a long ſquare Field is 
3 Perches, the breadth is 34, What's the 
of a ſquare Field that is equal to it? 
* aer. 40 Perches, 3 Tentbs. 
I Aud thus the fide of a Square, equal to any 
3 given Smperficies may be found, viz. by Ex- 
#ratting tbe ſquare Root of the Area. 
Sz. — — Roper gave to his Daugh- 
ter aRope with 2oKnats in it for herPortion, 
ro each Knot was tied 20 Purſes,” and in 
every: Purſe. was 20 Guineas, What had 
me for her Portion? Anſw.' $000 Guincas. 
+ 64. To find a Cube equal to any other 
| Veſſel, Example, I would know the fide of 
= Cube, that holds juſt a Hogſhead, vis. 
1 Gallons? Anſwer, 27 In. near, 
65. Admit a piece of Timber be 15 In- 
"ali ſquare, What muſt be the fide of ano- 
be cher e. 6 times as ſrong ? dnfoger, 36 
Oe ; ver. 121 
. ſhall conclude theſe Collection of | 
3% - Queſtions, as alſo, the whole Book with 
8 following Experiment and Account, 
Wich require an Arithmetick Calculation. 
By an Experiment the learned Dr Halley 
e at . ae, 0 found 2 5 


TH 


2 4 ig Os 
N : 

” ay ol 4 * 

% % 2 Ad T8 ? l 
@ CER uf 4 


1 
— 
EB 


. 


" # 
1 
” og es — 
* "Ws % E 
3 
* 
. 0 
* 
* en —_ 
Ip 3 —— —-—¼ 1 
2 r TE 
e eee rr ** 


f in the 


the Surface of any Veſſel of Water. 'Whence - 
every 10 quare Inches Sarface of "Ware  _ 


pint. This granted, tis equi 


near 3a Wine Pint, then every f 


hate of 15 eee 
Day, there did Fvaporate 23 * Inch fror 


will yield in Vapour a Cube Inch of Wa- 
ter. NOE W 28 3 Cubic inches ie 


what Quantity of Water will Byaporate th 
one days time from the Whole your, 
the NCI; which in a Medium 
mav mitted to be Dunes long, 
and 4 Degrees, broad. ts a F $ * 
From theſeDimendons s evident ihe Me. 
diterraxcan will contain 160 ſquare Deprees. 
of Sea, and conſequently 761760 ſquare 
Miles, now upon this Suppoſition that eve- 
ry 10 ſquate Inches yields a Cube Inch ot 
Water per 1 Diem, and ſo each ſquare Foot ä 
4 Foot ſquare. will yield a Gallon, and _—_ 
8 Tuns, and therefore 1 % 
ſquare 3 70 of 69 Eagliſb Miles will Eva. 1 _ 
moms, 3 Millions of Tuns, and conſequents ' i 
the whole Mediterranean will loſe tins © 
Came s Day 5280 Millions of Tuns of . 
Water. ; 
67. The faid»Dr. Haliy g ve an account 
w-anorher meeting of hs? iety, l 1 
the exceeding thineſs of Gold, which he 
computes from the account he had from 
the Gold Myer Drawers, which was this, 
the bei _ Gik * bs drawn from 


I 
I * 
hs 
* - 
+ 
g Fo 
; 
4 n 
5 
5 +. 
>» » 
2 
$ >: 5 
— _ 
ES. 
» - &Y 
* 
e 
na Oo 
+ "= 
—_ 
"+520 
1 
. 
** 4 
+ * 5 
=Y 
3x | 
py 
14 
S; 
F 
i 
"ol 
i 
I 
«$5 
» 
War 
n 
N 
72 
> 
—_ 
* 
© 
12 ; 
= ft 4 
1 N 
* we þ 1 
3 T3 
FX 
4 
1 1 
.- 
5 = 4 P 
2 TJ 
N 
» > 
— . 2 * 
vm; 2 
> 3 ; 
982 
4 1X 
=P 
* 
7 3h 
54 
2 
7 © tf 
» * 4 
- 1 * 
2 8 
* 7 
- ow” 
* > 
- Ox 
Ac 
V 
** 
©: x 
"50S 
| S 
* of 
# 4 
3 
1 
Oe A 
6% 
& ” 
5 4 
8 — 
- £3 
Ax bh 2 
4 
Y 
i 2 
* of 
Pa q 
3 
„ 
4” | 


2 
PF * * * 
— e 


Oviengrick 10 . af, Silver - al Inches in in 
ircumte „and 28 Inches long, Which 
hs r pound Troy, this is covered with 
Ounces old, that is 48 Ounces of 
Ounce of Gold, this they 
fing Wyer, that 2 Yards of 
but a Grain; whence tis evi. 
echt s Yards of ſuch Wyer weighs 
Stain, and conſequently; that one 
Grain of Gold covers the {aid 98 Yards, and 
that the w part of a Grain is aboye q of 
an Inch Io! long, 3 may be actually di- 
videdi into 10 equal Parts, and ſo the of 
Grain of Gold viſible without 2 Micro- 
.. | 
But to proceed, he tells you in the ame 
MY. Place, that the thickneſs. of ſuch Wyer is 
* * the is of an Inch. and then the Circumfe- 
* * EEE Senceof ſuch will be hut 7; of an Inch, near. 
mherefore 123 Grains of Gold cover 98 
1 3 Tards long, 3 an Inch broad, chat is 24 
FpPoot 2, this being granted, I demand how 
het: much Gold will Over a ſquar C. Mile, »that 
2 , 640 Acres?  Anſw. 24295; 16. 9 Ou: 
2 — Abu z Gr. %% br a IRS {ety 227 
| © 


* IHE | 
*. 
= 


* 


Re I any Hundi has Eſcap'd Corredtion, they 
. ones Lerſow from 4 Correm 
— r le Author's Houſe in Channel. i 
Now, ain 2 2 28 1. FL 10 3 6 34 4 2 2 * 


721 * 2 * 
nat WW "DING. 5 Cine 


- 


* 
\ o# T * 4 
„ 
9 
% : 
- * 
1 
1 . \ 
— 
a F TY 
* 
by 
a — 
4 
: 
i 6 \ 
. — 4 
- 
. - — 
” 
So 
. N 
— 
TRIED * * . 
1 1 A * 
1 D 
—— ata rf 
” = —1 * 
* 1 
* 
” 
FATS 
2 
4- 
Is. » 
7 
4 " 
. 
* * 
4 
* * 
— 
* 
. 
— 
. P 
* * 
— * 
- 
PR ” 
7 
*%y 
1 — 
« 
_ \ 
; 
% 
. 
«a 
” 


* 4yeued 


* 


44 © oo amp wy, *.. &.M 


