NOVISSIMiE - 

NOVISSIMARUM 
SATURNI, JOVIS , MARTIS, 
VENERIS, & MERGURII 
TABULA. 

Ad datam Planets a Sole diftantiam 

condita:, 

Et per T rigono metric plan <e Cavalerii 
Troblema XL fuppuPata, 

Qys Keplerianis , Hyrianis , & Streetianis Hypothe- 
fi^us mire fatisfaciunt, inferviuntque. 

xAcccdit infuper Tabula proportionalis pro latitudine Planetarum 
expedite rcperienda ? nec non pcrbre’vis calculi Hyriani 
facilitandi methodus 

A U C T O R E 

CANON. ANGELO CAPELLO 

A. P. Parmcnfi. 


VENETIIS, MDCCXXXIII. 

Ex Typography Antonii Mora. 
SUPERIORUM PERMISSU. 


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If 


r .* 



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M Bluflrtjfirmm ac Excellentiffimum D. D. 

COMITEM FRANCISCUM TERZI 

Siflae r Sanfti Nazarii , & Flexiar Dominum Co- 
lophonis , Marchionem Contignaci, Boemiar 
Regni , Moravia? ac Slellac Provinciarum Pa- 
tritium, nec non in eodem regno Do- 
: j . ! minum Kollinctz , Auczi n , Vuo- 
< ■* lofcovitz, Puduli , &c* 



JE font ( Illuflrifllme ac Excellerr- 
tiffime Domine ) meritorum vires, ea virtutis offi- 
cia, eaeque magnanimx mentis dotes , ut (e per cor- 
da hominum infinuent, intimas animae medullas pe- 
netrent;, Studioforum animos demulceant 7 & otife- 
- j ’ l a 2 quium 



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quium , amorem , a c fummam vel inter Jgnotos reve- 
rentiam proprio fibi jure -vindicent'. Quod de Tc 
( pace Tua ) me dicere poflfe inficiabitur nemo j quip- 
pe ilia Tua invi£K aniini praeflantia, prudential Tuae 
dotes eximix y ac pracipua , quae Te condecorant , 
mentis- ornamenta non tarn Patriis , verum etiam 
Principibus, Regibufque tarn charum, eorumque fa- 
miliaritati conjun£bum reddunt!,, ut .quidquid aliis ex 
eorum gratia trihuitur , Tibkex fummo meritorum 
jure debeatur . Tu non tantum litterarum ac feien- 
tiarum quaruncumque cultores protegis, fed & Cx- 
leftium motuum Amatores , qui fcilket in Ailronomi- 
cis rebus operam navant , benevolentia ac favore 
profequeris . Nec hoc minim , nam hujufmodi ftu- 
dii genus Heroica ingenia ad fublimia elevanda 110- 
bilitat , & hoc Principes in Gallia , Germania , ac 
ubique Terrarum fovent & patrocinantur . Non 
parvi negotii res eflet , fi laudes Tuas y ut debe- 
rem, ( quod etfi vellem haud poffem ) fingulatim 
enumerando exponerem. Tu enim Parentum , Avo- 
rum, ac Abavorum Tuorum decus ac ornamentum 2 
avitam nobilitafem Tuam integrum Boemiae Re- 
gnum praedicat : Te exterae Moravian ac Slefiae in 
unum colle&ae Provincial , ac ejufdem pcene infinite 
Regni gentes fuum Dominum declarant. -Neque hid 
inlignia Domus cTuae antiquiflimae monumefita in 
Tuas laudes excitanda funt , rin Oniverfum magis 
clara , quam quod hifee in paginis rudi fly-lo corn- 

men.- 


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ittendarei laborem Mitto Parentum tiiorum digni* 
tates eximias : mitto Principum familiaritates ac pu- 
blicas .adminiftrationes : mitto Ecclefiafticas curas : 
magnapimitatem , generofitatem , ac poene innumeras 
animi dotes mitto, quibus prae caeteris domus Tuae 
celfitudo refulget , quia hxc omnia tanquam in 
compendio unita in Te uno mirantur omnes , ad- 
mirabiturque non fine gaudio Pofteritas in Te ni- 
hil defiderari , quod *ab ipfa fperandum foret . Duo 
tauten’ hie ad conticendum me impelluntj fmgularis 
ilia ex una parte modeftia Tua , qua meritas con- 
temnis laudes , & incultus ifle ex alia verborum 
apparatus, qui aures Tuas fortaffe faftidiet. Ne me 
qua»fo audaciae incufes , ft Opufculum hoc Nomini 
Tuo dicandum propino > fed ea , qua Muficae har- 
monia frueris , eamque traftas , hilaritate cajleAium 
Corporum harmoniacos concentus excipe, 

if? qua divifa beatos 

Ejficiunt collegia tens* 

Hunc Tibi, cujufmodi ilt, calculi laborem in Sup- 
putatorum gratiam condi turn, ut publics debita?que 
erga Te fervitutis mea: teftimonium dico r Et ne 
( ut ait Sophocles ) labor labori, laborem tulijje njidea - 
tur , huic munihcentifllmi Patrocinii Tui ope leva- 
men dona, eritque fine labore labor. Quod fi mu- 
nus hoc tenuiflimum inter pretiofa Mufa:i tui *or- 
namenta , tanquam in Firmamento llelliculam collo- 
care non dedigneris j etiamfi nativi fplendoris nec 
’ ' ' j*. hilum 


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hilum pnrfeferat > mutuatitia taraen. > ut Luna d i» 
chotoma , fatis luce clarefcet > micabitque reflexis 
illuftratum radiis * Neque hoc Tibi gratum futu- 
rum defpero , quod animurrt nieum optime noyeris. 
ad majora dicanda paratum* 

-i t 

... ■ . , . IT - • 

;■ ^ • . ; ; % 

lllujlrijjimcc ac ExxUcntrJJim* Donmmnnis # 


f . ••t . . • ^ • 

l 

ObfervantifTimus 
Angclus Capellus. 


Venetiis anno 1752* M- V* ' rft ’ 

Pridic Nonas Febntarias • 

. ‘ . • »r , l •* . . ' ; : 

■ ’ . i • . : 1 V :/'>•; *: • t ; :• ■ ' . 11 

. . ' • *rt iftL'-tn'l! . it: 

- .-'i- ' ' ! 'i 

i 1 ) ' •' > ' j 1 • . -i 

5TU- 


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STUD IOSS IS IM O 

LECTORI 

' * * 1 " * 1 * * * 

i'. ; S* 


baler is , & june quidem miraberis StvdieMme Le- 
flor , quod T abulas ifas pro noviffima Planetarum 
aquatione , nec non pro torum Latitudine expedite 
reperienda publics juris facer e cur aver im . Verum 
ft rationes cmnes , qua me hoc facere impulerunt , 
perpendantur 5 procul dubio omnis admirationis 
... <aufa exulabit . Enimvero a Tabular um iflarum labo- 
re propter tllam , quant afferunt brevitatem in calculo , aquitatem 
in operatione , abflinepe ^aut quin T abulas ipfas Candidas is communi- 
tarem temper are non tot ui , O pracipue quia recentiorum Afronomo - 
rum nullus hoc fecit , fed Logarithms utuntur , quorum caufa erro - 
res non paucj , vt in fequenti Jntroduftione clarius patebit , oriri fo- 
lent Hac data occaftone calculi Streetiani ;tf Hyriani , qui fcilicet 
vx Hyrtt Tabuhs perficstur , facilitandi & decurtandi modus demon - 
jtratur . Cumque Tabula ijia Streetianis , Hyrianis , & Kepler ianis 
communes ftnt poterunt a Calculator thus , & rerum caleflium Obfer - 
vatonbus pro libito adbiberi . Cater um qui Tabular um ijiarum ufum , 
Cf mjhtutum intelligere jludent , in Trigonometria plana element is 6* 
LogantmniS' faltem inflruHos vellem , f quidem borum dejlituti ad cal - 
Cttlum feltct omine accedere nequeunt y & frufir a tempus in hoc excur- 
rendo Opufculo procul dubio conterunt . jQui vero bac non folum cal- 
lent y yerum etiam docere par at i funt , opus hoc brevitatis , & facili- 
* att j in fupputationibus ajfequenda gratia percurrere nolint , faltem 
nc&ligere , aut contemner e % telle incredibile ejl. Tabu l arum ufum Can- 
dtdatorum in gratiam uno atque altero exemplo explanare licebit , ut 
probe injtrufli libentius faciliufque calculorum in arenam defcendant . 
Alt am etiam pro latitudine Planetarum omnium Tabu/am Marte no- 
pro condidimus , quam proportionalcm vocamus , cujus ope , & fexa- 

genaria 



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genaria Tabula Planet a c'ujuslibet latitude rtperirl pot eft.' Unum hoc 
advert endurn fuperejl , ut qui novijfimis aquationum Tdbulit uti cu- 
piunt , prius errata qua dam a Typograpbi incuria , nefcio , an corru 
gentit exorta , bumaniter corrigant , qua in fine bujut adnotanda cu- 
ravi , ne incorrtlium opus evader et . Hand* enim ignorant Supputato- 
res in numeris quotidie verfati , cum de numerit agitur , vix, aut ne 
vix quidem errores ab accuratijfimi Emendantis oculis effugere pojfe ; 
arrellis vero femper auribus ad minutijfitua quaque adfiare laboris ejl 
pane improbi , ac tanquam ipfa elucubrare , ait Argolus ad LeSio- 
rem Tomo primo fuarum Ephemeridum . Qua omnia cum bumanijfimo 
prudentique LeSlori dill a fint , vent a baud indigna fore nory dubi- 
to , ut imprafentiarum fuperfedendum arbitrer . Vale 


V. . v/.'* ^ 



B R E- 


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9 


BREVIS 

AD TABULAS 

TRODUCTIO. 

Stronomi omnes, qui ante Kcplerum Adronomi* elliptic* Patron 
Planctarum motus ad Tabulas rcvocarc Huduerunt, nullum alium 
in Coelis motum praster circularem fit asquabilem admictebant , pu- 
tabancq, Planetas omnes circulariter moveri . Uc autem apparentem 
inasquabilitatem fol vcrc poflent , cos in circuit: exccntrico deferri da- 
tuere. Sed cum obfervationibus eorum Hypothefes egre fatisface- 
rent , aliam methodum excogitate opera: pretium fuit, fit quidem motum ellipticam 
admittendo, cujus inventio fagacillimo Keplero debetur , qua Planer* omnes cir- 
ca Solem in Orbita Elliptica , non verocirculari deleruntur; Hacquc lege ita tern- 
perari videntur eorum motus , ut per radiosa Planecisad Solem dudtisareas tempo- 
ribus ubique proportionates deferibant . Harum demenftratio cum apud Cl. Nevio- 
hum & Kepler urn extet , fit a Cl. Vifthvn in pradtddcnibus fuis A fit onomicis Can- 
tabrigias in publicis Scholis ttabitis , praocipue vero inprade&ione xxv i. exponatur , 
a nobis conful coed neglc&a. Hinc icquitur labulas otnnes , qua: novas Kepleri 
leges non fequuntur, imperfedtas cfle, fit Calo minimi: conferuientcs, ubi enim 
requationem augcre debent fepe diminuunt, fit £ contra, ut obfenationes omnes 
adhuc habitas prob£ tdlantur . Nos interim Adroncmi* amantifl.ini celcbriorcs *- 
tatisnodr* Aftronomos Kephrttm , Nevtonum , c affirm*, Hull ei urn , Hyrmm , 
Keil, Flamfiedikm , Vifthon , aliofque qui banc Icientiam illuftrarc quotidic non 
cedant, brevioriquopofiumusintervallocontequimur. Etqniaa calculorum labo- 
re ad invedigandos diaries I'lanetarum motus pro Ephemcridibns rite condendis 
nunquam vacavimus .- hac de caufa qua: ad calculum fpedant facilitandi ergo, a 
Tabularum etfi taediofa fupputatione non abdinuimus , utiiitatem a nobis colle&am, 
Tabulafq; ipfas calculorum Amatoribus, aliaq, limilia Adronomica opufcula fpon- 
ticommunicareparati. Tabul*nodr*,quasStudiofisexhibemus,ex problcmate x i. 
Putris Cavulerii confe&s fuerc ; f.'.cilis enim in iiiis ingredus , facilifquc per ufualcm 
Sexagenarians Tabulam proportio, fit proportions quantitas ultimi definienda, 
fit variasfupputationuin partes Logarithmis neceflari* harum Tabularum ope ex- 
cluduntur . Moleda enim ( quis nefeit ) Logarithmorum proportio, & pratipu^ cum 
inter prima gradus fcrupula calculatio vcrlatur , fir quia Lcgarithmorum Tabulas 
ab omni bus ( ut fcri accidit) Typographi mendisexpurgatas reperire vix poflibile 
edevidetur . Qua propter ultima Planetarum mquacio incorrect a evadit, fit erro- 
neusejufdem Planet* locus. Ncctam facilb error dignofei poterit, fi fupputatio 
fit, ut fasp£ effe fokt , inftantanea, qu*rendi gratia alicujus h.rronis locum obfer- 
vatum proTabularum confenfu cumCoclocomparando. Soli Ephemeridum Suppu- 
tatorcserrorcs, fi qui irrepferint , clar£ intuentur, ex diverfis videlicet Plancta- 
rum modbus interrupts, velexTabulis ad hunc ufum fadis locum computatum 

b con- 


I N 




io Introdu&io. 

confcrendo , uti nobis Ephemeridcs cit*uuuuo*s ante harum Tabularum conftru- 
dionem mulcoties evenit . 

Seddicctquis Tabulas iftas a Veteribus olim asJiticatas exifterc, quae anomalU 
crbis gradibus, feu Angulo comm*t*tioms inferviuuc ; extant euim apud Riccttlum , 
A‘fU!tet,GM*rinum ) Ai4ginum in fxp. Ephtm. aliofquc p.xne lnaumeros AudorCs . Cui 
rcipondetur calcs rcveraconditasfuilie Tabulas, fed non tub codon fundamento; 
difUntia.' enim Planeca a Sole , quas m*xim*t .fynattones vocant , infigniter difte- 
runc, & alias opera clones requirunc. Et fi cot habicis oblervacioaibus fidendum 
cfl, inulcum a vericace defledunt, & a noftris Tibulis h aid paru.n difcrepant. 
Majorem incerea , & minoremasquacijnemulcimam, feu, ucipft ajunt , comptfi- 
tam pro quibufcumque Planccis ex fupracicacis Audoribuscolledara hie afferre vo- 
lumus, uc corum diferimen apparcac . Igicur. 

PRO S AT V R NO. PRO }OTE. 


aEqu. major. 

.dEq 

u. minor. 

jtqu. major 

. aEqi 

j. minor . 


G. M. S. 

G. 

M. 

s. 

G. M. S. 

G. 

M. 

S. 

EX Rli'CIJLO 

7. 0. 0. 

0. 

4- 

49- 

IX. 0. 0. 

0. 

8 . 

5*» 

EX MILLIET 

5-57- — 

0 . 

5- 


10. xo. — 

0. 

9- 

— 

EX GVAR/NO 

8. 0. — 

— it* _i 

0. 

5- 

— 

IX. 0. — 

0. 

9- 

— 

EX MAG INO 

0 " 1 . —*• 

O. 

~T W ~ 

" - “ 

I «• 19 

O. 

9- 


Ex noftris T *b. 

7. 3. 10. 

O. 

4- 

50 . 

lx. 1 6. ip. 

0. 

9- 

O. 

PRO MARTE, 




PRO TENERE. 


EX RICCIOLO 

44 . 0. 0. 

0. 

XX. 


48. 0. O. 

0 . 

H- 

36. 

EX MILLIET 

36. to. — 

0. 

XX. 

— 

44-55- °- 

0. 

x 4 . 

5 *• 

EX GVAR/NO 

44 . 0. — 

0 . 

XX. 

— 

48 . 0. — 

0. 

*5- 

— 

EX MAG/NO 

49- 5- -* 

0 . 

XI. 

— 

49 . y. — 

0. 

XX. 

— 

Ex noftris T *b. 

48 . 55 . 57- 

0. 

XI. 

58 

48 . y 3. 17. 

0. 

*4- 

4 x. 


PRO 

M E R 

: c v 

R IO. 


*• 


oEquatio major. 



JSL qua to minor. 



EX RICCIOLO 

gr. xp. 0. 

0. 



gr. 0. 1 3. 

54- 



EX MILLIET 

gr. 17. xy. 

— 



gr. 0. 14. 

— 



EX GVARINO 

gr. xy. 0. 

— 



gr. 0. iy. - 

— 




EX MAG I NO gr. 24. y 6. — gr. o. 14. 

Ex ttofiris T Mb. gr. zp. 1 1. JO. gr. o. 13. zz. 

Ex quibus apparet Tabularum diflenfus , & ratio per quam Tabulas noflras no- 
viflimarumajquationum Planetarum in medium attulimus. Placuitpro Laticudine 
inveftiganda alias Tabulas ope Sexagenaris tan:umadhibendas conllruere , Suppu- 
tatoribus rera gracam faduri . 

Erumvero quo ad Latitudincm parti net abfque examinanda vetcrum Aftrono- 

mo- 


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Introdu6lio. Yi 

inorum non facts tuta metodo , Tabulas , quas proportionalcs vocamus , condidimus, 
noviflunsKepleri analogisinnixas. Neinpe 'Ltjinhs .mg alt commutation !! , ad fi- 
nnm anguli elongations ; itxTangent incltnationis Htliocentrica ad Tangent cm in- 
clinationis Gcoccntrica , qua eft Latitudo Planets qua; fit a , qua abfq; Logarithms 
in diciis Tabulis reperitur , ut paulo port videbimus . 

Aliud etiam volumen , cui titulusOrdo fappntandarum Eclip/ium Solis & Lhhx , 
conftruximus, quod lucem expedat, vidcbitque poll prsfens opufculumDcofa- 
vente, in quo Solis &Lunsfupputjrionesmira, & compendiola methodo pertra- t 
dantur . Solis fiquidem locus verus aEfque ullo partis proportionalis bcncficio , uni- 
co, utita dicam, intuitu reperitur i nec non Luna locus per breviores calculos, 
fexagenaria ubique proportione fervata indagari potell . Adelt deinde novi llima,qus 
Parallaxium omnium tricas amovet , Solis feu terrs eclipfes quolubet tempore com- 
putandimethodusfolacircini, & regulsopc, cum numerorum abfolutorum Ta- 
bula Logarithmica in minuta & fecunda iifque ad gradum unum ad ufum totius O- 
peris refoluta , fupputata. Alia etiam opufculaad calculum non minus utilia, 
quam fpedantia habemus, qua hie recenlcre locus non eft. Sed labores noftros 
videre fas eft , & comprobare , Tabularumque ufum exemplis Caodidatorum in 
gratiamexplanare, &patefacerc. 

Xhtomodo conditx fint noviflinu tequationis Planet arum 

omnium 7 * abula . 

CAPUT I. 

PUNCTUM I. 

O Miflis figuris , & triangulis ad demonftrationem & folutionem crurum alias ne* 
celfariis , brevitatis gratia folum Ca valcrii Problema exponemus , cui tota in- 
nititurnoftrasquationis'Iabula. Scilicet. VtfnmmacrHr*m y adeorum differen- 
tiam\ ita T angens Jemi {umma angnlontm , adtangentem differentia , qua addita 
femi-famma major cm , & dempta mtnorem angulnm desern.inat . Velclarius. Vt 
fumma dift antiarum telluris & Planets. dSoIe , ad ear am differentiam \ ita Tangens 
femi-fumma Anguli commutations, vel/emi-fumma complement! anguli ditli, fi f Me- 
rit extra fcmicirculum , ad Tangentem diff'erentia . Opcrando per Logarithmos 
dantur ex Tabulis Aftronomicis tam diftantia Planet a a Sole , quam Solis a Terra in 
Logarithms, & datur in calculo Angulus commutations quibusdatisreliquafic 
expedics . A Logarithmo diftantis Planets a Sole done Logarithmum diftantis 
Solis i Terra pro fuperioribus, e contra a Logarithmo diftantis Solis a Terra fub- 
trahe Logarithmum diftantis Planets a Sole pro inferioribus Planetis, addito ta- 
men radio to. ooooo. Logarithmo maioii, a quo fieri debet fubtradio, quafada 
oricturinrefiduoMefologarithmusingradus, & fradioncs graduum per Tabulas 
rdolvendus , a quibus fi detrahasgradus45. iterum refiduum hoc (quod nos veram 
Planets. dSole diffanti.im vocamus ) in Mefologarithmum convertendu merit , nddi- 
toque alio Mcfologarithmo femi-anguli dati, horum produdum erit alius Mefologa- 
rithmus , cujus valor a gradibusgraduumqucfragraentis femi-anguli dati ablatus af- 

b x fa- 


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ii Tabularum conftru&io. 

fcret in refiduo optatam Planet* *quation.tu . Nec dilumili modocondit* fiierunt , 
quas tibi exhibcmus , aquationum Tabula Veruraquiaad hac illuftranda calculi 
methodum quamdam in medium afferre opera pretium eft, hac qua fequuntur adno- 
tentur . 

Calculi Flamflediani , & Strcetiani metbodus . 


■y 


PUNCTUM II. 

Q Uoniam , quas proponimus, aquationum Tabula tarn Screetianis, quam Hy- 
rianis, &Kcpierianis calculis mire infervirepoffunt, dataoccafione& cal- 
culi perriciendi , & brevioris agendi modum in iftis Hypothcfibus demonftrare 
necefleeft. Primo igitur deStrectiana , poft dc Hyriana , dein de Keplcriana fup- 
puiacionedilferendnm erit. 

QOOad Streetii Tabulas Carolines di&as fpc&at, quas Cl. Vir Gkllielmus Vt- 
fihon in publicum dedit , nulla alia in calculis difficultas apparuit , quam locum So- 
lis, non Screetianis , fed Flamftedianis praaptis, utipfe docuit, reperire . Quo- 
niam verb ifta in Tabulis Solis motus njutnofiiomm pracejfitnem involunc, hanc il- 
ladefiderant .■ ideo ab invento loco Solis ex Flamftcdio praceftionem fubtrahere 
opus erat, ut Solis locus Streetii calculis accomodatus haberetur . Nos autem ut hanc 
calculi partem Suppucatoribus tolleremus, differenti ( fed qui in idem recidit) calcu- 
loufi fumus . Pianette longttudini kelio c s mr i c aB per Tabulas data ftatim aquino- 
fliorum praceftionem, quam Vi.fthon in fine calculi exponit, adjicimus, & in 
produ&oadcft Longitudo P/*»eu * b tqktnoUi* , quam nos Longttudtne/n cortrflani 
vocamus , qua a loco Solis Flamftediano fubtra&a in fuperioribus , vel loco Solis ab 
hac dempto in inferioribus Planetis, fit idem angulus commutationis , quern affert lo- 
cus Solis Streetianus, dimidiatoque angulo ft Logarit hmis , vel cum codon angulo ii 
Tabulis noftrisuti placet, catera, ut infra videbimus , ad calcuhim neccffaria re- 
quirimus . Quod autem angulus idem fit in appofico exemplo videre eft . 

s. o. / ;/ 

Daca fit Longitudo of* heliocentrica 4. 10. it. ip. 

Sitque Aiquino&iorum prasceflio addenda xp. to. 51. 

Erit Longitudo a* ab aquinodtio 5. p. ji, io. vel Long. cor. 

Locus 0 verus ex Flamftcdio 6 . o. ip. 30. 

Unde anguhis commutationis . o. 10. 77. 10. 

Modo verb Streetiano dempta fcilicet aquin. prac c fs. a Sole Flamftediano 
Erit locus 0 ex Streetio y. j. 18. ^ 

Longitudo cr* hclioc. fubtrahenda 4. jo. 11. ip. 

Angulus commut. ut prius o. io. 57. io- 

Et tali pado abfque ullo fcrupulo uti licet Sole FlamftcdianoinLongitudinibus 
Planetarum Strcctianis inveftigandis . Sed ut ad propofita redeamus, & calculum 
profequamur , docet Cl. Vifthon angulum fupradi&um commut., quam Veteresr 
MHomdliam orbit nuncupaverunt , dimidiarc , & ad gradusrcducere , invento tamen 
prius anguli complemento cum angulus femicirculum fuper.it , ejufque Tangcntem 
quarcrc, quacuroTangenteplanetadiflantia vet a a Solejuntta aliam Tangen- 

tem 


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Flamftediani & Streetiani calculi . 1 3 

te.naffert, quaingr.ulusit.loluta , dcuiptoprius .amo, Sc-j eodem dimidio ab- 
latadat aqu.trioncm ultimam quafitam , qua; in fupenonbus Orbis par i/l Axis , leu 
inequalities fecund a , in infcrioribus vero Planetis elongatio dicipir ; £ contra li vice 
differentiae fiat fumma,procreabitur in fuperioribus elongatio naximu.n in latitudine, 
ut infra videbimus, ufom habens . Hojc autc.n aquucio addita longitu.lini corrc&a 
„ pro fuperioribus Saturno, Jove, &Marte, vel loco Solis pro inforioribus Venere,& 

Mcrcurio in prinao femicirculo , & ablata in fecundo locum Planeta verum efficit . 

Exemplis melius calculi forma percipietur; Verumantequam ad exempla devc- 
niamus ad notionem dariorem aliqua prius pracognofcenda font . Scilicet cum lon- 
gitudinem Planet® heliocentric am dicimus , idem eft ac diccre longitudinem b Sole , 
Ceoctntricam verb c Terra vifam : clique vera Planet® longitudo . Cum dicimus 
longitudinem correclam , longitudinem Planet® mediamab JLquinoflio intelligimus. 

Cum de logarithmis agitur pro hoginthmo logarithm™ (inus t{\\nie\\\g<in&us 
pro Mefologarithmo logarithm™ T angentis . Radius fopponitur Temper conftare 
unitate & 6. cyphris pofita unitate cum cyphra pro cara&eriftica , & quinque aliis 
cyphris , nempe i o. ooooo. Cum in calculo addi debet radius faeis eft ft earaderifti- 
cam una decena audam , cumque demi debet una decena diminutam intelligas . His 
igitur notatis ftet pro exemplo . 

Quarat quit ex Streetianis T abulis 'if. longitudinem geocentric am feu verum locum 
'If. a Cl. f'iro Euftachio Aianfredio £ ononis, objervatum die prima f/tlii anno 172.4- bora 
IO. 10 . yenetiis hora 10. 14. 

Locus hoc tempore cx Flamftedil Tabulis in noftro Eclipfium volumine con- 
tends reperitur fign. 3. gr. 10. min. 1. fee. 11.& diftantia # a terra 5. 00718. unde 
exStreetiodantur fequentes calculi . 

S. G. M. S. G. M. S. 

Locus‘S heliocentricus p. 5. 36. 11 Inclin. hclioc. o. 37. 4. 

Praaceftio aBquin. addenda ip. 15. 3$. Difl. Of a O 5. 70606 

Longitudo correda 10. 4. 51. 47. Radius addendus 10.00000 

Locus & verus 3. to. 1. 11. Dift. Of cum rad. 15.70606 

Angulus commutationis 5 5. p- 15. Dift. a Ter. 5.00718 

Dimidium Anguli 77. 34. 41. Dift. Of k 0 M. 10.6987& 

Parall. orbis, feu aquatio add. V. 5 1. 51- Valet gradus 78.41.7 

Locus Of geocentricus 10. 10. 43. 3p. Ablatisgradibus 45. 

Ideftingradus 10.43. 39 - ^ Fitdiftantia vera 33. 41. 7 

Locus obferva tut 10 47. 3. ZZ. CujUs Mcfol. p. 81383 

Deficit calculus 3. 14. Dimidium ang. 77". 34. 41 

Ephem.Manfredii 10. ip. 14. Cujus Mefol. 10.65706 

Dcficiunt 17. 3p. Logarit. fomraa 10.48089 

Deme radium 10.00000 

. Reftat Mcfol. "1048089 _ 

Cujus valor 71.41.50 

Igitur parum aut nihil a Coelo aberrant no- Summa feu clong. 149. 17.31 

li ra quibus utimur Tabula. Diffi vel a quatio 5. 5 1. 51 

Interim fi placet indagari poteft ctiam Latitudo , qua ex praceptis Vifthon, 

alio- 


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14 Flamftediani & Streetiani calculi . 

aliorumque recentiorum in hac analogia , ut alibi diximus, fundatur. Vt Jinut 
Anguli commutation!! , ad (inum angnli elongationit ; it* tangent inclin Ationis he/it- 
centric*, adtangentem inclin Ationis geocerntric* , qu«e eft latitudes ver* Planctae. 

Harc facillimeinveftigatur, ft nempe Mefologarithmo inclin. helioc. per Tabu- 
las propriasrepertaaddaturLogarithmusfinus anguli elongationis , & d fuinma 
fa&adematurLogarithmuslinus anguli commurationis; namin refiduo habebitur 
Mefologarithmus inclinations geocentric® quefitas . 

Igitur in fuprapofito cxempio inventa fuit . 



G. M. S. 

Inclinatio helioc. 

0. 57. 4. cujus M. 8. 05x71 

Sinus Elongationis 

50. 4X. x8. cujus L. 9* 7°8id 

Summa 

17. 74085 

Sinus anguli com. 

14. yo. 55. fubtr. L. 9- 6 * 339 ' 

Reftac 

M. 8. 11746. 

Cujus valor 

0. 45. 5. pro latitudine 

Latitude! obfervata 

0. 44. XJ. 

Exceflus 

0. 0. 40. inobfervabilis 


Detur pro *lto extmplo qnarendks *5 locus anna 1 7x4. die prim * Mart'ii in V'enet* 
Meridian 0 tq»* li tempore , 


Dabunrur ex Streetio hoc inftanti 
S. G. M. S. 

5. 1. 55. 50. 

*9 if. 18. 


Longitudo $ helioc. 

Prasccflio asquin. addenda 
Longitudo corre&a 6. k 87 

Locus5ftvcrusexFlamft. 1 1. 1 1 . 7. 
Angulus comrautationis 
Complementum 
Ditnidium 

Elongatio feu aEquatio Tub. 

Verus 9 locus 10. 


48. 

¥>• 


6. xo. 1. x. 
y. 5>. 58. 58. 

7 9- 59- * 9 - 
ix. iy. 14. 
2.8. yx. 31. 
Nempe in gr. *8. yx. 31.2%. velrotundc 
x8. y 3. prmcise ut in noftris Ephemeridi- 
bus anni 17x4. Bononiat impreflis . 


Inclin. helioc. 

Dift. $iT. cum rad 
Dift.$d# fub. 
Refiduum 
Cujus valor 
Ablatis gradibus 
FicdilLvera^a & 
Cujus Mefolog. 

Semi -angulus 
Ejufdem Mefolog. 
Summa dempeorad. 
Valor fub4 femi-ang. 
Diff. feu Elongatio 


G. M. S. 
4. 47. 19. 
14 - 99*5 5 * 
4- 5958*5. 
104.0069 
68.19.x4. 

45; 

x5.19.x4. 
9. 65460. 
79.y9.x9. 
10.755x9, 
10.58789. 
*7-44-15 . 
ix. iy. 14* 


Inclin. helioc. 
Elongatio 
Produftum 
Angulus fubtr. 
Cujus valor 


Pro Latitudine. 
G. M. S. 


4. 47. 19. 

ix. iy. 8. 

xo. 1. x. 

x. 58. 13. 


M. 8.9x510. 

L. 9. 5x67.8. 
18 14988. 

L. 9- 55441. 

M. 8.71547. 


£fbe- 


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Flamftediani & Streetiani calculi . 1 5 

Ephemeridet habent mi nut a a. 58 .quippe gut omijfu fee wits minutum prirnum 
tan turn admittunt . 

Tabulas aquatiomm condere . 

PUNCTUM III. 

I Ntelle&a per appofita exompla fupputaodi mechodo, earn , qua ufi fumus pro Ta- 
bulis ajquationuai coudendis formaui orevibus verbis aperire haud difficile erit. 
Prim6 diflantiai Planets cujusiibct a oOie limites reperiro , & h ujus diftantiae gradus 
per columnas diflribuere opus tuic ; demu.u ad datam diftanriam lingu los anguli com* 
mucationis gradus dimidi are, &exprodutto Logarithnum di (lands , & femi an- 
guli proporcioncm cruere, ut abexeinplis paulo pod apponendis fatis fuperque coo- 
itabit. 

PlanetaB a Sole diftantis limes facile invenitur , comparata videlicet Planet* ma- 
xima a Sole, cum minima Solis a terra diftaacia , & £ contra minima Planet* a Sole 
cum maxima Solis a terra diftanria collata . Hocquc per Logarithmas expeditur fub- 
tradis minoribusa majoribus nutneris, addito tamen radio differentia, corumque 
valore per Logarithmorum Tabulas invelVgato, cuilidemas gradus 45. remanebit 
Planet* veraa Solediflancia . Q. E. 1 . 

Pro Sat Mr no ex Streetio 


Diflantia £ a £Jr maxima 
Diflantia a Terra minima 
Differentia 
Additur radius 
Et fit Melologarithmus 
Cujus valor ex Tab. Logar. 
Dempcis gradibus 
Reflac vera diflantia £ a 0 




6 . 00361. 

4 99159 . 

I. 01 102. 
10.00000. 

II. 01 101. 

84. 2 6. feri 

45 - 

39 - 


minima 

maxima 


5 - 913 74 - 
5.0072#. 

0.5)4645. 
10 00000. 
10.^45. 
83. 33. 
45 - 

38. 33. 


Igitur diflantia vera $ a Sole ncc ell minor gradibus 38. nec major gradibus 40. ergo 
dillantia dillribui potefl in tres columnas , cujus prima fit 38. media 3#. ultima 40. 
proporcionis caufa hinc inde excerpend*, fiquidem Saturni calculus hos limites nun- 
quam excedcrepoterit . Eadem prorfus operatione uti fas eft in aliis Planctis . Igitur . 

Pro }ovt . 

5.731541. minima 5.69454. 

4.99259. maxima 5.00729. 


Diflantia Of a Sole maxima 
Diflantia a Terra minima 
Differentia cum Radio 
Cujus valor ex Tabulis Log. 


M. 10.74382. M. 10.68725. 

gr. 7 9 - ¥>■ feri 7 8 - 1 3 - 

Dcmptis 45. reflat dift. vera Of a 0 34. 46. 33. 2 3. 

Vnde alt* tres column* d flantiam veram }ovis ex-hibebant , fcilicet 33.34. 35 - 

Pro Matte . 

Diflantia cr* a $ maxima 5.221 11. minima 5.14050. 

Diflantia a Terra minima 4.9 9239. maxima 5.00729. 

Differentia cum Radio M. 10.22852. M. 10.13321. 

Cujus Valor gr. 59. 25. fere 53. 39. 

Ecmptijg r.4 5 .reflabit vera diflantia Martit a Sole minor gr, 8.39. & major. gr. 14.23. 

Ig‘- 


Digitized by Google 



De Planetarum xquatione. 

Igitur opus erit cofuinws 6 . .napienau at> 8. uiquc ad 15. 
Pro Vtncrc . 


Diftantia 0 a Terra maxima 5. 00719. minima 4.99159. 

Diitantia 9 a ^ minima 4 1 8^7o. maxima 4.8' 108. 

Differentia cum Radio M. 10.15159. M.10.15051. 

Cujus valor gr. 54. 48. feri 5 3. 29. 

Demptis gradibus 45. reliant 9. 48. & 8. 29. 

Itaque Veneris diftanti* cribus columnis fatistacimus , nempi 8.9.10. qua; quia 
invent* fucre in MartciifdemcalculisutipolTumus, &Tabul..mfolam condcre, ut 
fecimus, qua pro Matte & Vcnere inlerviat , tituluin apponendo : Tabula aqma- 
tionis pro Martc & Venere . Rclidua Martis column* feorlim in Tabula debitfa re-' 
ponentur , incipiendo tamen a gradibus 10. uc fieri po/lit arearum collatio ad ufum . 
fexagenaria proporcionis . 

Pro Alercurio . 

Diffantia O a Terra maxima 5.00719. minima 4.99159. 

Diftantia 9 a 0 minima 4.4 Q ^p<5. maxima 4.66^46' 

Differentia cum Radio M. 10.51035. M. 10.31415. 

Cujus valor ex Tabulis gr.73. ia» f cr ® 64. 38. 

Demptis gradibus 45. remanebit difiantia miner Mercurii a Sole vera gr. 19. 38. & 
major gr. z8. 12. % 

Igitur column* numeraUuuur n-a^r. I9.fcilicct ufquead 19. Adformam cal- 
culi fie procedcndum erit, exempli gratia proSaturno. Gradus 38. Mc:ologarithmus 
reperitur ex Cavalerio 9. 89180. 98. Qyare mentis quinquenotis ultra caraderifli- 
cam9. additaque o. unitate, quia fexta figura medictatein decens fuperat ( quod 
inteliigi debet aliis in cafibus) fit Meiologarithmus9. 8918 1. incapitelibri, a quo 
fupputatioexordienda eft , prafigendus . Deindc pro anguli commutationis primo 
gradu affumatur Mcfologarichmus dimidii ejufdem gradus , qui jundus priori dabit 
Mefologarithmum , a quo fi deinatur radius , & per Tabulas cjufdem valor feu pro- 
portio exquiratur , hacque a dimidio gradus ex parte notati ablata afferet in refiduo 
aquationem qusfitam . Calculus exempli caufa pro primo & fecundo gradu anguli 
commutationis ad trescolumnas diftantia; vera Saturni a Sole fic fe habet . 


S IG N A 0 . 

Diftantia vera Saturni 4 Sole. 

Diftantia j 38. M. 9.89181. 

| 39. M 9.9^8? 7 40. M. 9 92381. 

Gradus 1 o. / // 

0. i / 0 / ll 

I. I o. 30. 0 7 94 o8<5 

0.30.0 7 940'Y ; 0. 30. 0.- 7 9408 6. 

Proportio ! 0. i?. xf>. - 7.83 367. 

0 14. 17. 7.84913 0 1? IO.-7.864O7. 

JR matio 0. 6. 34. 

O. 7.4?. 0. 4 'O. 


jTquatio lo. 13. 8. 


II. 1. o. o. 8.14101. 1. 0 0. A. la. 1 91. 1. 

Proportio j o. 46 52. - 8. 13473. 048 758.15019 o. to. io. 8. 16573. 


o. 1 1. 2 =;. 


Ec tali padogradui primo anguli commutationis in diftantia gr. 38. compctit *- 

qua- 


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De Phnetarum aequatione. 17 

quattomin. 6. $4. & gr4dui.1i. min.13. 8. in columna vcro diftanti®\jp. pro primo 
gradu habemus 5. 45. pro fecundo n.14; & indiftantia 40. min. 4. 50. in primo, 
5>. 40. in fecundo gradu anguli proTabula eondenda ,. cui fuperius notam jitUt 
proprimi, in(cr\us Subu-*bc proiecundi femicirculi gradibus, apponcs. Ncc ali— 
ter opcrano procedit in casceris Planecarum cakulis , quorum methodum in me- 
dium attuljcnus, uc videancCandidaci cujus operis, cujus Jaboris fie totuin fcmi- 
cireuluoa, feu gTadus 1 So*, pro quolibec Planet3 , idcmqut pro qualibet columna 
Aipputare, & prcportioncm ad fecunda ufque fcrupula eljecrc, uc ad integrant 
aequacionisTabulam perveniatur. Qua propter fiquilibetgradus, quatuor opera- 
„ tiones continec , qux clare patent.* primd Mefologarithroum dimidii gradus daci 
excendere: fecundo fumtaam facerecum Mefologarithmo dirtancias : certidprodu- 
• cti proportionem reperire : quarc6 proportionem invencam toilere a gradus dimidio ; 
erunc operationes a nobis fad® pro omnibus Planctis , exclufa corum diftantia 
41049. addicifque Logarichmis diftanci® 41065. Tabulas Latitudinis hlc non re- 
cenfendo. Adde etiam quod operationem quintain adjecimuscuilibttgradui , nem- 
pe nocando ex parte differentiam inter unum & alcerum gradum iniercedentem, 
necminori ftudio cjufdcm differentia progreffumobfervando, ut hie nobis errorcs 
qui in preportione cruendaincidere poterant, patefaceret; Cumque cjufdempro- 
f groflus ultra modum turbatus appatebat, itcrum adfupputationemexaminandam, 
iterumqueubiopuserat inftituendam animunj intendebamus. Summa igicur opera*, 
tionum pro ®quationun» Tabula evadit 45 5 6 f. 

Supputato integro Semicirculo , notaiifqqc in calccTabul® reliquis.fex fignis,. 
/iperordinem furfum procedendo fuos gradus adferibas, itautnumerus in latere 
dextro appofitus fit complementum alterius firiiftri la ten’s , Tabulam totam non tegrb 
pcrficicsex. gra. contra gradum primum feribegr. ap. contra a. a8.&c. utin no- 
flris Tabulis. , . • . 

T abulas nojlras exempli s comprobare , eammque ufum exponere . 

PUNCTUM IV. 

T Abulas ea, quara fuperius monftravimusmethodo conditas errare impoflibils 
eft, fiquidem ex iifdem Logarithmis, a quibus ipfae promananc incalculo 
sequationes, excerpt® fuere ; Nihilominus excmplis veritatemCaudidatis aperi- 
rciequumeft, immo&neceflarium. Unum duntaxatadvertendum erit, quodali- 
quando per calculum ex hifee Tabulis depromptum paucarum fecundarum excef- 
fus , vel defedus oriri poterit, qui fi magnus trientem , nunquam tamen rainuci 
primi femiffem actinget , qui cum minimus fit nec obfervationibus fubjici poflit , non 
immericoinconfiderandus venic . Et h®c pauca diferepantia non abaliofonce oritur, 
quam a Logarichmoruin figuris aliquibus neglect is ; omnes cnim figur® a nobis col- 
led® non fuere , nec colligi debueranc , nifi defidefatafuiflenc fecunda & tertia , 
qu® incalculo exprimi non folenc, fufficitenim in minuro primo ubique calculum 
confentire. Nec alia diligentia ufi funt qui Tabulas aliasaflronomicasfupputave- 
runt, & fuflkere omnes arbitrati funt logarithmorumfiguras quinqueadhibendo 
ultra caracterifticam , addica tamen uniutecum fextafigura mediecacem decen® 

• ' ~ .1 . c fupe- 


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i8 'Tabulatum Ufus. 

fuperat . Hacdecaufa prudentiflime P. Cavalcrius in fuo Trigonometric Opu/culo 
ex feptem figuris ultra caraderiflicam , duas novifliraas pundo diftinxit divifitque , 
lit foils quinque uti pro libitopoffent fupputatores ; irnmo ubi gradus in primis fra- 
dionibus conff ftit , aliqui 4. primas cantum figuras ultra caradcrifticam calculo fa- 
tisfacere conftancer afferunt . vidiriflbon pralediont XXIX. in Veneris latitudine , 
qui laticudinem geocentricatn per Logarithmos 4. tancum figuris retentis compu- 
tat . Nos vero in Tabulis aquationum Temper quinque adhibuimus . 

Itaque ad exempla. Verumquia prius intelligendus eft ncceflariusTabularura 
ufusj iJeode hoc aliqua differ ore haudincongruumerit. 

Quoad Tabulasaquationuin fpedat, ufus faciiis eft , nam vifo angulicommut. 
fignoinfronte , & gradu in latere finiftro , ft inter primacirculi fexftgna angulus 
verfetur, econtra obfervatoftgnoincalce, & gradu in dextto latere ft angulus ex- 
tra femicirculumcxiflat , habebiturin area columnar data diftantiae , quae iocapite 
notatur, pertinenti, fada ubiqueproportione ft ultra gradus minuta, &minuto- 
rum fragmenta adhaferint tam in angulo. quam indiftantia; Inangulo fcilicet fa- 
da collationcarealide gradu ingradum, in diftantia veroexcerpta differentia co- 
lumns uniusab altera . Qua omnia fequentibus exemplis patobunt. 

EXE M PLUM I. 

Datus fit angulus commut. pro Centre Signa a . gradus (. min. 1 J. fee. JO. Sitque tjufdem 
a Sole diftantia pergradus 45 . caftigata , ideft diftantia vera gr. 8. j 7. 40. hgrtjfu fafto in 
Tabula aquationum a* & Q obfervaro ftgno 11 . , & diftantia gradus 8 . fada comparationt 
cum columnagr. p. calculus fit perficitur 

In Tabula arquationis Veneris Tub Signo II. invenio. 


Cum gradibus 6. 

Cum gradibus 7, 
Differentia crefcens 
Pars proportionalis pro min. 

15. jo. addenda squationi gr. 6. 
jEquatio prima in dift. gr. 8. 
./Equatio s. in dift. gr. p. 
^quationum differentia decrefcens 
Proportio pro min. 57. 40. 
fubtrahenda a prima aequationc 
Reftduum, ideft asquatio qusftta 


in 

dift. 

8. 

in 

dift 

. p. 

0 . 

1 

ll 

'• 0 . 

l 

u 

3 7‘ 

47 - 

6 . 

* 7 * 

7- 

39. 

38. 

1 1. 

7 - 

21 ’_ 

JO. 

in. 


14 . 

.f • 

1. 


23 . 

»7‘ 


y- 

3 3 - 



21.’ 

*7^ 

5 2 * 

oc 

-'I' 


I. 

2 2 l 

!?• 

I 





39- 

37’ 



# 


38 . 

_± 




*7- 

14 ." 

3ft 





Per Logarithmos. 

Diftantia vera 9 a & gr. 8. 57 40. M. p. IP780. 

Dimidium anguli erit gr. 33. 6. JJ. M. p. 8144;. 

Summa dempto radio valet gr. j. ji, n. M. p. 01213. 

Reftduum vel aequatio 9 gr. 37. 14. 34. pr&cife utex Tabulis, 


EXEM- 


Digitized by Google 


Tabula rum Ufus. ip 

EXEMPLUM II. 


Detur angulus commulHionis pro Of Signet 3. gr. t j. 50. 41. cujusvera diflantia a 0 
fit gr. 54. 3 2. 

In Tabula squationis Of Tub Signo III. 'habeeur .' 



in 

dip. 

34 • 

in 

dip. 

3 5- 


G. 

M. 

S. 

G. 

M. 

S. 

JBquatio graduum 13. 

11. 

11. 

0. 

10. 

7- 

7* 

Differentia dccrefcens 


0. 

J 5 - 


1. 

2. 

Proportio pro min. 50. 42. demenda 


0. 

46. 


0. 


^Equatio correda raticne anguli 

TT7 

10. 

l 4- 

10. 

6. 

15 - 

<• Harum asquationum differentia dccrefcens 

1. 

3‘ 

5 9- 




Proportio fubtr. ab aquation; correda 


3 4- 

8. 




Refiduum vel asquatio Of 

10. 

36. 

6. 





Per Logaritbmos. 

Diftantia vera Of a gr. 34. 32. o. M. p. 83767. 

Dimidium anguli gr. 5*. 53. 21. M. 10. 12166. 

Summa dempto radio gr. 42. ip. 6 . M. p. pjp33. 

Differentia vel aquatio quafita gr. 10. 36. 5. 

Ex Tabulis uc fupra gr. 10. 35. 6. 

- — - - _ . 

Ex quibns evidentiflime patet Tabularum cum logarithms confenjut, nec alia, extm- 
fla in re tam clara apponenda funt . 

corollarium: 

Hinc fequiturcalculum perTabulas fadum, &aquumeffe, &calculo Loga- 
rithmicomulcobreviorem. ac expeditiorem ; fufficit enim in Tabulis diftantia vera 
Planet® a Sole, & angulus commutations. Qpapropter & complementum ultra le- 
micircuium, & anguli dimidium , & ejufdera dimidii logarithmus , &logarit. di- 
ftantia ver®, & horum Logarithmorum fumma , &proportio proculdubio evi- 
tantur. Calculus veroHyrianus mulcoraagis barum Tabularum ope expeditus eva- 
dit, quia in illo plures neceffari* funt operations, utfuolccovidcbimus. Enigi- 
tur pro fupputacoribus Tabularum noflrarum utiliras . 

De Tabula proportional! pro Planetarum latitudine 
expedite reperienda . 

C A P U T II. 

PUNCTUM I. 

P Erceptis qua: de squationum Tabulis dida funt, aliqua etiamde Latitudine 
differendi tempus eft . 

Putaviraus olim Tabulam generalem , quam promiferat olim , fed non dedit Ma- 
. c a ginus, 


Digitized by Coogle 



zo Dc Tabula* proportionali Latitudinis. 

ginus, proomnium Planetarum lacitudine in publicum dare; fed cum operations* 
nonpauca:, & raolefla: nimis forent , nulla alia potior , quam quse a nobis excogi- 
tata fuit , met hod us in mentetn venit. r.rWmwfcilicet propartioualem condidimus , 
cujus ope & fexagenariae Tabula: rep:ritur vera Planetx latitudo , ex angttlocoo** 
mutationis, & inclinations .Heliocentrica ex Tabulis aflronomicisdata. Equidcto 
(fiveranobis fatcri liceat) fumma ilia , qua prirax tfa’bdratx fucrunt Tabuls, 
has etiam non elncubralle peccatum nunquam credidimus , cum tanti non (it latitu- 
dinem etiam ad fecunda fcrupula elicere, necunius autalteri minutipymivarieta- 
temmagni faciunt Aftrooohi; cum ilium, quern habet loogitudo in obfervationi- 
busufum latitudo revera non habeat . M ox cameo ad fecunda ufque fcruppla hanc 
definirc curavimus. Methodum autem quoTabulas elaboravimus jam jam expo? 
nimus . • 1 i : - «■ ' 

• -T .. • v '.I.,- I 

Quomodo conflruEra fint pro Latitudinc proportionaltrs 'Tabula • 

PUNCTUM If. 

T AbuIx ift® , ot fopet ranuimus » per ralculum brcvioremitonditx faere propter 
fupraallatasrationes. Methodum autem paucisaccipe. Quia lexagenaria dc- 
fidcratur proportio incapitc libriad cakulum apti feribatur Mefologorithmusmi- 
nutorumdo. paucioribus quam fieti poceft potrs, «ritque8. 14 19. Huic addatur 
Logartthmus elongationis Planetx, dcindf abhorum Ada fumma detrahe LcgaiT- 
thmumanguli commutacionis, cujus valor eric optata pars proportioualis pro Tabula 
conflruenda . 

Igitur angulunt commutationis, & clongatioaem Planer* priusdari opus erit. 
Angulus commutationis habetuf cx fuppoiitiooe , elengatio vero non tarn facile 6 
dr fuperioribus toquamur , nam in inferioribus Planetis xquatio per Tabuias xqua- 
lionum inventa eft ipfa, tlongatio, dequa imprxfensfitquarflio. Qua dcre utelon- 
gatio in fuperioribus Planetis reperiatur » ft illos quos adhibuifli pro xquatione 
calculoshabes, proportioncm, quam pro aequatione a fc.rwanguloabftulifti , nunc 
addc, & habebis quxfitam dongationem. Quod fi forte prat manibus didos caf- 
culos non habeas, dongationem (k affequerjs. A dato angulocommutatioBis in 
gradusrefolatodemc .rquationem eidena angulodebitam., & inrefiduo habebi^op- 

tacam dongationem exempli gr. u ' u,i 

J Qssaratur elongatie Op ad angulum gradus 1 j.fhb d’flantiagr. 3 f ,cu{us aquatio in Tabula 
reperirttrgr .1. g4.4S.Hac agradibns 1 f. dempta dabit in refidmgr.il. 2 }. ll.fra elon- 
gations , 

Et fie proccdes ufque quo fieri poflit ab angulo commut. fubtra&io , qux in refi- 
duo quadrantem , feu gradus po.mon excedat ; tunc enim facilius ages fi anguli cona- 
plementum ad 1 80. gradus fumpferis , cui port aides xquationera repertam e. g. 

Datus fit angulus Sign a 4. gr. 5. , qua in gradus refoluta erunt gr. 125., cu)us complex 
mention ad 180. erunt gradus $5 .his addira aquation? gr. 6 . 10, j 1 . put a pro £ fiet clonga~ 
tk 4 l.lo.ft.Veir 6 tundi 6 t.il* . 

Si vero vix angulus tranfierit quadrantem , ita uc Cubtra&io fit minor quadrant : , 
tunc prima regula uti fas eft . Mempc ; 

i i Gctut 


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JDe Tabula proportionali Latitudinis. 21 

Detur angulns com. ingr.refolutus ideftgr. 96. ao. , fitquc aquatio congruent gr. 7. zo. 
hxc fubtrahi debet , nam refiduum fit S 9. minor quadrante . 

Si angulusfupra fomicirculum vcrfarctur omnia focus agenda eflcnt > fed no- 
flroincalculohisnonindigemus, fiquidem tunc Tabula eft completa, & cum eif- 
dein proportionibus revertitur ufquequo ad fuum principium perveniat . 

QuoadTabulxdifponendaeordinemattrnet, aliarum Tabularum ipfifiimus or- 
doforvetur, ncmpeproSaturno , Jove, & Vencre tribus columnis, proMarte8. 
&proMercurio 11. Unutn hie advertendum eft, quodTabula proportionalis pro 
Martcinforvirenequitpro Venero elongationisdiverfascaufa , qua propter calculo 
differenti pro quocumque uti fas eft . 

His bene perceptis pro Tabula Saturni& Jovis fufficiet calculo fubjicerequodlibec 
anguli lignum, incipiendo a iigno I pro quolibet diftantim gradu ufquc ad figna 
fox, naminaliofemicirculo fi notemus figna & gradus ut in alia aquationum Ta- 
bula foci mus, fatiserit. 

Fro facilitate calculi notandum, quod figni O gradui primo ipfa elongatio eric 
proportio in Tabula adferibenda propter identitatem gradus primi cum primo loga. 
rithrno. Qua propter initium Tabula; proportionalis Saturni, Jovis, &Martiseric 
elongatio data, &proJove, & Mercurioipfamettcquatio , & finis Tabulae, ideft 
ingradib. 29. figni V , vel in primo gradu figni VI. ( quod eodem recidit ) erit pro 
Venere, fit Mercurioeademac in Tab. aequatio,fod pro fuperioribus addendus erit 
gradus unusatquationi in Tabula repertm.- Igicur exempli caufa erit proportio pri- 
mo gradui figni O. debita pro Saturno in diftantia gradus 38. min. 57. fee. 26. fiqui- 
dem fubtrada aequatione min. 6 . 74. a gradu uno vel minutis 60. , erunt in reiiduo 
5 7. 16. & pro gradu primo figni Vi. fubeadecu columna ex data xquationemin. 8. 
27. erit proportio in Tabula admittenda gr. 1.8.27. Quod intelligi debet etiampro 
aliis Planetis. 


Itaque qutt'rcnda fit in gratiam exempli proportio pro Tabula Jovis prima columna, fei- 
licet ad diftantiam gradus 3 j-. : , ' - . 

Ex data rcgula erit SigniO. gradus primi elongatio & proportio eodem tempore 
in Tabula adnotanda gr. o. 49. 29. Eodem modopro fignol. reperitur Jovis aequatio 
gr. 5.7.44. , qua; dempta abangulo figni I. vel gr.70.dat in refiduo gradus 24.52. id. 
abjedis fecundis pro calculi facilitate erunt gr. 24. 51. pro elongatione j Ergo 
calculus fiedifpenatur. - ' 

iqgaritbmus immutabilis .j; ' .. .8. 2419. 

Elongatio figni I. gr. 24. fa. addenda ' L. 9. <5zj8 . 

- Summa Logaritbmorum 1 7.8657. 1 

JLngfius com* figni I. ideft gr. 70. fubtr. , L. 9- 6990 . 

Proportio quafita gr. o. 50. 28. x. ex M. 8. 16*57. 

Elongatio figni II; add. Log. immut. g.. 50. 77. L. 9. 8877 . 

Logmtbmorum fumma * 18. izptf. 

wdngultis com. e)ufdem figni in gr. refit. 60. ‘ L. 9. 9; 75. 

~ Proportio gr. 0. 55. go. ... ex M. 8. 1911. 



Digitized by Google 


22 Dc Tabula praportionali Latitudinis . 

liongarh ftgni III. addenda ut fupra gr. 78 . a L. 9- 9PQ4« 


Logaritbmorum colleSio 



18. 

23x5. 

^ tngulus com. ftgni III. gr. 90. 



'0. 

0000. 

Proportio dempto radio gr. 0. f8. 42. 

ex 

M. 

8. 

zixj. 

Elongatio Jtgni IV. add. Log. immuc. gr. 71. 

58 . 

L. 

9 - 

9775 - 

Logaritbmorum fumma 



18. 

aipz. 

^ tngulus commut. xqtuvaltns gr. 60. 


L. 

9 • 

911U 

Troportio gr. t. 5. 45. 

ex 

M. 

8. 

2817. 

Elongatio Jigiu V. addenda gr. 3 7. ZJ. 


L. 

9 - 

-1 

v°° 

JX 

Logaritbmorum produtlum 



18. 

OZ 5 y. 

0 tngulus com. ftgnis V. refpondens gr. 30. 


L. 

9 • 

6990. 

Troportio gr. 1. 12. 54. 

ex 

M. 

8. 



Troportio progr. 19. ftgni V. ex prxtntjjts gr. 1. id. 1 ». nam pro ftgnis Vi, & O. n*- 
tantur tres cyphrx o. o. o. nulla enim bic darur proportio . 

Tali methodoSaturni & Jovis Tabulam proportionalctn fupputavimus , & refi- 
duutn Tabulae per partes proportionates ampliavimus , quod in illisduobusPlanetis 
fatiseft. Ncc diffiroili tnodo alias Planetarum pcoportionales Tabulas conftruxt* 
mus, veruraproMarte& Venere, aliquandoetiampro Mercurioubi opusfuit , i» 
fignis videlicet IV. & V. ad qurmlibet anguli commutationis gradum proporriocal- 
culo rcpci ta fuit . Inrcliquisfignisnuncadiy, moxadio, vel adquinquegradus 
calculum fubivimus juxta differentia progreflum. Praftat jam Tabularum idarun* 
ufum traderc , ipfafque exemplis comprobare , quod pundtofequentifict. 

TaUtlavwn proportionalium pro Planetarum latititdine ujiis y 

cvxmpla * 

PUNCTUM III; 

T> Eperto per prsmilfassquacionumTabuIas Planets locoGeocentrico ad inve- 
J\. nicndamlatitudinemgeocentricam Tabula proportionalesa nobis conftru&ae 
confulenda funr , quorum ufus talis eric. Cum data ex calculis Planets diftantia ve- 
ra , & figno anguli commut. in fronte Tabula ope graduum ejuldcm anguli in latere 
iiniftro in primo Semicirculo, in dexrro autem pro fecundo inTcniturin area propor- 1 
tio, qua cum inclinationcHcliocentrica exTabulisdata aures regula» vet fexag. 
Tabula auxilfo larftudinem quafitam exhibebit . Analogia autem iftius opera tronis 
taliseft. Vt 60. ad inclinationem dat am ; itaproportionovifjimereperta , ad quartumnu- 
merum, feu ad Latitudinem optatam . Opcrando per SexagenariamTabularo, quod 
nihil facilius. vifa indinatione in fronte, & proportione in latere, vel vice verfa 
( iden enim eft) in area fenper Planets latitudohabebitur. Seddarius 

In appofitis exe nplis pro latitudinc Jovis a Cl. Manfredio obfervata , in venta fuit 
per Logarithtnosgr. ®. 45. 3. praflat nunc per hasTabulaseandem rnveftigare. 

EXEMPLUM L ' 

lnclinath Helioc. data fuit gr. o.ij.negleHis fecttndiscum diflantia Vianet tever* a 0 
gr. 3 J. 41. Ingraft* fafto in Tabulam Jovi defUnxtam iuvenio refpondere aitgulo commut . 

fgn. j. 


Digitized by Coogle 


. Tabularum proportionalium ufus. 23 

5. rotundc proptrtionem gr. i. is. qua: inTabuU Sexagenarut frontcobfervata, 
OrincUn. min. s 7. in latere, exbibet latitudmtmgr. o. 45. i.per Logarithm*! 45. s . 

Si quis majori diligentia uti vellet , reperiret per columnarumcollationem faftam 
proportionera rcfpondcotemgr.35. 41.7. eflegr. 1.12.44. quaa cum datainclina- 
tionemin. 37.4.afleretmin.44. 5 < 5 . 1 atitudoobfervata 44. aj.undeparumdiftatab 
opcrationc iogaritbmica , &magis acccditobfervatiom. 

EXEMPLUM II. 

ibidem data fuit pro latitudine inclin. Helioc.gr. 4. 47. Cum angulo fig. V f.gr. xo,& 
■difiantia vera gr. is. 1 9. *4. reperitur in Tabula propria proportio min. 37. iS. qua in Sc - 
xagenaria cum 4. 47. dant grains 2. 58. ut incalculo Logaritbmico fuperius allato . 

Aliaetiam excmpla vidcbimus paulo pod , ubi de calcuio Hyriano loquendum 
crit. 

Uaum hie tantum adnotandam venic , quod nempe cum invefligaDda lit propor- 
tio, qua: in anguli lignum O, vcl VI. & gradum primum verfatur, tunc temper 
accipienda crit proportio gradui primoaflignara . Ur c.g. fi quis quaereret latirudi. 
nem Martis cum angulo commutationis figni O. gr.o. min. 2 p. fubcolumna 1 i.eflec 
proportio vera quaerenda in fexagenaria Tabula ilia ipfa, quae gradui primo afli- 
gnatur, fcilicetmin. 35. 50. fed neexcmpla defint . 

Sit pro o'* Inclinatio gr. <x 5 y. 

Angulus commutationis ligna O. gr. o. m. 2p. 

Sitque ejus diflantia vera » 0 gr. <1. 

£rit ejus proportio 35. yx>. , qua: per auream regulam dabit queefitam la-» 
titudinem gr. o. 31. 51. vel rotunde o. 33. 

Per Logarithmof. 

Elong. anguli min. ap. debita eft min. 17. ip. L. 7. 7021. 

Inclinatio data gr. o. jj. M. 8. 1041. 


. Summa 15. po 63 . 

Angulus min. 2 9 . demendus L. 7. px< 5 i. , 

Rcftduum & valor gr. o. $ 1 . $ 1 . ut prius ex M. 7. p8ox. 

jiliud cxcmplum . 

Sit $ inclinatio gr. 2. 20. 

Sitque angulus commutationis Sig. VI. o. ij. 

Et ejus diftantia gradus $p. 

Ejus proportio tanquam li effee gr. x. datur gr. 1. 7. , qua: per fexagen. 
Tabulam affert pro Jlatitudine £ gr. 2. _j< 5 . ao. 


Per Logaritbmos . 


Inclinatio £ gr. 2. 20. 

M. 8. diaii 

Elongatio debita grad. 0. 16. 45, 

L. 7.45877. 

Summa 

16 . 2978 . 

Angulus min. 1$. demendus 

I. 7. 63 p8. 

Rejiduum ideft Latitudo gr. a. _j< 5 . ip. 

ex M. 8. "< 5 j 8 o. 


Alia igitur in re tam facili cxempla adducerc fupervacaaeum eft. 

Duo 


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24 Tabularuin proportionalium ufus.’ 

Duo tamen adhuc in computi gratiam adnotatu digna hie fubjicere volumus . Pri- 
me fi forte angulus commutationis iigna O. vel VI. pracife adsquet abfque ullis 
fragments, tunc indinatio Heliocentrica erit ipfa Planets latitudo. Secund6.fi in- 
clinatio lleliocentrica pracife gradum unum vcl minuta 60. attingat, tunc propor- 
tio reperta erit ipfa PJaneta latitudo , fi vero eadem indinatio fit gradus a. propor- 
tioduplicata , & fi 3. triplicata iatitudinemexhibebit , & fic de cateris . Qua pro- 
pter fi minuta quadara fuperfint notata ex parte prius prnportione , reliqua in 
fexagenaria quarenda font. Permodum exempli fit indinatio exTabulisdata gr. 
i.ao. fitqueproportio reperta min. 54. 50. Tuncdico progradu t. inclinationis die 
latitudinem min. 54. 30. fed per min. 20. additis min. 18. 10. latitudini *4. 30. fit 
vera latitudo gr. 1. 1 2. 40. Pluribus igitur immorari , majorique radio Peritosaflice- 
re incongruum cfi. 

De Calculo Hyriano , (5 s quomodo huic infewire pojfmt 

no fly a Tabula, 

CAPUT III. 

t * 

P U N C T U M • I. 5 

C Um Tabula noflnc , qui noviflimam Planctarura aquationem.afferuntcalcu- 
lis Hyrianis mire accomodari polllnt, hac data occafione nobis nova mechodus, 
cujus ope Hyrii fupputatio brevior, faciliorque evadit, innotuit, quam fiudiofis ape- 
i-irc hicpaucisconablmur . Sed prius videndum quomodo Tabula liuic calculo in- 
fervirequeant , & quern ufum habeant dus novifiimx a nobis confirudx in calculi 
gratiam, quod punclo fequenti innotefeet. Interea Tabula nofirs aquationum 
Hyrii calculi infervient, cum angulus commutationis fiat verc angnlus commutatio- 
nis, non vero angulus ad Solem . Hoc autem prsftabitur fubtra&o loco Planets ex- 
centricofidefuperioribus, econtra autem dempto Solis loco a Planeea , fi de infe- 
rioribus fiatquafiioj refiduum utroque incafu erit angOlus commutationis opta- 
cus. Infervient autem optime Tabula , quia Planetarum liraites ultra aquationum 
noflrarum terminos non evagantur ; Fa&a enimeomparatione difiantia minima $a- 
turni a Sole, & maxima Solis a terra, & vice verfa ut in' capite I. puntioj. re- 
peritur minor Saturni difiantiaa Sole vera ex Hyrii logarithmis , ablatisgradibus 
47. gr.j8.ii. fere, major verogr.ip. if. Sic Jovis difiantia minor gr. 3 3. 23. ma- 
jor gr. *4. 48. Martis& Veneris diftantia minor gr. 8. 28. major pro Veneregr. p. 
4 6. fed proMartegr. 14.16. Et pro Mercurio minor difiantia gr. 19. 31. major gr. 
28. ii.QuareidemferecumnumerisStreetianisadeficonfenfus; Ncc alia oppofitio 
fieri poteric , quam Planets curtatio in Logarithmis fuper allata difiantia ncglc&a , 

( dequa tamen infra habebitur ratio ) qua datam diftantiam augere aut minuere po- 
tefi. Verumcura hujuscurtationisincrementum aut decrementum nunquampluf- 
quam gradum primum difiantia promoveri , vel minus quam gradum ultimum 
ejufdem difiantia a nobis aflignatx retrahi poflit: ideo intra Tabulas nofiras Planets 
cujuslibet squationcs neceflario contineri apud omnes hujus feientix hiud ignaros 
in confcffo erit . 

Cur 


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De Calculo Hyriano. 15 

Cur condita fint Tabula ultima pro Tahulis Hyrii, taruruque ufus, 

P U N C T U M II. 

• iBQy ationis Saturni apud Hv riura , a pud nos autem squationis argumen- 

ci mcdii laiitudinis Tabulam non ad alium finem condidimus , camque ad quem- 
Jibetgradum produximus , nifi ad unum vicandumcalculum infupputationc, &fa- 
cilitandae proportions gratia, cui adjecimus curtationtm a ncbis ita nuncupatam, 
femper a diflantia Saturnia Soicdctncndam , ut fiat dijlantia curtata add'no taincn ra- 
dioincalculi refiduo. Tabulae hujusconftru&io & ufus taiisefl . ./Equationem quam 
Nodo addere praeccpit Hyrius > nos econtra ab arguraento latitudinis medio fubrraa 
himus,ut fiat argumentum vcrum, cujusopeinclinatio eruitur, quod idem eft, ut 
patet in appcfito exemplo. 

• Datus fit $ locus excentricus I ' 

Sitque ejufdem SI fubtr. 

Erit argumentum latitudinis medium 
^quatio SI addenda 
Quare verus SI locus 
Et argumentum verum 

• Ex noflra labula Argum. medium 
JEquatio ut fupra nunc fubtrahenda 
Verum argumentum latit. ut fupra 

Eodeminftanticumargumentovcrolatin „ 

turtatio , quam condidimus fumendo complemcntum arithmcticum , vel complemen- 
tum ad radium ex logai irhrao fccundo latitudinisextradhim i Hocque factum fuit, ne 
pofl inventam latitudinem 1 neccflitatem habeas quterendi in Tabulis Logarith -no- 
rum cofinum. ejufdem latitudinisjungcndum logarithmodifiantis Planets a Sole ex 
Tabulisdatae, fed excra&a curtatione,hacquedempra a logarithmo diflantia: , refi- 
duumadditoradioprofuperioribusdiftantiam curtatamexhibebit. Pro inferibrjbus 
autem additur radius logarithmo diflanti® Solis a terra , ut poflit derni logaritbmica 
Planet® diflantia . Qyx utclariuspateant ipfum Hyrii exemplumufurpare licebit . 
Invents fuit ab eodem diflantia ^ a § 4. 95 584. 

Et argum. latitudinis verum fig. 10. gr. 6 . 4 5 . 

Cum quo colligo in Tabula noflra currationem 
-Unde refiduum addito radio, feu diflantia curtata 
In Hyrio quoque diflantia curtata S. R. 

Hac conftru&a Tabula aliam etiam pro aliis Planetis appofuimus, ut abfquein- 
greffu in Logarithmorum Tabula intentum facilimethodohaberemus. 

Tabular , & Hyrii calculum cum roflris confcrre , & comprobarc. 
'PUNCTUM III. 

P Raeftat nunc idem exemplum Hyrii apponcre , demum per Tabulas noflras idem 
fupputare , & brevitatempromiffam, nec non facilitated! oflendere. ^£quatio 
noflra in calculis Hyrii cfl ipfa differentia femidifferentiae a femifumraa, quam ipfc 
alio fed prolixiori modo adhibet . Videamus exempla . 

« d Sup- 


s. 

G. 

M. 

S. 

9 - 

1 . 

34 - 

ii. 

10. 

<5. 

14- 

11. 

ToT 

*5- 

O. 

0. 




1 1. 

- • 10. 

7 ‘ 

13 . 

34. 

10. 

*4- 

11. 

48. 

10 . 

*5- 

O. 

O. 



j8. 

1 2. 

10 . 

24 . 

11. 

48. 

is. non autem 1 

cum 

medio colligitur 


Sub. 2.8 . 
14. 95 55 5 - 
14. 9J5 5 5 - 


Digitized by Google 


*5 Dc Calculo Hyriano. 

Supputatio Saturni pro armo 170 6. 16. OBobrts bora 10. 
matutina cum min. 25. tempore apparenti 
Roma : «c Hyrio . 


Lucus mcdius $ 
Aphelium fubtrabendurr 


Anomalia media 
dLquatio cemri fubtr. 


Locus £ exccntricus 
Anomalia vera 


Locus mcdius £ 
Argum. latitudinis med. 


dLjuacio fl addenda 
Verus locus Q 


Argum. latitud. verum 
Inclinaiio 

Redu&io add. 


Locus £ reductus 
Locus Terrae 


Angulus ad 0 T S R 
i ang. ad 0 



o. x6. 45. 7 
1J. ii. J? 


R 

S C Inclin. 

S Saturni 
Dirt. curt. 


S ' 

S R 

T. 45 " 
T. V. 


Angulus X 


T. 45." 

T. X 
T. femif. 
T. fenidiff. 


Conopl. & icmif. ang. 

76. 37. 27 



Semidifferentia ang. 

1 18. 5C 


1'ro Latitudine 

Angulus ad 1 erra S T R 

450. 6. 17 


S.TSR 

Verus locus 0 ab aqu. 

i 12. ft. 


S. $ T R 

Longuudo £ 

61. 25. 29 


T. ioclin. 

Vd 

71 2. 15 . 19 


1 



T, Latitudo 



Laiit. § Auflr 


Logarithmi 

“ 4 ? j)jj»4 
3. 99709 


9. 99971 
4. 95S« 4 


4- 9555<5 


14. 93556 

3. 99709 



10. 52785 
1 u 
71 °i%- 50 


9 - 69759 
8- 55*51 


id. 15111 
9 ■ < 55**4 


£adi* 


Digitized by Google 




















Dtf Calculo Hyriano 


27 


• • * t 

1 w A. ■ ‘ 

Eadem fupputatio partim ex Hyrio> partim 
ex nojirif Talmlis. 



- S. 0. 1 ll 

Logarithm! | 

Locus medius £ 

A pheliumfubtra hendum 

2. 2. 24. 7 

8. 29. 22. 

Dirt. $ a 0 
Curtario fubtr. 

4. 95584 

28 

Anomalta media ; 
.Equatio cencri fub. 

BS 9 

Dili. f> curt. 
Adde Radium 

4. 95S?tf 
10. 00000 

Anomalia vera 
Locus £ excencr. 

4. 29. 5 *. 5 1 
I. 29. 15. a f 

Summa 

Dift. 0 a Terra 

14. 955 5<* 
7. 99709 

ft 

Argum. latit. medium 


Put. $ a 0 
Cuius valor 

10. 9^5847 / 

87.0 47 - i* 

/Equacio argum. lub. 
Argum. latic. verum 

25. 51 
10. 6 . <\6. 10 

!KE 5 jh! 

45 - 

38 - 43 - >5 

Inclinauo 
Reducta’o add. 


eroportto pro aqu 
Sub cof. 7 8. 

cum Sig. 5. gr.3 
39 - 

Locus £ redudus 
Locus 0 verus 

‘1. 29. id. 57 
*7. h. }t. 4 6, 

£qu. 7* 34. 5J 
Diff. dea. 7. 9 
Pro 14. 5 j. i, 4<5 

3. 0 a 48 

.~ v" 6 ’ 3 

Sub. I. 29 

Angulus commucationis 
.Lquatio addenda 

KMSrSg 

9 - 3 L 5 C. 

1. aequ. J. 37. 7 

2. xqu. i. 59. 19 

2. 59. 19 

Verus £ locus 
Vel in Zodiaco 

2. 2. »j. 79 
n: a. 2 5 . 79 

Hjrum diff. 77. 48 


• - ^ * { 

i - 

rro 4 j. iy.iuD. 24 2 i.a 1. squatione 

jEqn.-vera7.8. 46 


r Pro latitvdine. 


Cum angnlo eoitmut. xir difiantia $ v:ra in Tabul « proportionali datur pro- 
portio gr. 1. 6. ip. lgitur ut min. 60., ad inclinationcm rcpertam gr. 2. 1. 55. , 
vtl fee. 737f.> >ta proportio gr. t. 6. ip. vel 3979-, ad 8151 . , vel gr. 2 . ly. 
5 i. pm £ latitudine, 

Alccrum etiam pro Planecatum inferiorum fupputatione afferemus exem- 
plutn ex eodem Hyrio. 


d a 


Sup - 


Digitized by Google 



















2 g De Calculo Hyriana.. 

Supputatio Mercurii anno 1707. Mali die 5. bora 10. 
matutiM cum rain. 'ii. ihrnp. appairi Aim- 
in' China ; ex Hyrio. 


Locus mcdius 9 
Aphelium fub trahendum 

Anqmalia media 
5 iquatio ce ntri addenda 
Locus § cxceiuricus 
Anomalia vera 


Locus SI Q 
Argumentum latitud. 


Indinatio 
Redudio addenda 


Locus 9 reduc tus .. J_ _ 
Locus Terra: • 


Ang. ad O T SR 
f angulus ad_£J 


Cocnpl. & femif. ang. 
Semidiff. anguli / 


AngulusadTerramS TK 
Verus locus & 


Longitude 9 
Vel 


/■ 2 


Dill. Log, S 9 
Dilh Log. S T 

1 R - " 

3 ‘SC Indin. 

1 s 9 

§• Did. curt. S R 

_ -ST 

3 - T. 4 y.» 

f T. V. 




T. 45. 


I. 6. 40.I — i 

I. it. 49. 4J. yjpro Lanrudine 
S. S T R 
g — S. SIR 
5 T. indin. 


T. Latitud. 
Latitudo Mcrid. 


i- 

65571. 

4 - 

004J 1. 

9 - 

99999 • 


<1572. 

3 • 

65571- 

14 - 

0043 1 . 

3 - 

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54860. 

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51. 41. 

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i 

20. 

51. 41. 

9 • 

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53 10* 

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9: 276. 

1 1. 

50779. 

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IX. 16. 


8. 18761. 
7 - 7 ??M- 
16. 01085. 
8. 378 10. 
J — 64165! 
jo.® 15. 6. 


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Dcr.'Calculo Hymno . : ; £ 

Eadm fupputatio partimcx Hyrii y partial rx rrf- 
Jlris Tabulis ad unguem refpondcns Hyria- 

nis Calculi s . 

.7 1 ; . L f 0 A U *1 



S. 0. 1 ll 


Logati hmi 

Locus medius Q 
Aphelium fubtraheid. 

6. a8. zp. 13 
8. 13. 14. 7 

Uifl. Q a 0 
Curtatio fubtr. 

7 - 6557 * 

1 

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tyEquacio eentri adH 

10. v ».$, -tft 6 
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3 - 65571 

14. 00431 

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tor ap. w. 23 
7. iz. Z< 5 . 30 

Dift. $ a 0 
Cujus valor 

10. 34&60 

tfy.® yi. 4* 

locus ii Q 
Argumentum latitud. 

l/ll. *• H 
y. 27. 14. 16' 

Auferuncur gr. 
Dift. $ a 0 

45 

20. yi. 41 

Inclinatio 
Reduttio addenda 

0. 18. 36 

•q \\\ u 7 

Froportio pro xqu. c 
$ub 4 v col. to. 

um fig .5 .gr .28 
21. 

locus Q redudus 
Locus 0 fubtrahen<L_ 

7. 12. 17. 31 
1. 13. 49. 45 

£qu. 1*^44. 45 

Dift. deer. yz. 24 

- i.° 36. 1 3 
48. 4 

Angulus cominucationis 
<£qu. feu Elong. add. 

z8. 37. 72 

Tro 37.72. 33. y 

Sub. 30. zi 

,;1. 6. 40 

1. £qu. 1. 11. 40 

1. 5. 51 

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1. 14. 5 6. 2$ 

t. .®qu. i. 5. .51 


Vel in 

>14. y 5 . 25 

liarumdifF. y. 48 


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|/£qu. vera 1. < 5 . 40 

.vel hlongatio | 


Pro Latitudim . 

{ * v v j i r v. j ;. •• 

Fafta coinparttiane artarumxD. & zu cum angnli [ignis y. gr. zS. &e.J>rovenit pro- 
portio min. 4 8. 44. Data igitur Q htituime min, 18. id. , infiitutaqu e ut in alio 
ctlculo analogia: fcilitct. Vt6\ min. ad 48*44. ; it a 18. 36. ad 4. nUmerkm, idtfl ad 
min. 1 5. (. prxcife ut in HrntT. 

Vides igitur quara brerior & tutior fit calculus nofter per fexagenarium compu- 
tum , & quomodo exctnplucn hoc ad ungueitt Hyrianx fupputationi refpondeac , 
parun*& fere nihil diflcc Saiurni fuppuratvo, excedit eoimHyrium in longitudine 
fee. 10., deficit in lalitudiae fee. 14. Qua propter abje&is fccundis njinutiis mutuus 
erit confenfus . Ergo abfquc ullo fcrupulo uti quifquc.poceric noftris Tabulis ad fup- 
putationesfacilitandasnonnihil du rta nda fq ue.i> u pereft nu nc videndum fi Tabula iftx 
Kepleri Tabulis fatisfactanc, quod pun&o I V. , & noriflunodemonftrabicur. 



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30 De Tabulis Keplerianis. 

Quomodo Tabula noJ}r* Keplerianis Tabulis 
inferrjire pofftnt . 

punctum iv: 

E Xpraemiflisnulli diibitandum fupereft quia edam KeplerianisTabulis noftrte 
xqueac Hyrianisinfervirevaleant; ica ut de hoc verba facere fuperfluumvi- 
deatur. Adtollcndam tamen fufpicioncm omnem cujuslibet Planers limites, feu 
raaximam & minimam aSolcdiftandam , turn abHyrio, turn a Kep'cro , cum a 
Streetioaquoxquaciones noftrs pendent, collc&am in medium afferre volumus , 
utquifquepro lubito perferutetur & nofeat initiura & terminum didarum arqua- 
rionum tarn proculabeffc a Planetaruin Jimicibus; ita utfidarecur cur ratio quafi 
gradus parte major, (quajdari in h is Hypothelibus reveranon eftpoflibile) ad hue 
non segre accomodari poffent. Dantur itaque 


Dijlantia nxra a Sole demptis gradib. 45. 


1 Ex Streetio 

Kcplrro 

Hyrio | 

• • 

|G. M. 

2PC 3 

t&mm 

_ : J maxima 

Saturnl i minima 

nQ 

fm " 

■ 

39 ' *5 

3 8 V 

T • S maxima 

I° v,s X minima 

34 46 

33 2 3 

■ 

34 47 

33 2* 

Martis £ ®?*“ ua 
l. minima 

14 a j 

8 jp 

14 z 6 

8 39 

14 X7 

8 37 

Veneris •> max . ,ma , 
< minima 

9 4« 

8 xp 

9 4<5 

8 t 18 

mm 

MercuriiJ maxi[Da 
(, minima 

28 1 a 

1 9 3* 

28 11 

l 9 3 n 

*8 14] 

tp 171 



Patent igiturdats Planetarum diftancis fibi mutuo refpondentes . Qpa propter 
frex data Planet® diflantiaa O vera , & angulo commutadonis oritur ejufdcun 
Planets squatio, concludendum eric squadones noftrashifee diftandisaqua liter 
procedentibus , squaliter etiam infervire polk. Idem dici poterit de latitudinum 
Tabulis , quippe qua in analogia fupracitatis Audoribos communi fundantur, 
Hscque in gratiam Candidarorum dida lint . Interea fi Peri tor um anresper tot 
proportionis tarn facilis repetitiones fadastaedio affecimus(iflis enimfols Tabulae 
abfquculla explication fads fuperque fuiflent ) veniam pedmus> cum hate potius 

Tyro- 


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De Tabulis Keplenanis. 31 

Tyronum quano Profieencium in gratiam elucubrata ac cxplicata , non veto 
eruditis demonftraeionibus , ut fieri folet, iJluftrata fint. Verum fi Tabularum 
noflrarum raethodus, & fundamencum, nec non calculi facilifas , & quadam 
alia, quae hoc in Opufculo-coneinentur, calata fuiflenc, inflicueonoflro agre 
fatisfadum fuifle non cam a. nobis , quam a plcrifque hujus fcientia: baud 
ignaris in confiffo cfTet . Quo<l fi illi noftri , quatenus quales fine, laborcs, 
uti fperaraus , Candidate accepci fine ; brevi , Deo favenee , cempore Eeli- 
pfiurrr fupputandtriim Vulumcn , quod in hiijuj introdudionc promifimus , aff<S 
remus , cujus ope abfquc ulla alia methodo , Libro , aue Prxcepeore pocerit 
quifquc Eclipfium omnium prxteriea.ru m , prafentium, & fucurarum qualita- 
cem , & quantitacem facillime ubique loci dignofeere, ac perferutari. Sed pro 
Eclipfium fupputandarum ordine Opus aliud in lucem prodie , cui titulus , 
^4 ST &OSOTHI~{ MERIC*4, five flrwomica fupputandi ratio in Li- 
bras IF. digefla , quorum I. Calefiium Corporum longitudiucm , ac latitudiritm exhi- 
bit. II. Tfovam Eclipfium methodum tradit . III. Troblrmata ^ iflronomica pro- 
movet . IV. Ephemeridum conftruttionem docct . Qua omnia Tomum primum 
conftituunt ; in fecundo enim Tabula omnes Aftrofophi* univerfali infervien- 
tes contincntur. 


FINIS. 


7^on- 


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tr.'rn ' 


U 

r 


* * > ^ r • f /• f 

• * p /{ .:' j. i J I 

1 K . r - * ~ • ' - '■>■■ j-« ■' / j lit - (i, i : " p.j J . rrrrr> r - ■> ■ y 

Nonnuth in Taiklis Qjt.t/f * Inuto jTf Corri^e. 


Pag.. x e dire&o ' gr. 5. fab co!. y 

Pag. 5. gr. z. fdb ’col; 4 

lbicf. ' gr. zo. Tub cohult. 

Pag. 8 . gr. p. fub cb .• r 

Pag. tt. gr. 11. fub co . 1 1 

Ibid. gr. 17. fub co . 4 

Ibid. gr. jo. fub co . y 

Pag. is.' gr. 1. fub col. j 

Pag. ij. 'gr. ap. fub ccri. ulr. 

Pag. 14* gr. ay. fub col. j 

Ibid. : *' gr.‘ 17. fub cad.col. '' 1 

Pag. a ri. gr. ay. fub col. z 

Pag. za. gr. ip. fub col. 4 

Pag. jp. io calcc ubi figna Ang.~ *» 


5 10 z7 

f ; y 

^5? 5 

3 5 l *9 

y 5* 18 

6 M 56 
10 10 41 
iz 7 ay 
ao 44- -54 
J>8 4» 47 u 
99 »» 1 

ay zp 2 
i<* 4? p 

VIIL 


y »o *7 

f >7 5 

<5 yy y 

.* 3 5 * 58 
' 4 5^ i? 

<* J * ztf 
II lo 41 
IZ 7 75 

’ a P ‘ 44 44 
3 8 V i7 
jp z» ry 

‘ • xj jp • t 
it 4j © 

VII. 


1 


Digitized by Coogle 


T A B U L A 

iEQU ATIONIS 


ULTIMO S ATURNIj JOVIS*' 
MARTIS , VENERIS , ET MERCURII 


Ad quamliht Planet# A Sole dijlantiam . 





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2 


iEquatio Saturni 


~ 4 DDE 


Ang.i O. 


38 


G |G. M. S.jG. M. S.G. M. S. |G. M. S. G. M. S. G. M. S.l 


it |r n ya 


o y 6 


4 8 5 4 


7 34 39 7 * 0 

il 19 10 7 4 55 

7- 47 5<5'5 8 47 

7' 4 8 2 97 11 75 

7 57 0.7 t<s 22 


20 j p ii i yi a* 1 35 2 4 y8 37 4 18 48 3 37 ya 10 


ai a iy 381 37 ya 1 39 37 y 3 42 4 aa 51I3 41 iy 

aa a 21 33 a 3 »7 1 44 111 y 8 24 4 atf yaj3 44 75 

*3 a 38 y a 8 40 1 48 44! y 13 2 4 30 452J3 47 y a 

*4 a 341*2 14 at 3313 3 17 75 4 74 4 2 7 5 * 4 


5 aa 
5 2 <5 
5 70 

5 75 


70 >3 10 34I2 43 aS'a ip 43] jy 43 itf 4 y5 33I4 p 8' o 


OV'O .CO 


















iEquatio Saturni* 


III. 


8 


G. M. S. G. M. S* G. M. S.' 


006 005 00 

04 96 0375 o 14 

t 326 o 44 

a 7 6 1 2p y o j8 

* 35 6 1 17 

1 jtf j * 7 

a o 5 17 

1 y <5 5 X o 

6 1 4<? 5 o 44 

6 1 29 y o 24 



** 


20 - 6 
at 6 

22 5 

23 5 

24 6 


2f 6 
26 6 

37 6 

38 6 
29 <5 


jo !7 


4? 9 5 4 8 »5 4 5* 5 

47 7 5 49 4 5» 21 

49 ay JI 154 53 33 

50 47 5 5* 5 1 4 54 39 

5 2 29 y 54 »a 4 55 4 2 


52 2 

50 12 

4» 1 7| 5 
4^ 12 

44 0 


5 

5 

0 

0 

\ 6 

4 

59 

a9 

0 

4 

5* 

S3 

n 

4 

58 

1 2 


54 3,5 55 *314 5 5 37 | 6 4 1 39 5 

55 *7,y 5<* 3° 4 57 a8 | <5 39 9 5 

y «5 46 y 37 33 4 58 14; 6 36 32 5 

57 58,5 5 s a8 4 y8 y<Sj <5 33 44 

59 315 59 15 4 59 30 <5 3 ° 5 * 


<5 27 49I3 


IX. 



39 14I4 , i l 4 ° i 0 1 

VIII. An s* 



















^Equatio Saturni 


DDE 


25 5*1 
20 41 
15 23 
9 5 8 

4 26 


27 oj 
22 52 
l8 40! 
14 24) 
10 y 1 


23 22 1 
iy 81 
6 52 o 
58 3 5 o 
yo 1 6 o 


44 3 
37 18 
30 3 > 
>3 43 
itf y2 


9 59 ° 
3 4 ,o 
yff 70 

49 9 ,o 
42 10 o 


3 ° I3 55 48 3 I 8 3 * 1 * 4 2 33 


57 9 1 
yi 30 

43 5 ° 
40 9 

34 27 


3 V B T H E 

An§. 

fc 


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^Equatio Jovis . 


»3 X 
14 X 


15 X 

16 X 

17 X 

18 3 
*9 L 
xo 3' 
XI } 

xi 3 

23 3 
14 


10 31 o 
XI z { o 
51 33P 
41 JO 


5 1 33 o 
3 20 

r 3 | * 
14 o 1 
34 X7 1 


44 54 1 
55 IP * 
5 43 1 
16 6 x 
xd x8 x 


3d 48 IX 

47 <* 1 

57 H i 

7 38 2 
17 5 M 
x8 33 
38 1x3 

48 xo 3 

58 X4 3 

8 x 7 3 


P 4<* 
ip 3X 
xp 18 
3P 3 


48 48 o 
58 3x o 
8 id 1 
17 jp 1 
X7 4X 1 


37 XX 
47 2 

5d 41 
6 ip 

15 5<5 


X5 31 x 
35 4 i 
44 37 i 
54 8 x 
3 ?<* 
13 3 x 

xx X7 3 

3i 4P 3 
41 10 3 
5° 2-8 3 


44 56 

53 54 

x 5X 

11 4P 
xo 44 


13 5P 

xx 4d 

3 l 33 

40 18 

4P o 

57 4 i 

d XO 

14 57 

2-3 32- 
32- 5 


7 44 

17 Xd 

x<S 5 
3d 4X 
4d 13 


55 41 5 
5 d 5 
14 x 7 5 
X 3 44 5 

Ji_5d 
4 x 46 

51 9 i 

o 8,6 
p * <» 
J7 53jg_ 
xd 3p d 
35 20:7 
43 55 7 

52 257 
o ?o 7 


2 p 37 5 
38 18 S’ 
46 5<5|5 
55 2 p 5 
3 5815 
ix X315 
20 44! 5 

2p o 5 

37 13 <5 
45 21 d_ 
_ 53 25 j 6 
1 X3|d 
p 15 d 
17 4 d 

X4 47 6 


6 


a 5 P 15 
10 57 x 4 
i8 5 c 23 
xd 41 xx 
3 4 xd xi 
4 x 7 10 

4P 45 ip 

37. 18 18 

448 17 

IX 13 id 

ip 33 i5 
xd 4 p 14 
34 o 
4i 5 
48 7 


53 3 
1 53 
8 38 
13 18 


xd 50 8 43 XO 

X. 

















5 


u£quatio Jovis 



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iEquatio Jovi$ 



0 

1 
X 

5 

4 

11 38 17 10 33 44 
11 33 46 10 xp xx 
11 x8 58 10 X4 46 
11 X3 53] 10 ip yd 
11 18 33 10 14 y3 

y 

11 ix yS 

10 p 3d 

d 

11 7 y 

10 4 X 

7 

11 0 yd 

9 y8 14 

8 

10 y4 x8 

9 yi 15 

9 

10 47 47 

9 4? y8 




15 10 

1 6 p 

17 p 

18 p 
ip p 


io p 
XI p 
xx 8 
xj 8 
X 4 8 


M 8 
xd 8 
X 7 8 
x8 7 
xp 7 


1 4 p 

53 

44 

** **! 

M yo 


id 8 , 
d IX 
5d O 
4 y ii 
?4 49 


15 49 , 

ix 3 6 

1 7' 

49 m 

57 *8: 


9 5 15 
8 yy 17 

8 47 4 
8 38 40 
8 30 o 


•8x1 d 
8 11 58 
8 x 37 
7 55 1 
7 4? iy 


7 55 15 
7 M y8 
7 11 5° 
7 1 yi 
d yi o 


8 d X3 
7 59 6 
7 yi 5 8 
7 45 y<y 

7 3d o 


7 17 y<* 

7 19 58 

7 11 8 

7 117 

<y 53 35 


d 44 X9 
d 35 14 
d xy 47 
d id ix 
d d X4 


7 *5 

7 i 1 

5° 

7 0 
d 47 
d 34 

9 

18 

14 

d xo 

5 6 

d 7 

x 5 

y y5 41 


34 I ** 


G. M- S. G. M. S. 


<5 59 yy| y 5<y mi 5° 

X 9 

x8 

y iy 191 2 7 
y 14 yil 16 


y 11 xd 

4 59 0 

4 y7 0 

4 xd 0 

4 4 xi5 

4 y j 

4 2.7 5<y 

5 y9 5y 

4 ix 40 

3 4 d IO 

5 57 

5 5 1 59 

3 4i 15 

5 J 9 © 

5 2-7 5 

5 y *y 

5 n 5d 

X yi x 4 

x yd x 

x 37 x 7 

x 40 XI 

x X3 xy 

x X4 3y 

x 9 19 

x 8 4y 

1 55 7 

1 yx 4P 

1 40 yx 

1 3d yo 

1 xd 34 

1 xo 47 

I IX 13 

1 4 4 x 

0 y7 yo 

0 48 34 

0 43 X4 

0 3X X3 

0 x8 yd 

0 id ill 

O 14 x 8 



SUB T H E 


Digitized by Google 


























-^Equatio Martis & Veneris 



SUBTJ^t^HE 


Digitized by Google 


ov<a oo'c 










iEquatio Martis & Veneris. 


D D E 

Ang.j 
) DiltJ" 

II. 

III. 1 

8 | 9 | 10 

8 1 9 ) 10 | 

| G. G. M. S* G. M. S.|G. M. S., 

G. M. S* G. M. 5 . G. M. S. ’ 

0 

1 
X 

3 

4 

15 ai 40 X4 46 3114 ix 14 

25 46 3'2-5 10 1x 24 34 13 

x<S 10 24 25 33 50 24 57 8 

2<5 34 40 25 57 24)25 ip 59 

xd 58 20 <5 3 ; 2 ? 42 45 

37 0 03d 0 0:35 0 0 

37 xi 40^36 xo 39 35 *9 39 

37 43 113d 41 p 35 39 8 

38 4 33 37 1 2 9 35 5 8 k 5 

38 x 5 46 37 xi 38, jd 17 33 

3 o 

2-9 

x8 

2-7 

Xd 

5 

6 

7 

8 

9 

27 23 1 Ixd 44 18 2d 5 2d j 

*7 47 V 7 7 39| 2 <5 18 3 

28 11 7^7 30 5<5 x .<5 50 35 1 

>8 35 4 .*7 54 «|X 7 *3 3 

28 58 57 18 17 I 5 I 2 7 J 5 25; 

' 

37 4 * 37 j 

38 * 15 

38 XI x 
38 40 xd 
38 59 39 

3d 36 x8 
3d 55 ix 
37 *3 43 
37 32 . « 
37 50 d 

2-S 

24 

2-3 

XX 

XI 

to 

11 

IX 

>4 

2J> 22 4 < 5,28 4O l8| 

29 46 30 29 3 Id 

30 IO IO 2$> 26 g 

30 3? 4 <5 *9 48 57 
30 57 17 30 II 39 

27 57 4*1 

28 ip 52 
23 41 5p 

29 3 59 
29 2.5 53 

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40 4P x8 39 37 xd 

41 p 16 39 5<S 0 

41 x8 49,40 14 xo 
41 48 9^0 3X x5 

38 7 58 

38 2.5 34 

38 41 57 

39 0 5 
39 1 <5 5 <5 

xo 

*9 

18 

*7 

id 

i) 
1 6 
I? 

18 

19 

31 20 42 

31 44 2 

32 7 17 
32 30 26 
3 s 53 3 ° 

3 ° 34 15 

30 Jd 45 

31 ip 10 

31 41 2p 

32 3 42 

2 9 47 4 *j 

30 p 22 

30 30 57 ' 

30 52 2dj 

31 13 48 

42- 7 15 ; 4 ° 5 ° 14 
4X xd 8 41 7 49 

4 1 44 45 j 4 * 2 5 7 
43 3 7 , 4 * 42 - 8 
43 xi i4'4i 58 51 

39 33 30 

39 49 47 

40 5 48 

40 xi 30 
40 ?d ?3 

15 

14 

*3 

IX 

11 

xo 

XI 

XX 

2-3 

14 

33 16 28 32 25 48 

33 39 lojjx 47 46 

34 1 15 33 9 39 
34 J 4 44 33 3 i 24 

*34 47 i 7 33 53 2 

31 35 2 

31 5d p 

32 17 p 

32 38 0 

31 58 44 ! 

43 39 4 42 - 15 ** 

43 5 ^ 35 ; 4 2 3 * 2i 
'44 *3 5 ° 42- 47 8 

44 3o 43,43 1 33 
44 47 xo 43 17 38 

4 ° 5 * 57 
41 d 3p 
41 XI 0 

41 34 58 
41 48 34 

10 

9 

S 

7 

d 

2-5 

xd 

17 

x8 

xo 

35 9 43 34 H 3 2 |33 19 *91 
35 32 1 34 35 54 3 3 39 45 ! 

35 54 12 34 57 8 34 0 3. 

3d 16 id 35 18 14 34 xo ii, 

' ?d 38 12I35 39 1 1 34 40 IO ' 

45 3 35 43 32 - ip| 42 - * 45 

45 19 x8 43 4d 37)42- 14 31 

145 34 59 44 0 3 l j42- 2 <5 50 

45 5 ° ^,44 *3 59 , 4 2 38 42- 

46 4 4944 17 o'4X 50 9 

i 5 

h 

1 1 

30 1 37 0 0! 0 0 

'35 0 0 

4<5 19 9 44 39 35 43 1 1 

* ° 
Ang 

1 IX. 

VIII. 


S U B T H E 


B 


Ang. 


Digitized by Google 






-<£quatio Martis & Veneris - 



48 18 3 145 4P 41 43 17 4 14 45 zp iz 54 4Z 11 
48 18 4<5 45 36 4p 4 3 1 33 11 57 13 10 xd ip 
48 7 * 45 11 0 4x44 6, 9 3 id 7 5 3 17 d 

47 53 x 3 45 5i°4xx4 4J <5 4 47 5 17 *7 4 

47 37 3 X ' 44 4<* << 4*- 3 5 3 7 18 z jp 14 x 

I47 ip z 1 '44 14 4d 4 1 _jp p jo o do o o l o 


14 *7 5 

ii 7 4 

56 50 3 

3P 11 1 

zo o 1 


VII. 




Digitized by Google 















^Equatia Martis * 






















12 


^Equatio Martis 



G ]C«. M. S.G. M. S.G. M. S. I G. 
o in 17 41111 1 7, 11 44 15 I 11 


C 11 

1 11 
i 13 

3 *3 

4 13 


5 14 


17 41 li 
41 i n 
6 ii 11 
30 38 ij 
54 5 ? 13 




1 7 11 44 15 

14 53 11 7 15 
48 J5j 11 30 43 
11 17 ii 53 5 i 
35 58 13 i<S 55 


I 


M. S.G. 
17 37 n 
50 13 11 
11 45 11 
35 i <5 ‘ 2 - 
57 45 12- 




10 41 10 
31 4^ 11 
54 38 11 
1 <5 34 1 1 
38 17 ii 




M. S. | 

53 37 1 o“ 
15 1 19 
36 13 18 
57 451 17 
19 r 1«5 



ao si 47 


JO I14 II I4'i3 35 4^13 o 13I 11 14 1811 48 3 I'll II 11 


X. 


S U t T » I 


Digitized by Google 




























iEquatio Martis . 


IG. M. S.jG. M. S.'G. M. S. I G. M. sI|G. M. S.!g. M. S 



5 

xd 28 
id 50 
z 7 1 3 
J -7 35 


27 57 
18 ip 
2-8 4 1 

ip j 

ip 25 


IP 47 
3 ° 9 
30 30 
30 51 
5 i «3 


23 ° 15 

2 J xi 48 
13 43 ip 

24 ~4 44 

Z 4 xd 4 


xd X 5 xd x 7 X 4 47 18 
3 15 48 xo xj 8 27 
35 xd 10 7 25 xp 30 
3 xd 31 4 p X 5 50 x 8 
15 Xd 53 Xd Xd II xo 


41 x 7 14 57 xd 31 5 

jx 17 36 xx xd jx 44 
5 P 27 57 4 i 37 U 17 
5 P 2-8 18 55 2-7 33 45 
53 z 8 40 1 x 7 54 1 


41 |xp I 0 x 8 14 IX 
xx j xp xi 5 3 { x 8 34 id 

57 z 9 4 1 39 18 54 13 
xd jo 3 17 xp 14 x 
48 30 x; 4 8 Jxp 33 43 


xx Z 4 
xx 45 
X 3 d 
X 3 xd 
2-3 47 


H 7 
X4 x8 
x 4 48 
25 8 

2-5 2p 


x 8 xi 48 
xi xx 8 
p xx xS 
51 xx 48 
z 8 13 8 


5 P 2-3 28 
24 l 23 48 
43 24 7 
55,24 27 
x 14 46 


3 1 XI IX XX 
4 X 21 31 51 

48 21 51 14 
48 1 22 10 31 
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TABULA 

PROPORTION ALIS 

PRO LATITUDINE SATURNI JOVIS, 
MARTIS , VENERIS , ET MERGURII 
*Ad quamlibet Planet* a Sole diflantiam 


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£ 3 Aog. 


Digitized by Coogle 



Tabula Proportionals 


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'Ang. 


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36 54 


3<* 57 


o 3 7 

-& 12 
o 37 

o 31 
o 57 


o 37 
o 57 
o 57 

0 37 


17 O 

20 O 
22 O 

25 O 
27 i o 


50 o 
52 o 
3 5 o 
37 0 


o 37 40 o 


37 5° 0 

_1Z 5i 0 
37 55 0 

37 57 0 
37 59 0 


38 10 
38 15 



38 12 

38 14 

38 17 
38 19 
38 22 


3» H 
38 27 
38 29 
38 32 
38 34 


38 37 
38 39 
38 42 
38 44 
58 47 


38 49 
38 52 
38 54 
38 57 
38 59 






0 

36 52 0 

37 13 

0 

37 55 

0 

38 29 

0 

39 

2 

0 

3(5 54 0 

37 s-5 

0 

37 58 

0 

38 32 

0 

39 

5 

0 

36 5<5 0 

37 17 

0 

38 0 

0 

38 34 

0 

39 

7 

0 

3<5 59 0 

37 3o 

0 

38 3 

0 

38 37 

0 

39 

10 

0 

37 1 0 

37 33 

0 

38 (5 

O 

38 40 

0 

39 

21 




































Tabula Prop6rtionalis 

LstTlTUDlUE M^KTIS 


Ang. 

I. 

Dift. 

8 

* 


IO 

1 1 


IZ 


G. 

G. 

M. S. 

G. 

M. S. 

G. 

M. S. 

G. 

M. S. 

G 

M. S. 


o 

0 

55 14 

0 

55 5 <* 

0 

36 1 9 

0 

37 3 

0 

37 36 

30 

I 

0 

55 5 ° 

0 

3d t 

0 

36 3d 

0 

37 1° 

0 

3 7 43 

19 

t 

0 

55 36 

0 

36 s> 

0 

36 41 

0 

37 Id 

0 

37 49 

18 

3 

0 

55 4 ^ 

0 

36 15 

0 

36 4 p 

0 

37 13 

0 

37 5 * 

17 

4 

0 

J 5 48 

0 

3d tt 

0 

3 d 55 

0 

37 i 9 

0 

38 3 

id 

5 

0 

55 54 

0 

3d z8 

0 

37 1 

0 

37 36 

0 

38 g 

15 

6 

0 

3d 0 

0 

3 <S 54 

0 

37 8 

0 

37 4 i 

0 

38 id 

14 

7 

0 

3d d 

O 

36 41 

0 

37 »5 

0 

37 49 

0 

38 13 

2-3 

8 

0 

3# 11 

0 

5<5 47 

0 

37 ii 

0 

37 55 

0 

38 1 p 

tt 

9 

0 

3d 18 

0 

36 54 

0 

37 18 

0 

38 t 

O 

38 3 <* 

11 

dO 

0 

36 2.4 

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37 0 

0 

37 34 

0 

38 8 

0 

38 43 

IO 

1 1 

0 

5d 30 

0 

37 d 

0 

37 4 i 

O 

15 

0 

38 49 

19 

It 

0 

5d 3d 

0 

57 15 

0 

37 47 

0 

38 11 

0 

38 5d 

18 


0 

5d 41 

0 

57 19 

0 

37 54 

0 

38 17 

0 

39 3 

>7 


0 

3d 48 

0 

57 15 

0 

38 0 

0 

38 34 

0 

39 10 

Id 

*5 

0 

5 <* 54 

0 

57 5 i 

0 

38 7 

0 

38 41 

0 

39 18 

15 

id 

0 

57 1 

0 

57 4 * 

0 

38 17 

0 

38 51 

0 

39 id 

14 

17 

0 

57 «*■ 

0 

37 5 i 

0 

38 id 

0 

39 1 

0 

39 3 d 

13 

18 

0 

57 n 

0 

38 1 

0 

38 3<5 

0 

39 11 

0 

39 45 

It 

J 9 _ 

0 

57 5 i 

0 

38 n 

0 

38 45 

0 

39 10 

0 

39 55 

1 1 

to 

0 

57 41 

0 

38 ti 

0 

38 55 

0 

39 30 

0 

40 5 

IO 

ti 

0 

57 51 

0 

38 3 ° 

0 

39 5 

0 

39 40 

0 

40 14 

9 

tt 

0 

58 5 

0 

3 * 4 ° 

0 

39 !4 

0 

39 49 

0 

40 14 

8 

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0 

58 13 

0 

38 50 

0 

39 14 

0 

39 59 

0 

40 34 

7 

i 4 

0 

58 15 

0 

39 0 

0 

39 34 

0 

40 8 

0 

40 44 

d 

15 

0 

58 55 

0 

39 9 

0 

39 43 

0 

40 18 

0 

40 53 

5 

td 

0 

58 45 

0 

39 19 

0 

39 53 

0 

40 17 

0 

4 i 3 

4 

17 

0 

58 55 

0 

39 18 

0 

40 t 

0 

4 ° 37 

0 

41 it 

3 

t8 

0 

59 5 

0 

39 38 

0 

40 it 

0 

40 47 

0 

41 11 

t 

19 

0 

59 I* 

0 

39 48 

0 

40 it 

0 

40 57 

0 

41 3 i 

1 

50 

0 

59 15 

0 

39 58 

0 

40 31 

0 

41 7 

0 

4 i 4 i 

0 







X. 




Ang. 


F 


Ang. 


Digitized by Google 
































Tabula Proportionalis 

T\0 L^TITUDI'KE M^BJTIS 




Gt>ogle 

















Tabula Proportionals 


PJ^O LUTITlfDl'ii'E MURJIS 






G. M. S. G. M. S* I G. M. S. 


o 40 33 
o 40 47 
o 41 I 
O 41 IJ 
o 41 29 


o 41 43 

o 41 57 
O 41 I I 
o 41 15 
o 41 59 


o 41 53 
o 45 *5 
o 45 55 
° 45 55 
o 44 i 5 


44 55 
44 55 
4 > J 5 


0418 

0 41 41 

0 41 17 

0 41 <jz 

0 41,2.1 

0 41 5<5 

0 41 31 

0 43 6 

0 41 36 

0 41 10 

0 41 45 

O 43 20' 

0 41 50 

0 41 14 

0 42. 59 

0 43 34 

0 41 4 

0 41 38 

0 43 13 

0 43 48 


42. 18 
41 31 
42. 4 <5 
41 O 
45 14 


45 5 ° 
45 49 
44 9 
44 

44 5 c 


45 10 
45 50 

45 51 

46 11 
46 31 


46 5 


44 5 
44 ii 

44 40 

45 o 
45 2.0 


45 4 1 

46 1 
46 zz 

46 44 

47 5 


0 

43 *7 

0 

43 4 1 

0 

43 55 

0 

44 9 

o' 

44 2-3 

0 

44 38 

0 

44 5<5 

0 

45 15 

0 

45 35 

0 

45 55 

0 

4/5 15 

0 

46 3d 

0 

4<5 57 

0 

47 

0 

47 39 

0 

48 0 

0 

48 xi 

0 

48 42. 

0 

49 3 

0 

49 24 


48 34 

48 55 

49 i* 
49 57 
49 58 




44 i 
44 

44 50 
44 44 
44 58 


45 15 
45 5 * 

45 5 o 

46 10 


46 30 








































I 


44 Tabula Proportionalis 

V HO l^titudjt^e m^pjis 


Ang. IL 


Dift. 


I I 


i 


*3 _ 


14! 


15 



G. 

M. S* 

G. 

M. S. 

G. 

M. S. 

G. 

M. S. 

G. 

M. S. 


o 

0 

4* 7 

0 

41 4 z 

0 

4Z id 

0 

4Z 51 

0 

43 24 

30 

1 

0 

41 ZI 

0 

41 5 <5 

0 

4Z 30 

0 

43 5 

0 

43 37 

3-9 

X 

0 

4i 35 

0 

4Z 10 

0 

4Z 44 

0 

43 19 

0 

43 52 

z8 

S 

0 

41 49 

0 

41 44 

0 

4 X 58 

0 

43 33 

0 

44 5- 

2-7 

4 _ 

0 

4Z $ 

0 

4Z $8 

0 

43 1* 

0 

43 47 

0 

44 29 

zd 

5 

0 

4 z 17 

0 

4Z 5z 

0 

43 2-d 

0 

44 1 

0 

44 33 

xs 

6 

0 

4 z 31 

0 

43 

0 

43 40 

0 

44 15 

0 

44 47 

24 

7 

0 

4Z 45 

0 

43 *0 

0 

43 54 

0 

44 2.9 

0 

45 * 

23 

8 

0 

4 z 59 

0 

43 34 

0 

44 8 

0 

44 43 

O 

45 >5 

XX 

9 

0 

4? i3 

0 

43 48 

0 

44 2-x 

0 

44 57 

O 

45 2.9 

ZI 

IO 

0 

43- 2-7 

0 

44 i 

0 

44 3* 

0 

45 11 

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45 43 

zo 

1 1 
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n 

0 

43 4 1 


44 16 

0 

44 5° 

0 

45 2.5 

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45 57 
4 d 11 

4d Z5 

19 

18 

27 

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43 55 

44 9 

0 

44 

44 44 

O 

O 

4T T 
45 18 

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O 

45 39 
45 53 

O 

O 

14 

0 

44 13 

0 

44 58 

0 

45 3i 

0 

4d 7 

O 

4d 59 

Id 

15 

0 

44 3 8 

0 

45 13 

0 

45 47 

0 

4d xi 

O 

4<5 53 

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id 

O 

44 5 6 

0 

45 3i 

0 

4d 4 

0 

4<5 37 

O 

47 9 

24 

17 

0 

45 25 

0 

45 50 

0 

4d z^ 

0 

4 d 54 

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47 2-d 

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0 

45 35 

0 

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0 

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45 55 

0 

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0 

47 3 

0 

47 32 

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0 

4d 15 

0 

46 50 

0 

47 2.J 

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47 52 

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48 z* 

10 

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0 

4d 36 

0 

47 1* 

0 

47 44 

0 

48 IX 

O 

48 43 

9 

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0 

46 57 

0 

47 32- 

0 

48 5 

0 

48 33 

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49 4 

8 

23 

0 

47 1* 

0 

47 53 

0 

48 zd 

0 

48 54 

0 

49 15 

7 

2-4 

0 

47 39 

0 

48 13 

0 

48 47 

0 

49 2d 

0 

49 47 

d 

15 

0 

48 0 

0 

48 34 

0 

49 8 

0 

49 37 

□ 

50 8 

5 

zd 

0 

4$ XI 

0 

48 55 

0 

49 2-9 

0 

49 38 

□ 

50 zg 

4 

17 

0 

48 4Z 

0 

49 i<5 

0 

49 5° 

0 

50 zo 

□ 

50 51 

3 

z8 

0 

49 3 

0 

49 37 

0 

50 11 

0 

50 4 z 

0 

52 13 

z 

19 

0 

49 14 

0 

49 58 

0 

50 JZ 

0 

51 4 

0 

5i 35 

1 

3° 

0 

49 45 

0 

50 19 

0 

5o 53 

0 

51 zd 

0 

52 57 

0 


I Ang. , 


Ang. 


Digitized by Google 























Tabula Proportionals 

TI {0 L^TITUDIHE M^t\TlS 





0 

0 

47 5 3 

48 15 

0 48 58 

0 

49 * 

0 

49 2-7 

0 

49 13 

0 

50 xo 

0 

50 48 

0 

51 17 

0 

51 47 

0 

51 18 

0 

51 5 ° 

0 

53 »4 

0 

54 0 

0 

54 3 8 

0 

55 18 

0 

55 59 

0 

5<5 41 

0 

57 M 

0 

58 7 


58 51 

5 9 3 5 


0 

50 31 

0 

5 ° 59 

0 

51 x 7 

0 

51 y <5 

0 

yx x <5 

0 

51 57 

0 

53 19 

0 

54 1 

0 

54 37 

0 

55 15 



0519 

0 51 45 

0 51 3 <5 

0 yx ix 

0 51 4 

0 yx 40 

0 yx 3X 

0 53 7 

0 53 x 

0 53 37 

0 53 33 
0 54 5 
0 54 38 
0 yy ix 
0 yy 50 

0 54 8 

0 y4 40 
0 55 3 

0 55 47 
0 y <5 X4 

0 56 30 

0 57 4 

0 y7 11 

0 57 44 

0 57 53 

0 58 X5 

0 y8 36 

0 59 7 

0 5 9 ip 

0 yp 4p 


G. 

M. S. 

0 

50 ip 

0 

50 41 

0 

5 i 4 

0 

yi x8 

0 

5 i 5 i 

0 

w. 

*» 

*■« 

oc' 

0 

51 45 

0 

53 i 3 

0 

53 40 

0 

54 10 










Digitized by Google 





























Tabula Proportionalis 


TF^O LsAT IT U Dl'H.E M^FJJS 


111 


G. M. S. I G. M. S. 


5° 55 
51 15 
51 

yx x 

5X xy 


5X 51 
55 18 

53 4<* 

54 11 
54 4i 



51 x<5 
51 48 
51 11 
5i 54 
51 57 


55 15 
55 49 
54 17 

54 45 

55 11 




















Tabula Proportionalis 

THO l^TITUDl’HE M^^TIS 

~ ~TVT 



Digitized by Coogle 




























Tabula Proportionals 

T^O L^fTITUDl^E 
























Tabula Proportionals 

TF^O L^iTlTUDlTiE MUFJ1S 



iz 35 
id 55 
21 o 
X4 51 
x 8 xo 



io jd 

13 58 
17 xp 
xi 7 

14 54 


x8 48 
3X 4? 
3d 58 
41 13 
4 * IP 


G. M. S. 


7 IP 
10 35 
13 41 
id 54 
xo 15 


X3 40 
X7 d 
1 ° 39 
14 17 
17 5 <* 


41 38 ' x 
45 21 1 

49 » x 
5 * 41 2 


X 

5 P 47 

1 

3 10 

3 

d XI 

3 

9 id 

3 

11 57 

3 

14 id 

3 

id 14 

3 

17 52 

3 

ip 19 

3 

xo 0 


( j. 

JV>. s. 

1 

50 5 

I 

5x 14 

I 

54 15 

1 

5d 40 

1 

58 57 


X 

4 

2-7 

X 

7 

7 

X 

10 

5 3 

X 

IX 

44 

X 

15 

17 


18 37 
xi 34 
M l<* 
27 4i 
|o 45 


l 3 45 
id 17 
18 50 
xi 30 
X4 6 


* 33 5 i 

x xd 39 

x 3d 5d 

X xp IX 

x 39 5d 

2 3 1 41 

x 4X 5d 

x 34 II 

x 45 48 

X 3d ?x 

x 48 35 

2 j8 44 

x 51 14 

x 40 53 

x 53 48 

1 4 X 53 

x 5d 3 

2 44 42 

x 58 5 

x 4d rd 

2 5 P 5 * 

2 47 IP 

3 I XX 

x 48 5 i 

1 2 15 

2 4 P 46 

1 1 50 ; 

x 50 48 

1 4 14 ! 

x 51 6 






Digitized by Google 

































Tabula Proportionalis 

T\0 L^TITUDir{E MANTIS 


Ang- 






V. 






Did. 


1 1 


12 


13 I 


M 

I 

“gT 

G. 

M. S. I 

G. 

M. S. 

G 

M • S# 1 

G. 

to. S- 

— 

M. S. 


o 

1 

51 0 

1 

50 5 

1 

48 3 

1 

45 59 

1 

43 53 

3 ° 

i 

1 

54 10 

I 

52 14 

1 

50 1 

1 

47 45 

1 

45 29 

29 

X 

1 

j6 46 

I 

54 25 

I 

51 58 

1 

49 32 

I 

47 5 

z8 

3 

1 

59 l 7 

1 

5<5 40 

I 

53 58 

1 

51 xo 

1 

48 41 

27 

4 

% 

1 47 

I 

58 57 

1 

5 * 3 

1 

53 J° 

1 

50 XX 

2(5 

5 

% 

4 2-7 

1 

1 17 

1 

58 8 

1 

55 2 

1 

52 0 

25 

6 

1 

7 7 

l 

3 4 1 

1 

0 31 

1 

5<5 55 

1 

53 4 o 

24 

7 

% 

lo 5 3 

X 

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1 

1 14 

1 

58 48 

1 

55 20 

23 

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1 

11 44 

1 

8 37 

1 

4 3<5 

X 

0 4X 

1 - 

57 0 

XX 

9 

1 

15 37 

1 

11 7 

1 

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X 

2 39 

1 

58 42 

XI 

10 

1 

18 37 

1 

13 45 

1 

9 2 

X 

4 3<5 

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0 XJ 

xo 

1 1 

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n 34 

1 

16 17 

1 

Hi 6 

X 

6 30 

X 

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1 9 

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1 

14 36 

1 

18 50 

i 

IJ 17 

■ 

9 xt 

X 

3 4 i 

18 

13 

1 

27 4 i 

1 

11 30 

1 

15 41 

X 

10 18 

X 

5 19 

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14 

1 

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1 

14 6 

X 

17 '<5 

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X 

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1(5 

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1 

33 5 i 

1 

16 39 

1 

xo 6 

X 

14 X 

X 

8 x8 

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1 <5 

1 

36 5<5 

X 

19 11 

1 

11 10 

X 

»5 47 

X 

9 5<5 

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17 

1 

39 5 * 

1 

3 i 43 

1 

14 18 

X 

17 31 

X 

1 1 15 

>3 

18 

1 

42 5<5 

X 

34 11 

1 

16 18 

X 

19 IX 

X 

12 49 

IX 

19 

1 

45 48 

X 

3 <5 31 

X 

x8 ix 

X 

xo 48 

X 

14 9 

1 1 

10 

1 

48 3 5 

1 

38 44 

1 

30 1 

1 

XX 18 

X 

15 X4 

10 

n 

1 

51 14 

1 

40 53 

1 

31 48 

1 

23 44 

X 

id 34 

9 

ii 

1 

33 48 

1 

42 53 

1 

33 21 

X 

25 1 

X 

17 37 

8 

13 

1 

5<5 3 

X 

44 42 

X 

34 49 

1 

16 IX 

X 

18 37 

7 

14 

1 

58 5 

1 

4(5 i <5 

1 

36 9 

1 

27 14 

X 

19 27 

<5 

• 2-5 

1 

59 5 1 

X 

47 39 

1 

37 13 

2 

x8 6 

X 

xo 10 

5 

16 

3 

1 11 

X 

48 51 

1 

38 7 

1 

x8 5x 

X 

xo 4(5 

4 

17 

3 

2 35 

1 

49 4*5 

1 

3 « 53 

1 

29 27 

X 

xi 17 

3 

i 9 

3 

3 50 

1 

50 48 

1 

39 42 

1 

30 10 

X 

xi 50 

X 

29 

3 

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X 

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1 

39 53 

1 

30 17 

X 

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0 

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0 0 

0 

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0 

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VI. 





Ang. 


Ang. 


Digitized by Googli 

JSa. ^ 


Tabula Proportional] s 


TAP L^iTlTUDl7{E MEA.CVA.U 


















s * 


Tabula Proportionate 

P^O l jIT IT U Dl'H'E MEHCVKri 


Ang. O. 


Dift. 


z 4 


2 5 


z 6 

*7 J 

28 

29 

r 

— 

G. 

gT 

M. S 

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M. 

S. G. 

M. S. 

G* 

M. 

S. 

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G. 

M. S. 

d 

o 

o 

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0 

0 

0 

0 

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0 

0 

0 

0 

0 

0 

0 

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1 d 58 

0 

16 

0 

0 

15 XX 

0 

H 43 

0 

14 

3 

0 

1 3 *2. 

19 

% 

o 

16 39 

0 

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0 

0 

15 XX 

0 

14 43 

0 

14 

3 

0 

13 XX 

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3 

o 

id 40 

0 

1(5 

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0 

15 *3 

0 

14 44 

0 

14 

4 

0 

13 X* 

27 

4 

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16 41 

0 

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X 

0 

15 14 

0 

14 45 

0 

14 

5 

0 

13 24 

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5 

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1 6 41 

0 

16 

3 

0 

15 2.5 

0 

14 4 ^ 

0 

14 

d 

0 

13 24 

15 

6 

0 

16 43 

0 

i <5 

4 

0 

15 16 

0 

14 47 

0 

14 

d 

0 

13 X5 

24 

7 

o 

1(5 44 

0 

16 

5 

0 

15 xd 

0 

14 47 

0 

14 

7 

0 

13 xd 

23 

8 

o 

id 45 

0 

id 

d 

0 

15 27 

0 

14 48 

0 

14 

8 

0 

13 27 

XX 

9 

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1(5 4(5 

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id 

d 

0 

15 18 

0 

14 49 

0 

14 

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0 

1 3 17 

XI 

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1(5 47 

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id 

7 

0 

15 Xp 

0 

14 

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0 

14 

9 

0 

13 x 3 

xo 

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0 

id 

8 

0 

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0 

14 

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0 

14 

10 

0 

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19 

12. 

o 

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0 

id 

9 

0 

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0 

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11 

0 

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0 

id 

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0 

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14 

52 . 

0 

14 

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0 

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17 

14 

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i <5 51 

0 

id 

11 

0 

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0 

14 

33 

0 

14 

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0 

13 3 i 

id 

15 

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16 5X 

0 

id 

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15 33 

0 

14 

54 

0 

14 

13 

0 

13 32 

15 

id 

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0 

Id 

13 

0 

15 34 

0 

14 53 

0 

14 

14 

0 

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14 

17 

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1(5 54 

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id 

14 

0 

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0 

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14 

15 

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13 33 

13 

18 

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15 

0 

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57 

0 

14 

id 

0 

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