None
(References are to sections unless otherwise stated.) Abbreviations 80 Acute angle 19 triangle 23 Addition of angles 39 of line-segments 10 Adjacent angles 39 parts of a polygon 134 parts of a triangle 21 Alternate exterior angles . . 88 interior angles 88 Alternation 24G Altitude of a parallelogram . . 137 of a trapezoid 137 of a triangle 24 Analysis of proof 175 of problems ....... 177 Angle, acute, obtuse, right, reflex, oblique 19 at the center of a circle . . . 18o exterior of a triangle .... 81 inscribed in a circle .... 185 inscribed in  Angles, adjacent 39 addition of, sum of .... 39 complementary 70 multiplication and division of . 39 subtraction of 39 supplementary 70 vertical 70 Antecedents 242 Apothem of a regular poly- gon 'M2 Approximate area 306 measurement .... 235, 305 Approximate ratio .... 240 Arc of a circle 12, 184 intercepted by an angle, . . . 185 subtended by a choril .... 184 Area, approximate 306 of a circle 'Ml, 416 of a polygon :W9 of a rectangle . . . 300-307, 414 of a sector of a circle .... 364 of a segment of a circle . . . 365 of a surface 302 Aristotle page 31 Axial symmetry 164 Axioms . 60,61,82,96,119,392, 407,409,411,412,416 on numbers 241 Axis in a graph ^^68 of symmetry 164 Base of a parallelogram . " . . 135 of a trapezoid 136 of a triangle 24 Bhaskara 318 Bisector of an angle .... 19 of a line-segment 50 Broken line 11 Center of a circle 12 of a pencil 431 of a regular polygon .... 342 of similitude 434 of symmetry 169 Central angle 185 symmetry 169 Chord of a circle 181 Circle, arc of 184 area of 361, 416 circumference^of . .' . 352, 416 277 278 INDEX. (References are to sections unless otherwise stated.) Circle, circumscribed .... 225 definition of 12 diameter of 181 escribed 229, Ex. 4 inscribed 228 inside of, outside of 180 length of, perimeter of . . 352, 416 secant of 182 segment of 220 tangent to 183 Circles, equal 187 intersecting 186 tangent 186 Coincidence 19, 27 Commensurable segments . 236 ratios '238 Compasses 33 Complementary angles . . 70 Composition 246 and division 246 Concave polygon 160 Conclusion 78 Concurrent lines 228 Congruence 27 Consequents 242 Constants 380 Construction of figures ... 44 of regular polygons . . . 163, 333 Continued proportion . . . 267 Converse theorems .... 98 Convex.polygon 160 Corollary 104 Corresponding angles ... 88 parts of polygons 255 parts of triangles 29 Curved line 11 Decagon 424 Definition, technical .... .389 Degree of an angle .... 17 Demonstration . . 59, 79, 80, 391 type of . . ■. . 83 Dependence of variables . . 380 Diagonal of a polygon . . 134, Wd Diameter of a circle .... 181 of a parallelogram 137 of a trapezoid 137 Direct proof 175, 399 Direct tangent to tw^o circles 403 Discussion of a construc- tion 122 Distance between two points . 61 from a point to a line . . . 114 Dividers 33 Division of line-segments . . 10 external, internal 425 harmonic 425 in extreme and mean ratio . . 421 in proportion 246 of angles 39 of the circle 333 Dodecagon .... pages 82, 235 End-point of a segment . . . 8, 13 of a ray 9 Equal, equivalent 27 circles 187 Equiangular figures ... 22, 160 mutually 255 Equilateral figures . . ,22, 160 Euclid . . . pages 3, 31,40, 141 Eudoxus page 140 Exterior angle of a triangle . . 81 angles of parallel lines ... 88 External division . . . 252, 425 segment of a secant .... 274 Extreme and mean ratio . , 421 Extremes 242 Figures, geometric ..... 12 congruence of 27 constructions of 44 symmetry of 164 Fourth proportional . , . 291 Geometric proposition ... 59 Geometric solid 3 Geometry 1 Gothic arch, pages 109, 151, 197, 204 Graphic representation. Chapter VI Harmonic divisions .... 425 Hexagon, regular, pages (55, 67, 76, 78, 82, 108, 174, 177, etc. Historical notes, pages 3, 31, 38, 40, 42, 128, 140, 162, 167, 193 Hypotenuse 23 Hypothesis 78 INDEX. 279 (References are to sections unless otherwise stated.) Incommensurables, 236, 240, 305, 368 Indirect proof ... 91, 176, 394 Inscribed angle in an arc . . 220 angle in a circle 185 angle in a segment .... 220 circle in a triangle 228 triangle in a circle .... 225 Intercepted arc 185 Interior angles 88 Internal division . . . 252,425 Inversion 246 Isosceles trapezoid 136 triangle 22 Land surveying . . . 283, 284 Legs of a right triangle . . 23 Length 3 of a circle 352, 416 of a segment 232, 407 Limit of apothem 383 of area 384 of perimeter 384 of rotating secant ..... 386 Line J, 3, 4, 5, 7, 11 half-line 9 of centers 403 -segment 8 Lines, concurrent 228 oblique, obtuse, perpendicular . 19 parallel 89 Lobachevsky .... page 38 Loci, determination of, pages 50-52, 226-227 problems, pages 52, 64, 83, 92, 96, 97, 102, 103, 111, 120, 148, 149, 158, 175, 179, 226, 228, 233, etc. Major and minor arcs ... 184 Maxima and minima . . . 443 Mean proportional .... 293 Means 242 Measurement, approximate, 235, 306 of angles 17,202 of line-segments 232-237 of the circle 349 exact 232,301,304 Median of a triangle .... 157 Methods of attack . . . 174-177 Minute of angle 17 Multiplication of angles ... 39 of line-segments 10 Number 241, 407 Numerical measure . 232, 302, 407 Oblique lines, angles .... 19 Obtuse triangles 23 Octagons . . . pages 78, 79, etc. regular . . pages 146, 147, 187, 198, 202, 235, etc. Opposite parts of figures , 21, 134 Origin of ray 9 Outline of proof 52 Parallel lines 89 axiom 96 rulers 288 Parallelogram 135 Pencil of lines 431 Pentagon 424 Perigon 17 Perimeter of a circle .... 352 of a polygon 160, 267 Perpendicular 19 bisector of  Point 1, 3 Polygons 160. regular 332 similar 256 Practical measurement 235, 306 Preliminary theorems, (52-69, 72-76, 189-198, 307 Problems of construction . 44 Projection 436 Proof 59, 391, 392 by exclusion 86 direct, indirect . . 91, 175, 176, 394 Proportion 242 Proportional division . . . 242 Proposition, geometric ... 59 Protractor 18, 33 Pythagoras . . pages 40, 130, 140, 162, 167 280 INDEX, (Keferences are to sections unless otherwise stated.) Quadrant 208 Quadrilaterals 134-137 Radius of circle 12 of regular polygon 342 Ratio 238,242,408 approximate 240 commensurable 239 of similitude 434 Ray 9 Rectangle 135 Reflex angle 19 Regular polygon 160 Rhomboid, rhombus .... 135 Right angle 19 triangle 23 Scalene triangle 22 Secant 182 limiting position of .... 386 Second of angle 17 of arc . .^ 202 Sector of a circle 203 area of ^564 Segment of a circle 220 of a line 8 Semicircle 184 Sides of an angle .... 14, 106 Similar figures 27, 256 Sine of an angle 279 Solution of problems . . 177-178 Square 135 Subtended angle 286 arc ■. . 184 Subtraction of angles .... 39 of line segments 10 Sum of angles 39 Summaries, pages 75, 10(5, 145, 169. 194 Superposition .... page 14 Supplementary angles ... 70 Surface 2 Symbols of abbreviation . . 80 Symmetry 164-173 problems involving, pages 81, 82, 93, 94, 101, 109, 150, 205, 229, 233, etc. Tangent to a circle 183 circles 186 to two circles 403, 404 Technical words 389 /Tests for congruence . 32, 35, 40 xThales pages 3, 17 Theorem 59 Third proportional .... 293 Transversal 88 Transverse tangent .... 403 Trapezoid 136 Triangle . 21-24, 41, 157, 225, 228,' etc. Undefined words 389 Unproved propositions . 60, 391 Variables Chapter VI dependence of 380 limit of 384 Variation, continuous .... 366 Vertex angle of a triangle . . 24 Vertical angles 70 Vertices of a polyuon .... 160 of a quadrilateral 134 of a triangle 21 Whole secant 274 Zero angle 16 OF THE UNIVERSITY OF UNIVERSITY OF CALIFORNIA LIBRARY xe last date stamped below. OCT S3 19'^'' !2Mar5 2l' 130ct'59L0| REC'D LD APR 2 9 1960 i^ N^ /'^ v$> ^^ ^ > 21-100m-12,'46(A2012sl6)4120 # -V" (7442.7 UNIVERSITY OF CALIFORNIA LIBRARY mmmmimmm§ li ill I r^^^^^'^^^^^^ jilj! iiibi|[|llifsili!j| i i. 