Index 459 crossbar theorem, 106 cubic polynomial, 314 cut by a transversal, 149 cutting off a segment, 74, 297 cyclic polygon, 262, 263 is convex, 262 cyclic quadrilateral, 264, 276 cyclic triangle theorem, 263 dart, 183 decagon, 157 decomposition lemma convex, 201 parallelogram, 203 defect of a polygon, 328, 371 of a triangle, 328 of an asymptotic triangle, 351 defect addition theorem, 328 for asymptotic triangles, 353 defect formula, 372 defined terms, 23 definition descriptive, 2 logical, 2 mathematical, 401 degree in angle measure, 85 of a polynomial, 314 density of real and rational numbers, 438 Descartes, Ren´ 33, 311 descriptive definition, 2 diagonal of a polygon, 156 of a square, 234 diagonal criterion for convex quadrilaterals, 176 diagonal scaling theorem, 226 diameter of a circle, 247 length of, 248 difference of sets, 425 different (meaning not equal), 25, 393 differential geometry, 135, 373–374 direct proof, 410 disjoint sets, 425 disjunction, 386 proof of, 415 displacement vector, 124 distance as a primitive term, 54 between real numbers, 57 from a point to a line, 147 from a point to a segment, 147 from a point to a set, 146 in plane geometry, 54, 56 in taxicab geometry, 138 in the Cartesian plane, 125 in the Poincar´ disk, 132 properties of, 59 distance postulate, 56 distance-preserving function, 57 distinct (meaning not equal), 25, 393 divides, 434 divisible, 434 dodecagon, 157 domain of a function, 428 of a variable, 394 dot product, 125 double angle formula for cosine, 242 for sine, 242 double elliptic geometry, 35 doubling a cube, 308, 317 doubling a square, 305 dropping a perpendicular, 142 edge finite, of an asymptotic triangle, 351 of a polygon, 156 of a triangle, 103 edge line, 158 edge-line lemma, 158 element of a set, 423 Elements of Euclid, 1 elliptic geometry, 11 double, 35 single, 35, 41, 136 elliptic parallel postulate, 38 empty set, 424 endpoint of a ray, 71 of a segment, 65 of an arc, 254 endpoint independence of asymptotic rays, 348 enunciation (in Greek proofs), 6 equality in Euclid’s Elements, 3 in modern mathematics, 25, 393 of functions, 428 of ordered pairs, 426 of sets, 424 equiangular polygon, 159
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