CONTENTS vii
Geminus pages 222-284
Attempt to prove the Parallel-Postulate . . . 227-230
On Meteorologica of Posidonius . . . . 231-232
Introduction to the Phaenomena attributed to Geminus 232-234
XYJ. SOME HANDBOOKS 235-244
Cleomedes, De motu circulari ..... 235-238
Nicomachus ..... ... 238
Theon of Smyrna, Expositio rerum mathematicarum ad
legendum Platonem utilium ..... 238-244
XVII. TRIGONOMETRY: HIPPARCHUS, MENELAUS, PTO
LEMY 245-297
Theodosius ......... 245-246
Works by Theodosius ....... 246
Contentis of the Sphaerica ...... 246-252
No actual trigonometry in Theodosius . . . 250-252
The beginnings of trigonometry ..... 252-253
Hipparchus 253-260
The work of Hipparchus 254-256
First systematic use of trigonometry .... 257-259
Table of chords 259-260
Menelaus 260-273
The Sphaerica of Menelaus ..... 261-273
(a) ‘ Menelaus’s theorem ’ for the sphere . . 266-268
(ft) Deductions from Menelaus’s theorem . . 268-269
(y) Anharmonic property of four great circles
through one point 269-270
(ô) Propositions analogous to Eucl. VI. 3 . . 270
Claudius Ptolemy ........ 273-297
The MndriunTiKtj (jvvTa^ii (Arab. Almagest) . . . 273-286
Commentaries ....... 274
Translations and editions ..... 274-275
Summary of contents ...... 275-276
Trigonometry in Ptolemy ...... 276-286
(a) Lemma for finding sin 18° and sin 36° . . 277-278
(ft) Equivalent of sin 2 d + cos 2 d = 1 . . . 278
(y) ‘Ptolemy’s theorem’, giving the equivalent of
sin (d — c/j) = sin d coscj) — cos d sin 0 . . . 278-280
(Sj Equivalent of sin 2 -|d = i(l — cosd) . . . 280-281
(e) Equivalentof cos{d + <£) = cosdcos(/) — sindsin<p 281
(£) Method of interpolation based on formula
sin a/sin ft < «/ft > « > ft) . . .281-282
(77) Table of chords 283
(d) Further use of proportional increase . ■ . 283-284
(i) Plane trigonometry in effect used . . . 284
Spherical trigonometry : formulae in solution of
spherical triangles ....... 284-286
The Analemma ........ 286-292
The Planisphaerium ....... 292-293
The Optics ......... 293-295
A mechanical work, Uepl pon5>v ..... 295
Attempt to prove the Parallel-Postulate . . . 295-297
