CONTENTS xiii 
65-117 
67-69 
69- 70 
70- 74 
74-76 
76 77 
77 
78- 79 
79 
79- 82 
82- 84 
84- 90 
85- 86 
86- 89 
89- 90 
90 
90- 91 
91-98 
94-96 
96-97 
97-115 
97-112 
108-110 
112-118 
118-115 
115-117 
118-140 
118-121 
121-122 
122-128 
128- 189 
129- 180 
130- 187 
187-139 
139-140 
141 169 
141-142 
143- 144 
144- 149 
150-154 
154-157 
158-162 
162-165 
165-169 
VI. PROGRESS IN THE ELEMENTS DOWN TO PLATO’S 
TIME pages 170-217 
Extract from Proclus’s summary . . . . 170-172 
Anaxagoras 172-174 
Oenopides of Chios ........ 174-176 
Democritus 176-181 
Hippias of Elis 182 
Hippocrates of Chios 182-202 
(n) Hippocrates’s quadrature of lunes .... 183-200 
O) Reduction of the problem of doubling the cube to 
the finding of two mean proportionals . . . 200-201 
(y) The Elements as known to Hippocrates . . 201-202 
Theodoras of Gyrene 202-209 
Theaetetus 209-212 
Archytas 213-216 
Summary .......... 216-217 
VIT. SPECIAL PROBLEMS 218-270 
The squaring of the circle 220-235 
Antiphon ......... 221-228 
Bryson .......... 223-225 
Hippias, Dinostratus, Nicomedes, &c. .... 225-226 
(«) The quadratrix of Hippias ..... 226-230 
(¡3) The spiral of Archimedes 230-231 
(y) Solutions by Apollonius and Carpus . . . 231-232 
(*) Approximations to the value of n . 232-235 
The trisection of any angle . . . . . 235-244 
(«) Reduction to a certain vticris, solved by conics . 235-237 
(3) The veîiais equivalent to a cubic equation . . 237-238 
(y) The conchoids of Nicomedes 238-240 
(Ô) Another reduction to a vevcns (Archimedes) . . 240-241 
(e) Direct solutions by means of conics (Pappus) . 241-244 
The duplication of the cube, or the problem of the two 
mean proportionals 244-270 
(а) History of the problem v 244-246 
(/3) Archytas 246-249 
(y) Eudoxus 249-251 
(&) Menaechmus ........ 251-255 
(f) The solution attributed to Plato .... 255-258 
(f) Eratosthenes 258-260 
(q) Nicomedes ........ 260-262 
(б) Apollonius, Heron, Philon of Byzantium . . 262-264 
(i) Diodes and the eissoid 264-266 
(V) Sporus and Pappus 266-268 
(X) Approximation to a solution by plane methods only 268-270 
VIII. ZENO OF ELEA 271-283 
Zeno’s arguments about motion ..... 273-283 
IX. PLATO 284-315 
Contributions to the philosophy of mathematics . . 288-294 
(a) The hypotheses of mathematics .... 289-290 
O) The two intellectual methods .... 290-292 
(y) Definitions ........ 292-294