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ENGLISH INDEX 
581 
(Pytha- 
object 
al,qui- 
igin of 
gyptian 
ims (1) 
al 28-9: 
adianic’ 
system, 
, bow 
itroduc- 
>g 36-7, 
37-9; 
, Apol- 
medes’s 
'8, 114: 
. 328. 
volume 
70-1: 1 
-even’, 
numbers 
: d is 
tic 138, 
174-5 : 
on-ivise 
in ele- 
_r 69. 
f Euclid 
-4. 
ontents, 
ii. 175, 
86, 187, 
11, 212, 
>5-439 : 
40, on 
multi 
means 
orks of 
conics 
of Euclid and Apollonius 438, 
proof of focus-directrix property 
ii. 120-1; commentary on Euclid 
358, ii. 356-7, on Book X 154-5, 
209, 211, ii. 193 : commentary on 
Euclid’s Data 421-2, ii. 357, on 
Diodorus’s Analemma ii. 287, 
scholia on Stjntaxis ii. 274: on 
classification of problems and 
loci (plane, solid, linear) 218-19, 
ii. 117-18, criticism on Archimedes 
and Apollonius 288, ii. 68, ii. 167: 
on surface-loci 439-40, ii. 425-6 : 
on Euclid’s Porisms 431-3, 436-7, 
ii. 270, ii. 419-24 : on ‘ Treasury 
of Analysis ’ 421,422,439, ii. 399- 
427 : on cochloids 238-9 : on quad- 
ratrix 229-30, ii. 379-80, con 
structions for,ii. 380-2: on dupli 
cation of cube 266-8, 268-70: on 
trisection of any angle 241-3, 
ii. 385-6, veiais with fegard to 
parallelogram 236-7 : on isoperi 
metry (cf. Zenodorus) ii. 207, ii. 
211-12, ii. 390-4. 
* Paradoxes ’ of Erycinus ii. 365-8. 
Parallelogram of velocities 346, ii. 
348-9. 
Parapegma of Democritus 177. 
Parmenides 138. 
Paterius ii. 536-7. 
Patricius ii. 318, 319. 
Pebbles, for calculation 46, 48. 
Pentagon, regular : construction 
Pythagorean 160-2; area of,ii.327. 
Pentagram, Pythagorean 161-2 (see 
Errata). 
‘ Perfect ’ numbers 74-5 : list of 
first ten ih. : contrasted with 
‘ over-perfect ’ and ‘ defective ’ 
ih. : 10 with Pythagoreans 75. 
‘ Perfect ’ proportion 86. 
Pericles 172. 
Pericles, a mathematician ii. 360. 
Perseus 226 : spiric sections ii. 
203-6. 
‘Phaenomena’= observational as 
tronomy 17: 322, 349. 
Philippus of Opus 354: works by, 
321 : on polygonal numbers 84, 
ii. 515 : astronomy 321. 
Philolaus 67, 72, 76, 78, 86, 158, 
ii. 1: on odd, even, and even-odd 
numbers 70-1: Pythagorean non 
geocentric astronomy attributed 
to, 163-4. 
Philon of Byzantium 213 : duplica 
tion of cube 262-3: Philon, Ctesi- 
bius and Heron ii. 298-302. 
Philon of Gadara 234. 
Philon of Tyana ii. 260. 
Philoponus, Joannes, 99, 223, 224 n. 
Phocaeans 7. 
Phocus of Samos 138. 
Phoenician alphabet, how treated 
by Greeks 31-2 : arithmetic ori 
ginated with Phoenicians 120-1. 
‘Piremus’ or ‘peremus’ in pyramid 
126, 127. 
* Plane ’ loci 218. 
‘Plane’ problems 218-19. 
Planisphaerium of Ptolemy ii. 292-3. 
Planudes, Maximus, 117, ii. 453, ii. 
546-9. 
Plato 19,22,24,121,142»., 170,176 : 
Qeos aelyecoperpH 10 : suyeape- 
Tprjros ehriTU) iii, 24,355 : on educa 
tion in mathematics 19-20, 284: 
on mathematical ‘arts’, measure 
ment and weighing 308, instru 
ments for, 308-9, principle of 
lever 309 : on optics 309, 441 : 
on music 310 : Plato’s astronomy 
310-15: on arithmetic andlogistic 
13-14 : classification of numbers, 
odd, even, &c. 71-2, 292 : on 
number 5040, 294: the Geometri 
cal Number, 305-8 : on arithme 
tical problems 15, ii. 442 : on 
geometry 286-8, constructions 
alien to true geometry ih. : on 
tology of mathematics 288-9: 
hypotheses of mathematics 289- 
90 : two intellectual methods 
290-2 : supposed discovery of 
mathematical analysis, 120, 212- 
13, 291-2 : definitions of various 
species of numbers 292, figure 
292-3, line and straight line 293, 
circle and sphere 293-4 : on 
points and indivisible lines 293 : 
formula for rational right-angled 
. triangles 81, 304 : ‘rational ’ and 
‘ irrational diameter of 5 ’ 93, 
306-7 : Plato and the irrational 
156, 203-5, 304: on solid geo 
metry 12-13,303 : on regular and 
semi-regular solids 294-7 : Plato 
and duplication of cube 245-6, 
255, 287-8, 303 : on geometric 
means between two squares and 
two cubes respectively 89, 112,