582 
ENGLISH INDEX 
201, 297, 400 : on 4 perfect ’ pro 
portion 86 : a proposition in 
proportion 294: two geometrical 
passages in Meno 297-308 : pro 
positions ‘on the section’ 304, 
324-5. 
4 Platonic ’ figures (the regular 
solids) 158,162, 294-5, 296-7. 
Playfair, John, 436. 
Pliny 129, ii. 207. 
Plutarch 84, 96, 128, 129, 130, 133, 
144,145,167,179, ii. 2, 3, ii. 516: 
on Archimedes ii. 17-18. 
Point: defined as a ‘unit having 
position ’ 69, 166 : Plato on points 
293. 
Polybius 48, ii. 17 «., ii. 207. 
Polygon : propositions about sum 
of exterior or interior angles 144: 
measurement of regular polygons 
ii. 826-9. 
Polygonal numbers 15, 76, 79, ii. 
213, ii. 514-17. 
Polyhedra, see Solids. 
Porism (1) = corollary 372: (2) a 
certain type of proposition 378, 
431-8 : Porisms of Euclid, see 
Euclid : of Diophantus, see Dio- 
phantus. 
Porphyry 145: commentary on Eu 
clid’s Elements 358, ii. 529. 
Poselger, F. T. ii. 455. 
Posidonius ii. 219-22 : definitions 
ii. 221, 226 ; on parallels 358, ii. 
228 : versus Zeno of Sidon ii. 
221-2 : Meteorologica ii. 219 : 
measurement of earth ii. 220: on 
size of sun ii. 108, ii. 220-1. 
Postulates: Aristotle on, 336: in 
Euclid 336,374-5 : in Archimedes 
336,. ii. 75. 
Powers, R. E. 75 n. 
Prestet, Jean, 75«. 
Prime numbers and numbers prime 
to one another 72-3: defined 73: 
2 prime with Euclid and Aristotle, 
not Theon of Smyrna and Neo- 
Pythagoreans ib. 
Problems : classification 218-19 : 
plane and solid ii. 117-18 : pro 
blems and theorems 318, 431, ii. 
533. 
Proclus 12, 99,175,183, 213, 224«., 
ii. 529-37 : Comm, on Eucl. I. ii. 
530-5 ; sources ii. 530-2 : 4 sum 
mary’ 118-21,170, object of, 170- 
1 : on discoveries of Pythagoras 
84-5,90,119, 141,154: on Euclid 
I. 47, 145, 147: attempt to prove 
parallel-postulate 358, ii. 534: on 
loci 219 : on porisms 433-4: on 
Euclid’s music 444: comm, on 
Republic 92-3, ii. 536-7 : Hypoty- 
posis of astronomical hypotheses 
ii. 535-6. 
Prodicus, on secondary education 
20-1. 
Prolate, of numbers 108, 204. 
Proof 370, ii. 533. 
Proportion : theory discovered by 
Pythagoras 84-5, but his theory 
numerical and applicable to com- 
mensurables only 153, 155, 167: 
def. of numerical proportion 190: 
the 4 perfect ’ proportion 86 : 
Euclid’s universally applicable 
theory due to Eudoxus 153, 155, 
216, 325-7. 
Proposition, geometrical: formal 
divisions of, 370-1. 
Protagoras 202: on mathematics 
23, 179. 
Prou, V. ii. 309. 
Psammites or Sand-reek oner oi Archi 
medes 40, ii. 3, ii. 81-5. 
Psellus, Michael, 223-4«., ii. 453, 
ii. 545-6. 
Pseudaria of Euclid 430-1. 
Pseudo-Boetius 47. 
Pseudo-Eratosthenes: letter on du 
plication of cube 244-5. 
Ptolemies: coins of, with alphabetic 
numerals 34-5: Ptolemy I, story 
of, 354. 
Ptolemy, Claudius, 181, ii. 198, ii. 
216, ii. 218, ii. 273-97: sexa 
gesimal fractions 44-5, approxi 
mation to 7t 233: attempt to prove 
parallel-postulate 358, ii. 295-7 : 
Syntaxisii. 273-86, commentaries 
and editions ii, 274-5, contents 
of, ii. 275-6, trigonometry in, ii. 
276-86, 290-1, Table of Chords 
ii. 259, ii. 283-4, on obliquity of 
ecliptic ii. 107-8 : Analemma 
ii. 286-92: Planispheriumü. 292- 
3, Optics ii. 293-4, other works ii, 
293 ; 7re/A pcnrav ii. 295 : wepl 8tn- 
crräcrecos ib. 
Pyramids : origin of name 126: 
measurements of, in Rhind Papy 
rus 126-8: pyramids of Dakshfir,