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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,