76, 202, 
develop- 
224, ii. 
use ii. 
38, 489. 
185, ii. 
Porisms 
nultiples 
eek sys- 
tion ib. : 
Babylo- 
309, ii. 
on arith- 
on divi- 
-18 : on 
jf Eucl. 1 
lels 858: 
lel-postu- 
nnal way 
ee conics 
work on 
on Posi- 
i. 281-2: 
.menu ii. 
lensuration 
etry) 16-17. 
I (Archytas) 
tween two 
mbers), two 
milar solid 
201, 297, 
between 
, 215. 
Philolaus’s 
-pt 120-2: 
education 
. 453, ii. 
II) 365-7: 
j47. 
. 547. 
anslator ot 
363, 367, 
252, ii. 262. 
ENGLISH INDEX 
.77 
Ghetaldi, Marino, ii. 190. 
Girard, Albert, 485, ii. 455, 
Gnomon : history of term 78-9: 
gnomons of square numbers 77- 
8, of oblong numbers 82-3, of 
polygonal numbers 79 : in appli 
cation of areas 151-2 : use bj r 
al-Karkhi 109-10: in Euclid 379 : 
sun-dial with vertical needle 139. 
Gomperz, Th. 176. 
Govi, G. ii. 293 n. 
Gow, J. 38. 
Great Year, of Oenopides 174-5, 
of Callippus and Democritus 177. 
Gregory, D. 360-1, 440, 441, ii. 127. 
Griffith, P. LI. 125. 
Gunther, S. ii. 325 «., ii. 550. 
Guldin’s theorem, anticipated by 
Pappus ii. 403. 
Halicarnassus inscriptions 32 - 3, 
34. 
Halley, E., editions of Apollonius's 
Conics ii. 127-8, and Sectio ratio 
nis ii. 175, 179, of Menelaus ii. 
252, ii. 262, of extracts from 
Pappus ii. 360, of Serenus ii. 519. 
Halma, editor of Ptolemy ii. 274, 
275. 
Hammer-Jensen, I. ii. 300 n., ii. 
304 n. 
Hankel, H. 145, 149, 288, 369, ii. 
483 
Hardy, G. H. 280. 
Harmonic mean (originally ‘sub 
contrary ’) 85. 
Harpedonaptae, ‘ rope-stretchers ’ 
121-2, 178. 
Harun ar-Rashid 362. 
Hau - cal culations (Egyptian) ii. 
440-1. 
Hecataeus of Miletus 65, 177. 
Heiben, J. L. 233 n. 
Heiberg, J. L. 184, 187 n., 188, 
192 «., 196-7 «., 315, 361, ii. 203, 
ii. 309, 310, 316, 318, 319. ii. 519, 
ii. 535, 543, 553, 555«. 
Helceph 111. 
Hendecagon in a circle (Heron) ii. 
259, ii. 329. 
Henry, C. ii. 453. 
Heptagon in a circle, ii. 103: 
Heron’s measurement of, ii. 328. 
Heraclides of Pontus 24, ii. 231-2: 
discovered rotation of earth about 
axis 316-17, ii. 2 3, and that Venus 
and Mercury revolve about sun 
312, 317, ii. 2, ii. 244. 
Heraclitus of Ephesus 65. 
Heraclitus, mathematician ii. 192, 
ii. 359, ii. 412. 
Hermannus Secundus ii. 292. 
Hermesianax 142«., 163. 
Hermodorus ii. 359. 
Hermotimus of Colophon 320-1 : 
Elements and Loci ih., 354. 
‘ Herodianic ’ (or ‘ Attic ’) numerals 
30-1. 
Herodotus 4, 5, 48, 65, 121, 139. 
Heron of Alexandria 121, ii. 198, 
ii. 259 : controversies on date ii. 
298-307 : relation to Ctesibius 
and Philon ii. 298-302, to Pappus 
ii. 299-300, to Posidonius and 
Vitruvius ii. 302-3, to agrimen 
sores ii. 303, to Ptolemy ii. 303-6. 
Arithmetic: fractions42-4, mul 
tiplications 58, approximation to 
surds ii. 51, ii. 323-6, approxima- 
tion to cube root 64, ii. 341-2, 
quadratic equations ii. 344, in 
determinate problems ii. 344, 
444-7. 
Character of works ii. 307-8 : 
list of treatises ii. 308-10. 
Geometry ii. 310-14, Definitions 
ii. 314-16: comm, on Euclid’s 
Elements 358, ii. 310-14 : proof of 
formula for area of triangle in 
terms of sides ii. 321-3: duplica 
tion of cube 262-3. 
Métrica ii. 320-43: (1) mensu 
ration ii. 316-35: triangles ii. 
320-3, quadrilaterals ii. 326, 
regular polygons ii. 326-9, circle 
and segments ii. 329-31; volumes 
ii. 331-5, (Swpto-Koy ii. 332-3, frus 
tum of cone, sphere and segment 
ii. 334, tore ii. 334-5, five regular 
solids ii. 335. (2) divisions of 
figures ii. 336-43, of frustum of 
cone ii. 342-3. 
Mechanics ii. 346-52 : on Ar 
chimedes’s mechanical works ii. 
23-4, on centre of gravity ii. 350-1, 
352. 
Belopoetca 18, ii. 308-9, Catop- 
trica 18, ii. 294, ii. 310, ii. 352-4. 
Dioptra ii. 345-6, Pneumática 
and Automata 18, ii. 308, 310. 
On Water-clocks ii. 429, ii. 536. 
Heron, teacher of Proclus ii. 529. 
Pp