576 
ENGLISH INDEX 
Data 421-5, Divisions {of 
figures) 425-80, ii. 336, 339. 
Elements: text 360-1, Theon’s 
edition 358, 360, ii. 527-8, trans 
lation by Boëtius 359, Arabic 
translations 362, ancient com 
mentaries 358-9, editio princeps 
of Greek text 360, Greek texts of 
Gregory, Peyrard, August, Hei 
berg 360—1 : Latin translations, 
Athelbard 362-3, Gherard 363, 
Campanus 363-4, Coramandinus 
365: first printed editions, Rat- 
dolt 364-5, Zamberti 365 : first 
introduction into England 363 : 
first English editions, Billingsley, 
&c. 369-70: Euclid in Middle 
Ages 365-9, at Universities 368- 
9: analysis of, 373-419 : arrange 
ment of postulates and axioms 
361: 1.47, how originally proved 
147-9 : parallel-postulate 358, 
375, ii. 227-30, ii. 295-7, ii. 534 : 
so-called ‘Books XIV, XV’ 419- 
21. 
Mechanics 445-6 : Music 444- 
5, Sectio canonis 17, 90, 215, 
444-5: Optics 17—18, 441-4: Phae 
nomena 349, 851-2, 440-1, ii. 
249: Porisms 431-8, lemmas to, 
ii. 419-24 : Pseudaria 430-1 : Sur 
face-Loci 243-4, 439-40, lemmas 
to, ii. 119-21, ii. 425-6. 
Eudemus 201, 209, 222 : Histon) of 
Geometry 118, 119, 120, 130, 131, 
135, 150, 171 : on Hippocrates’s 
lunes 173, 182, 183-98: History 
of Astronomy 174, 329, ii. 244. 
Eudoxus 24, 118, 119. 121, 320, 
322-4 : new theory of proportion 
(that of Eucl. V. ii) 2, 153, 216, 
325-7 : discovered method of ex 
haustion 2, 176, 202, 206, 217, 
222, 326, 327-9 : problem of two 
mean proportionals 245,246,249 
51 : discovered three new means 
86: ‘general theorems’ 323-4: 
On speeds, theory of concentric 
spheres 329-34, ii. 244 : Phaeno 
mena and Mirror 322. 
Eugenius Siculus, Admiral, ii. 293. 
Euler, L. 75n., ii. 482, ii. 483. 
Euphorbus (= Pythagoras) 142. 
Eurytus 69. 
Eutocius 52, 57-8, ii. 25, ii. 45, ii. 
126, ii. 518, ii. 640-1. 
Exhaustion, method of, 2, 176, 202, 
217, 222, 326, 327-9: develop 
ment of, by Archimedes 224, ii. 
35-6. 
False hypothesis: Egyptian use ii. 
441 : in Diophantus ii. 488, 489. 
Fermat, P. 75 n., ii. 20, ii. 185, ii, 
454, ii. 480, ii. 481-4: on Porisms 
435. 
Fontenelle ii. 556. 
Fractions: Egyptian (submultiples 
except §) 27-8, 41: Greek sys 
tems 42-4 : Greek notation ih.: 
sexagesimal fractions, Babylo 
nian 29, in Greek 44-5. 
‘Friendly’ numbers 75. 
Galilei 344, 446. 
Geeponicus, Liber, 124, ii. 309, ii. 
318, ii. 344. 
Geminus 119, ii. 222-34 : on arith 
metic and logistic 14 : on divi 
sions of optics, &c. 17-18 : on 
original steps in proof of Eucl. 1 
32, 135-6: on parallels 358: 
attempt to prove parallel-postu 
late ii. 227-30 : on original way 
of producing the three conics 
ii. Ill: encyclopaedic work on 
mathematics ii. 223-31: on Posi 
donius’s Meteorologica ii. 231-2 : 
Introduction to Phaenomena ii. 
232-4. 
Geodesy (yewdaiaia) = mensuration 
(as distinct from geometry) 16-17. 
Geometric mean, defined (Archytas) 
85 : one mean between two 
squares (or similar numbers), two 
between cubes (or similar solid 
numbers) 89-90. 112, 201, 297, 
400 : no rational mean between 
consecutive numbers 90, 215. 
‘ Geometrical harmony ’ (Philolaus’s 
name for cube) 85-6. 
Geometry : origin in Egypt 120-2 : 
geometry in secondary education 
2°-L 
Georgius Pachymeres ii. 453, ii. 
546. 
Gerbert (Pope Sylvester II) 365-7 : 
geometry of, 366 : ii. 547. 
Gerhardt, C. J. ii. 360, ii. 547. 
Gherard of Cremona, translator of 
Euclid and an-NairM 363, 367, 
ii. 309; of Menelausii. 252, ii. 262. 
Ghetaldi, 
Girard, Al 
Gnomon : 
poiygoi 
cation 
al-Kark 
sun-dial 
Gomperz, 
dovi, G. ii 
Gow, J. 31 
Great Ye: 
of Callij 
Gregory, I 
Griffith, F. 
Günther, g 
Guldin’s t 
Pappusi 
Halicaruass 
34. 
Halley, E., 
Conics ii, 
nis ii. 17 
252, ii. 
Pappus ii 
Halma, edi 
275. 
Hammer-Je 
304 n. 
Hankel, H. 
483. 
Hardy, G. H 
Harmonic i 
contrary ’) 
Harpedonap 
121-2, 178 
Harun ar-Ba 
Hau - cal cub 
440-1. 
Hecataeus ol 
Heiben, J. L 
Heiberg, J. 
192 196 
ii- 309, 310 
ii- 535, 54c 
Helceph 111. 
Hendecagon 
259, ii. 329 
Henry, C. ii. 
Heptagon ir 
Heron’s me 
Heraclides of 
discoveredi 
axis.316-17. 
1623.2