572
ENGLISH INDEX
making ii. 18, on Aristarchus’s
hypothesis ii. 8-4.
Conics, propositions in, 438-9,
ii. 122-6.
Cubic equation solved by conics
ii. 45-6.
On Democritus 180, 827,
equality of angles of incidence
and reflection ii. 353-4, integral
calculus anticipated ii. 41-2, 61,
62-3, 74, 89-90; Lemma or Axiom
of A. 326-8, ii. 35 : vevaeis in, ii.
65-8 (Pappus on, ii. 68): on semi
regular solids ii. 98-101: triangle,
area in terms of sides ii. 103:
trisection of any angle 240-1.
Archytas 2, 170, 212-16, ii. 1 : on
fj.adrjfj.nTn 11, on logistic 14, on 1
as odd-even 71: on means 85, 86:
no mean proportional between n
andn+1, 90,215: on music 214;
mechanics 213 : solution of pro
blem of two mean proportionals
214, 219, 245, 246-9, 334, ii. 261.
Argyrus, Isaac, 224 n., ii. 555.
Aristaeus : comparison of five regu
lar solids 420 : Solid Loci (conics)
438, ii. 116, 118-19.
Aristaeus of Croton 86.
Aristarchus of Samos 43, 139, ii. 1-
15, ii. 251 : date ii. 2 : cn<d(]nj of,
ii. 1 : anticipated Copernicus ii.
2-3: other hypotheses ii. 3, 4:
treatise On sizes and distances of
Sun and Moon ii. 1, 3, 4-15, tri
gonometrical purpose ii. 5 : num
bers in, 39 : fractions in, 43.
Aristonophus, vase of, 162.
Aristophanes 48. 161. 220.
Aristotelian treatise on indivisible
lines 157, 346-8.
Ax-istotherus 348.
Aristotle 5, 120, 121 : on origin of
science 8 : on mathematical sub
jects 16-17 : onfii-st principles,de
finitions, postulates, axioms 336-8.
Ai’ithmetic: reckoning by tens
26-7, why 1 is odd-even 71 : 2
even and px-ime 73 : on Pytha
goreans and numbex’S 67-9 : on
the gnomon 77-8, 83.
Astronomy : Pythagorean sys
tem 164-5, on hypothesis of con-
centi’ic spheres 329. 335, ii. 244.
on Plato’s view about the earth
314-15.
On the continuous and infinite
342-3 ; proof of incommensura
bility of diagonal 91: on principle
of exhaustion 340 : on Zeno’s
paradoxes 272, 275-7, 278-9, 282:
on Hippocrates 22 : encomiunx on
Democritus 176.
Geometry : illustrations from,
335, 336, 338-40, oxx parallels
339, proofs differing from Euclid’s
338-9, propositions not in Euclid
340, on quadratures 184-5, 221,
223, 224 n., 271, on quadratux-e
by lunes (Hippocrates) 184-5.
198-9: on Plato and regular
solids 159 : curves and solids in
A. 341.
Mechanics 344-6,445-6: parai-
lelogi’am of velocities 346 : ‘Aris
totle’s wheel’ ii. 347-8.
Aristoxenus 24 n., 66.
Arithmetic (l j = theory of numbers
(opp. to \oyinTiKTj) 13—16 : early
‘Elements of Arithmetic’ 90, 216:
systematic tx'eatises, Nicomachus
Introd. Ar. 97-112, Theon of
Smyrnal 12-3, Iamblichus,Co oxixi.
on Nicomachusll3-15, Domninus
ii. 538. (2) Practical arithmetic :
originated with Phoenicians 120-
1, in primary education 19-20.
Arithmetic mean, defined 85.
Arithmetica of Diophantus 15-16,
ii. 449-514.
Arithmetical operations: see Addi
tion, Subtraction, &c.
Arrow of Zeno 276, 280-1.
Aryabhatta 234.
Asclepius of Tx-alles 99.
Astronomy in elementai’yeducation
19 : as secondary subject 20-1.
Athelhard of Bath, fix-st translator
of Euclid 362-4.
Athenaeus 144, 145.
Athenaeus of Cyzicus 320-1.
‘Attic’ (or ‘Herodianic’) numerals
30-1.
August, E. F. 299, 802, 361.
Autolycus of Pitane 348 : works
On the moving Sphere 348-52, On
Risings and Settings 352-3 : rela
tion to Euclid 35Î-2.
Auverus, C. ii. 26.
Axioms : Aristotle on, 336 ; = Com
mon Notions in Euclid 376 : Axiom
of Archimedes 326-8, ii. 35.
Babylonians
system oi
gesimal 1
proportio:
Bachet, edi
454-5, ii.
Bacon, Eogx
Baillet, J. ii
Baldi, B. ii.
Barlaam ii.
Bax-ocius ii.
Barrow, I., i
70 : on Be
Bathycles D
Baudhayana
Baynard, D.
Benecke, A.
Benedetti, G
Bertrand, J.
Bessarion ii.
Besthorn, E.
Billingsley,
Bjornbo, A.
Blass, C. 29£
Blass, F. 18£
Boeckh, A. I
Boetius 37,
Euclid 351
Boissonade i
Bouxbelli, Ex
Borchax-dt, I
Borelli, G. A
Bouillaud (I
556.
Braunmuhl,
288, ii. 291
Breton (de C
Bretsclineide
ii. 539.
Brochard, V.
Brougham, I.
Brugsch, H.
Bryson 219, i
Burnet, J. 20
Butcher. S. I
Buzengeiger
Cajori, F. 281
Calculation, ]
46-8, addil
52, multip
52- 3 (Eussi
53- 8, divis:
of square n
63-4. ii. 34
Callimachus 1
