530 
ENGLISH INDEX 
52-3, Greek58-4, ‘Russian’ 58n.: 
examples from Eutocius, Heron, 
Theon 57-8: Apollonius’s con 
tinued multiplications 54-7. 
Multiplication Table 53. 
Murran, an angular measure ii. 215. 
Musical intervals and numerical 
ratios 69, 75-6, 85, 165. 
Myriads, ‘ first ’, ‘ second ’, &c., nota 
tion for, 39-40. 
Nagl, A. 50. 
an-Nairizi: comm, on Euclid 363, 
ii. 224, ii. 228-30, ii. 309-10. 
NasTraddin at-Tusi : version of Eu 
clid 362, of Apollonius’s Co7iics 
ii. 127 : of Ptolemy ii. 275. 
Naucratis inscriptions 33. 
Nemesius 441. 
Neoclides 319. 
Ner (Babylonian) (= 600) 28, ii. 
215, 
Nesselmann, G. H. F. ii. 450-1, ii. 
455-6. 
Newton 370, ii. 20, ii. 182. 
Nicolas Rhabdas 40, ii. 324 n., ii. 
550-3. 
Nicomachus of Gerasa 12, 69, 70, 
72, 73, 74, 76, 83, 85, 86, ii. 238, 
ii. 515: works of, 97: Introductio 
arithmetica: character of treatise 
98-9, contents 99-112, classifica 
tion of numbers 99-100: on ‘per 
fect’ numbers 74, 100-1: on ten 
means 87: on a ‘Platonic’ theo 
rem 297: sum of series of 
natural cubes 109-10. 
Nicomedes 225-6, ii. 199: cochloids 
or conchoids 238-40: duplica 
tion of cube 260-2. 
Niloxenus 129. 
Nine, rule of, 115-16: casting out 
nines ii. 549. 
Nipsus, M. Junius, 132. 
Nix, L. ii. 128, 131, ii. 309. 
Noel, G. 282. 
Number: defined, by Thales 69, by 
Moderatus, Eudoxus, Nicoma 
chus, Aristotle 70; classification 
of numbers 70-4: ‘ perfect ’, 
‘over-perfect’ and ‘defective’ 
numbers 74-5, ‘ friendly ’ 75, 
figured 76-9 : ‘oblong’, ‘prolate’ 
82-3, 108, 114, similar plane and 
solid numbers 81-2, 90, solid 
numbers classified 106-8 : ‘ the 
number in the heaven ’ (Pytha 
gorean) 68, ‘number’ of an object 
69. 
Numerals : systems of, decimal, qui 
nary, vigesimal 26 : origin of 
decimal system 26-7 : Egyptian 
27-8 ; Babylonian systems (1) 
decimal 28, (2) sexagesimal 28-9: 
Greek (1) ‘Attic’ or ‘Herodianic’ 
30 - 1 : (2) alphabetic system, 
original in Greece 31-7, how 
evolved 31-2, date of introduc 
tion 33-5, mode of writing 36-7, 
comparison of two systems 37-9 ; 
notation for large numbers, Apol 
lonius’s tetrads 40, Archimedes’s 
octads 40-1. 
Nymphodorus 213. 
‘ Oblong’ numbers 82-3, 108, 114: 
gnomons of, 82-3. 
Ocreatus, 111. 
Octads, of Archimedes 40-1. 
Octagon, regular, area of, ii. 328. 
Octahedron 159, 160, 162: volume 
of, ii. 335. 
‘ Odd ’ number defined 70-1 : 1 
called ‘ odd-even ’ 71 : ‘odd-even’, 
‘ odd-times-odd’, &c., numbers 
71-4. 
Oenopides of Chios 22, 121 : dis 
covered obliquity of ecliptic 138, 
174, ii. 244: Great Year of, 174-5 : 
called perpendicular gnomon-wise 
78,175 : two propositions in ele 
mentary geometry 175. 
Olympiodorus 444. 
One, the principle of number 69. 
Oppermann ii. 324 n. 
Optics : divisions of, 17-18 : of Euclid 
441-4 : of Ptolemy ii. 293-4. 
Oval of Cassini ii. 206. 
Oxyrhynchus Papyri 142. 
Pamphile, 131, 133, 134. 
Pandrosion ii. 360. 
Pappus (see also Table of Contents, 
under Chap. XIX)ii. 17-18, ii. 175, 
180, 181, 182, 183, 185, 186, 187, 
188, 189, 190. ii. 207, 211, 212, 
213, ii. 262, ii. 337, ii. 355-439 : 
on Apollonius’s tetrads 40, on 
Apollonius’s continued multi 
plications 54-7 : on ten means 
87-9 : on mechanical works of 
Archimedes ii. 23-4 : on conics 
( 
of Ei 
proof 
ii. 12( 
358, i 
209, 5 
Eucli 
Diode 
scholi 
classi 
loci (j 
ii.117 
and .A 
on sui 
on Eu 
ii. 27C 
of An, 
427: c 
ratrix 
struct 
cation 
trisect 
ii. 381 
parall 
metry 
211-1! 
‘ Parado: 
Parallele 
348-9. 
Parapegt 
Parmenii 
Paterius 
Patricius 
Pebbles, 
Pentagoi 
Pythag 
Pentagra 
Errata 
‘ Perfect' 
first i 
‘ over-p 
ib.: 10 
‘ Perfect ’ 
Pericles ] 
Pericles, 
Perseus 
203-6. 
‘ Phaenon 
tronom 
Philippus 
321: o 
ii. 515: 
Philolaus 
ii. 1: o: 
number 
geocent 
to, 163-