Index 273
sources 80
transfers of knowledge 95–8
Chinese Remainder Theorem 78, 91
chord of an angle (Crdθ)68
Circle Limit III, (Escher) 192
circles
Archimedes’ work 61–2
area of157–8
in Euclid’sElements 38
circular motion, heavenly bodies 66, 67
cissoid 184
city-states, Greek 43
coined money, introduction of 43
Commercium epistolicum 166
common measure (greatest common divisor) 54
common notions, Euclid 37, 38
completeness of a system 222
componendo rule 74
computable numbers (Turing) 220, 256–7
computers, invention of 243–6
computer science 236
conchoid, tangent to 184
cone, volume of, Archimedes 48–9
Confucianism 81
Conics(Apollonius) 58
conic sections
Descartes 150
in Greek mathematics 58
consistency of a system 222
constant of curvature (K) 203
construction of geometry 201–3
continuum, doubts 215–16, 252
continuum hypothesis, Cantor 217
conversion factors Babylonian 30
coordinate geometry, Descartes 149–51
Coordinates of Cities(al-B ̄ır ̄un ̄ı) 124–5
Copernicus
influences 147
theory of planetary motion 152
copying of manuscripts, editing problems 41
cosineseetrigonometric ratios
cosine formula, in spherical and hyperbolic
geometry 209
counting rod numbers 86
counting rods, Chinese 85–8
use, description inNine Chapters 83
counting symbols, invention of 16
Coxeter, H., S., M. 192
‘crisis of foundations’ 215
cube
doubling of 6, 58 –9
multiplication of 60
as Platonic solid 46
cubes, difference between (Viète) 148
cubic curve, graph 150, 151 , 256
cubic equations
Omar Khayyam’s work 116–17
Tartaglia, Niccolò 144–5
cuneiform numbers 23
cuneiform script 15
Cuomo, Serafina, on Roman mathematics 69–70
curvature of space, constancy 204–5
curve-drawing machine, Descartes 150, 156
curves
description of 180
generation by motion 169–70
cuts 215 –16
definition 231
cybernetics 239
cycloid 170D’Alembert 180
dal Ferro, Scipione 144
Dao De Jing(Lao-Zi) 81
Daoism (Taoism) 81
day length 50
de l’Hôpital,Analyse des infiniment petits, pour l’intelligence des
lignes courbes 179
de Montmort, Pierre 1, 166
decimal fractions
in Islamic mathematics 120–1
Stevin’s work 149
decimal place-value numbers, and Chinese counting rods
87–8
Dedekind, Richard 214–16, 230
Dedekind cut 215 –16, 231
deductive structure, Greeks 38, 44
Dehn & Wirtinger 226
Delsarte, Jean 240
democratization of mathematics 235, 237
Democritus 40, 48–9
Descartes 112, 133, 149–51, 162
curve-drawing machine 156
finding of tangent to a curve 175
on Greek mathematics 39
ideas on infinity 197
Newton’s opinions 177
descriptive geometry 198 , 236
Devaney, Robert 248
diagrams, use in Greek mathematics 37, 38, 44
Dialogue on the Two MajorWorld-Systems(Galileo) 153–4
Dialogues(Plato) 33
Dieudonné, Jean 10–11, 223, 240
differential geometry 183
differentiation
relationship to integration 171–2
see alsocalculus
dimensional renormalization 253
Diophantus
algebraic notation 66
Arithmetic 111
Dirac’s functions 253
Dirichlet 229
Discourses on Two New Sciences(Galileo) 153–4
distributive law 5, 48
divergent series, Ramanujan’s work 229
division of polynomials, al-Samaw’al 119 –20
division problems, Babylonian Fara period 27
documentation
Babylonian mathematics 18–20, 21–2
Chinese mathematics 79
dodecahedral space 225