278 Index
Pascal 165
use of the infinite 151
use in Chinese mathematics 92, 95
Peano, axiom systems 206
pentagon, construction of 52– 3
ab ̄u-l-Waf ̄a al Buzj ̄an ̄ı’s method 107– 8
Perron, on set theory 219
perspective 143
Philo of Byzantium 59
philosophy
relationship to mathematics 216–17
and set theory 218
physics, late twentieth century 251–4
place value number systems 22
plagiarism 165, 166, 175
planetary motion
circular motion restriction 66
Kepler’s ideas 152– 3
Newton’s ideas 176
Ptolemy’s models 69
Plato 33–5, 40
Meno50, 51–2
Republic 50
Theatetus 49
views on geometry 194–5, 198
Platonic solids 46
Platonicus(Eratosthenes) 58–9
Playfair’s axiom 190
‘Plimpton 322’ 25
Plutarch, on Archimedes 60–1
Poincaré 192
fundamental group 226
topology 223–4
Poincaré model 203
pointed field problem,Shushu Jiuzhang
(Qin Jiushao) 95– 6
political choices 261
polynomials
al-Samaw’al’s work 117–20
use in Chinese mathematics 92
powers, table of, al-Samaw’al 118
presentism 6, 7, 48
Princeton 239
Principia(Newton) 163, 164, 176–8,
186, 197
Principle of the Excluded Middle 231, 232
priority dispute, the calculus 165–6
procedure texts 20–1
Proclus 44, 47, 190
on parallel postulate 195–6
as source of Greek mathematical
history 41
product rule, differentials 179, 180
programming 245–6
projective geometry 199 , 204
proof
by contradiction 219
existence proof 137
Greek deductive structure 38, 44
proportion 139
Eudoxus’s theory 47proportions
theory of 3
see alsoratios
Ptolemy 40
Almagest66–9, 75–6
theory of planetary motion 152
puzzle-solving 8
Pythagoras 40, 44–5
Pythagoras’s theorem, in Euclid’sElements 38
Pythagorean sect 46
construction of pentagon 52– 3qibla, determination of 124–5, 131 , 195
Qin (Ch’in) dynasty 81
Qin Jiushao 90, 91, 92, 93
introduction of zero symbol 87
pointed field problem 95–6
use of ‘equations’ 94
quadratic equations
al-Khw ̄arizm ̄ı’s work 111– 12 , 125–6
Babylonian mathematics 25, 30
formula 111
Th ̄abit ibn Qurra’s work 112–14, 127–8
quadratic maps 248–9
quadratic problems, Heron’s solutions 65
quadrature description of curves 180–1
quadrature of lunes, Hippocrates 56
quadrilateral, Lambert’s 201
Quaestiones super Euclidem(Oresme) 136–7, 139, 155–6
quantum theory 252–3
questioning, role in history 3
Qur’an (Koran) 124Rademacher 229
Ramanujan, Srinivasa 228–9
Rashed, Roshdi 102–4
al-Samaw’al 119–21
Islam 123–5
ratio, Euclid’s use of term 38
ratios
Euclid’s theory 35, 45, 48
extreme and mean (golden) 49, 53
in Greek mathematics 49–51
irrational 46
real numbers, Dedekind’s definition 215
reciprocal tables, Babylonian 23
reconstruction, role in history 41–2, 48–9
rectangular arrays, Chinese mathematics 88–90
rectification description of curves 180–1
regular solids
al-K ̄ash ̄ı 128
Platonic 46
Reidemeister 226
Reidemeister moves 227
relativism 9
religion, role in Islamic mathematics 123–5
remainder theorem, Chinese 78
repeating decimals 149
Republic(Plato) 50
revolutions in science 8
revolving bodies, area (fromPrincipia) 186