Index
π
Archimedes’ approximation 61–2, 157
estimation in Keralan mathematics 167, 168
Landau’s definition 238
transcendence of 221
Note: Page numbers initalicsrefer to figures.
abacus schools 141–3
Abbasid dynasty 109
Ab ̄uK ̄amil 115–16
absolute measurement 200–1
abstraction of thought 43
in Babylonian mathematics 18–19, 20–1, 24–6
in Chinese mathematics 88
twentieth century 240
acceleration, uniform 154
accounting methods 142
acute angle hypothesis (HAA) 190– 1
Akkadians 15
al-B ̄ ahir fi-l jabr(al-Samaw’al) 104, 117–20
Albert of Saxony 136
discussion of squaring the circle 137–8
al-B ̄ır ̄ un ̄ı 95, 124–5, 195
ideas on velocity 152
Alexandrov, P. 224, 250
Alexander, J. W. 226, 227
al-Far ̄ab ̄ı 113
algebra
analytic Art,The(Viète) 146, 147–8
Descartes’ notation 149
Diophantus 66
Islamic 103–4, 108
ab ̄uK ̄amil’s work 115–16
al-Khw ̄arizm ̄ı’s work 110–11, 125–6
al-Samaw’al’s work 117–20
Omar Khayyam’s work 116–17
origins 110–14
texts of 16th,17thcenturies 147
Algebra(‘Bourbaki’) 256
algebraic geometry, rings and ideals 230
algorithms
Leibniz’s use 174, 186
military uses 260–1
al-K ̄ash ̄ı 104, 105 , 117, 120–3, 128–9
Mift ̄ ah al-his ̄ab 104
regular solids 128
al-Khw ̄arizm ̄ı (Muhammed ibn M ̄usa) 125–6
Hisab al-jabr wa al-muq ̄abala103, 110
Almagest(Ptolemy) 66–9, 75–6
al-Ma’mun 109
Al-Mas’ ̄ud ̄ı95
‘alogoi’ ratios 35
alphabetic writing, invention of 43
al-B ̄ ahir fi-l jabr 104
al-Uql ̄ıdis ̄ı 104, 114
arithmetic (Kit ̄ ab al Fus ̄ul f ̄ ı al-His ̄ab
al-Hind ̄ı) 106–7
use of decimals 121
Ambassadors,The(Holbein) 142
anagrams, use in scientific communications 165
Analyse des infiniment petits, pour
l’intelligence des lignes courbes
(de l’Hôpital) 179
analysisseecalculus
Analyst,The(Berkeley, George) 179–80
Analytical Engine (Babbage) 243
Analytic Art,The(Viète) 146, 147–8
angle of parallelism ( (p)) 202–3
angles of a triangle theorem, proof 210 –11
angle-sum, spherical triangles 200
anonymous publication 165
anxiety and modernism 218
Apollonius 40
Conics 58
planetary motion 67
apotomes 53
applications of mathematics 261
approximation procedures, in Chinese
mathematics 96–7
Arabic mathematicsseeIslamic mathematics
arc, Keralan calculation 167 –8
Archimedes 40, 41, 60–2, 64–5
approximation ofπ 157
area of circle 157–8
finite universe 194
infinities 151, 153
Measurement of the Circle137, 138
and Newton’sPrincipia 177
volume of cone 48–9
area
Archimedes’ method of measurement 61
of cardioid 182– 3
of circle157–8
in Euclid’sElements 38
of triangle, Heron’s formula 64–5
area law, Kepler, Newton’s version 177– 8 , 186
argument
role in history 3
scholastic methods 136–8
Aristotle, method of argument 137