INDEX
Acerbi, F. 76, 112, 115
algebra 65, 66, 85, 91, 99, 103, 104, 105, 106, 116, 119, 129, 133, 137–140, 144
analysis 21, 39, 41, 47, 57, 76, 95, 111, 144
Apollonius 18, 44, 61, 68, 72, 74, 76, 147
Arafat, W. 146
Archimedes
translations from 19, 21–22, 67–71
works by
Cattle Problem 62
Conoids and Spheroids 38, 62
Measurement of Circle 113
Two Books on Sphere and Cylinder 11–29, 39, 41, 60, 62, 64, 75, 103, 105, 110, 111, 113, 114, 130, 131, 135, 183
Sand-Reckoner 60
Method 61, 62, 110
Spiral Lines 62
manuscripts:
Codex A 130
Bodl. Heb. D. 4 131
Istanbul Fatih 3414 131
Aristarchus 60
Aristotle 148, 153, 184
aura 58, 59, 63, 119, 120, 124, 125, 126, 136, 142, 187, 190
backwards-looking justifications 74, 82
Benjamin, W. 58
calculation 100, 110, 112, 138, 140, 141, 142, 162, 164, 171, 185, 188
canon 120, 121
canonical terms 56, 57, 134, 139, 185
Cattle Problem, see under Archimedes, works by
Clagett, M. 130
commentary practices 73, 95, 119, 126, 133
competition, mathematical 29, 38, 46, 60, 61, 62, 129, 132, 171, 172, 180
composition of ratios 116, 118
cone 12, 13, 32, 109, 110, 115
conic sections 26, 27, 29, 36, 52, 53, 58, 72, 88, 89, 90, 95, 134, 135, 149, 158, 169, 174, 180, 189
hyperbola 18–19, 25, 26, 27, 28, 31, 34, 35, 36, 44, 51, 52, 55, 68, 70, 78, 79, 80, 88, 89, 91, 158, 165, 168, 173, 174, 180
parabola 18, 22, 23, 25, 26, 28, 31, 34, 35, 36, 52, 55, 67, 68, 70, 77, 78, 80, 81, 86, 89, 91, 93, 158, 165, 168, 174, 180
ellipse 43, 44, 49, 51, 52, 55, 58, 96
Conoids and Spheroids, see under Archimedes, works by
Conon 60
Corry, L. 190
Cuomo, S. 116, 121, 122
cube 109, 155
cut-and-paste 69, 107, 108, 109, 165
cylinder 109, 115
Decorps-Foulquier, M. 18
Democritus 60
deuteronomic culture 8, 65, 121, 122, 123, 126, 127, 129, 133, 135, 136, 140, 141, 184, 186, 187, 190
diagrams 30, 31, 58, 59, 79, 84, 88, 96, 108, 109, 124, 125, 150, 152, 158, 163, 165, 166, 174
Diocles 30, 39–54, 55, 56, 57, 58, 61, 64, 76, 95, 96, 97, 122, 124, 125, 129, 130, 131, 132, 160, 171, 176, 177, 181
translation from 39–44
On Burning Mirrors 39, 95
Dionysodorus 29–39, 45, 52, 53, 54, 55, 56, 57, 58, 61, 64, 95, 97, 129, 130, 131, 132, 160, 165, 171, 176, 177
translation from 33
Diophantus 116, 141
Doric dialect 71
duality of geometry and algebra 15, 28, 29, 35, 36, 54, 95, 97, 114, 140, 161, 162, 164, 187
Elements, see Euclid
ellipse, see under conic sections
elliptic language 100, 161
epi-locution 18–19, 29, 66, 97–120, 125, 126
equalities 167, 168, 169, 170, 171, 182, 183, 186
Eratosthenes 23, 61
Euclid 9, 61, 76, 118, 125, 147, 149, 154, 184
Eudoxus 60
Eutocius 9, 18, 30, 32, 36, 39, 44, 58
Chapter 2 passim 128, 129, 130, 133, 136, 142, 165, 174, 181, 187
translations from 93–94, 117–118
formulaic expressions 98, 109, 161
Fowler, D. H. F. 74, 103
fractions 102
Fried, M. 1
functional relations 29, 42, 65, 92, 94, 95, 96, 168, 181, 187
Gandz, S. 142
geometrical algebra 3, 4, 101
see also duality of geometry and algebra, algebra
generality 14, 15, 29, 46, 54, 56, 57, 81, 85, 92, 124, 151
‘given’ 43, 44
Goldstein, C. 8, 190
Ibn Al-Haytam 131, 135, 136, 147, 165
Heath, T. L. 21, 25, 26, 27, 28, 35, 53, 85, 86, 90, 137
Heiberg, J. L. 75, 83, 99, 101, 104, 130
Hero 112, 113, 141
Herreman, A. 104, 190
Hogendijk, J. P. 178
Hoyrup, J. 141
hyperbola, see under conic sections
Hypsicles 61
imagination 79, 81
isoperimetric figures 115
Jones, A. 115, 116
Abu’l-Jud 131, 134, 135, 159, 167, 172, 173, 174, 176, 177, 179, 181, 191
Khayyam 9, 20
chapter 3 passim 189, 191
translation from 155–160
works by
Division of a Quadrant of a Circle 144, 145
Algebra 145–186
manuscripts
BN Arabe 2458 152
Al-Khazin 131, 134, 135, 146
Al-Khwarizmi 129, 133, 137–144, 145, 185
Klein, J. 1, 4, 5, 6, 7, 8, 38, 53, 54, 91, 124, 128, 186, 190
Knorr, W. R. 10, 30, 72, 122
limits on solubility 66–97, 134, 136, 150, 165, 167, 168, 174, 176, 179, 180, 189
Lloyd, G. E. R. 172
Lorch, P. 130
Al-Mahani 131, 133, 135, 136, 137, 144, 146, 172, 189
Al-Mamun 137, 159, 185
Mansfeld, J. 121
measurement 115
Measurement of Circle, see under Archimedes, works by
Menaechmus 174
Method, see under Archimedes, works by
method of exhaustion 154
Moerbeke 84
Mugler, C. 99
Nicomedes 23, 61
Nicoteles 61
numerical symbols 83, 84, 85
Pappus 115, 116, 121, 122, 123
parabola, see under conic sections
parallelepiped 20, 109, 110
pasch axioms 90
Plato 23
prism 100, 109, 110
proportion 34, 37, 47, 48, 52, 55, 56, 107, 110, 115, 116, 119, 142, 168, 169, 170, 171, 182, 183
Ptolemy 112, 113
Ptolemy Euergetes III 61
pyramid
Pythagoras’ theorem 43, 53, 56, 90
Al-Quhi 131, 132, 135, 136
Rashed, R. 39, 132–142, 152, 155, 178, 180
rectangle 48, 53, 58, 108, 164
reductio arguments 154
Saito, K. 89, 184
Sand-Reckoner, see under Archimedes, works by
Schramm, M. 168
Sesiano, J. 143
Sezgin, F. 130
Shakespeare 120
similar triangles 23, 42, 47, 48, 52, 55, 58, 169
sphere 11, 12, 13, 14, 30, 32, 33, 40, 45, 55, 56, 58, 114, 132, 183
Sphere and Cylinder, see under Archimedes, works by
Spiral Lines, see under Archimedes, works by
square 109, 162
symbols 83, 84
tables 149, 151
Abu Tahir 146
Theon of Alexandria 114, 115, 123
tool-box 89, 90
Toomer, G. J. 39
Al-Tusi, Sharraf Al-Din 129, 131, 178, 179, 180, 181, 185, 189, 191
Unguru, S. 1, 3, 4, 8, 27, 91, 99, 128, 190
Vahabzadeh, B. 155
Vitrac, B. 154
Winter, H. J. J. 146
Woepcke, F. 132–142
Youschkevitch, A. P. 142
Zeuthen, H. G. 2, 3, 4, 9, 86
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