History of Hindu Mathematics: A Source Book v2.c18: Index

History of Hindu Mathematics: A Source Book v2.c18

Language: English

Index

v2.c18.7

Algebra 1;—defined 1; Distinction from arithmetic 2; General features 1; Importance of—4; Name for—1; Origin of—6; Scope of—5

v2.c18.13

Âryabhaṭa I 9, 17, 38, 40, 49, 51, 61, 62, 63, 82, 83, 87, 88, 91, 93, 99, 100, 131, 132, 134;—’s problem 95, 101

v2.c18.14

Âryabhaṭa II 67, 87, 88, 92, 104, 106, 109, 135, 136

v2.c18.21

Bakhshâlî Manuscript 13;—characters 15;—work 297, 300

v2.c18.22

Bakhshâlî treatise 9, 12, 14, 15, 16, 30, 36, 37, 42, 43, 47, 48, 49, 60, 258

v2.c18.25

Bhâskara I 87, 91, 92, 93, 99, 100, 110, 117, 118, 131, 133, 238, 284;—I’s Rules 99, 118; Mahâbhâskarîya of—89

Bhâskara II 1, 2, 3, 4, 5, 9, 10, 12, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 34, 36, 38, 39, 41, 47, 57, 58, 59, 65, 69, 70, 76, 83, 88, 92, 111, 112, 113, 116, 117, 120, 121, 125, 126, 127, 129, 133, 136, 141, 142, 143, 144, 147, 150, 151, 152, 153, 155, 161, 162, 163, 164, 166, 171, 174, 176, 177, 178, 179, 181, 183, 184, 186, 189, 190, 192, 193, 194, 196, 198, 199, 201, 206, 208, 211, 214, 215, 217, 237, 238, 240, 245, 246, 247, 249, 250, 253, 254, 255, 256, 261, 265, 267, 268, 269, 270, 271, 274, 275, 276, 277, 278, 280, 281, 282, 283, 285, 286, 287, 289, 290, 291, 292, 294, 296, 302, 304; Bîjagaṇita of—19, 20, 31, 34, 42, 46, 65, 142, 181, 250

v2.c18.27

Bhâskara’s Lemma 162, 163

v2.c18.28

Bhâskara’s Rule—57, 68, 110, 119, 121, 128, 162, 302

v2.c18.29

Bhâvanâ 148; antara—148;

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atulya—148; samâsa—148; tulya—148 Bhâvita 26, 35 Bîja 1, 4, 5 Bîjagaṇita 1, 2, 3, 65, 88, 90, 139 Bińdu 14 Brahmagupta 1, 4, 5, 9, 10, 11, 17, 20, 21, 22, 23, 25, 26, 31, 33, 35, 40, 41, 43, 44, 54, 55, 57, 62, 63, 64, 67, 70, 74, 75, 82, 83, 85, 87, 89, 91, 92, 117, 121, 125, 127, 132, 143, 145, 147, 157, 158, 160, 161, 173, 174, 175, 176, 181, 206, 207, 210, 211, 222, 223, 225, 227, 233, 234, 235, 236, 239, 240, 251, 252, 259, 260, 264, 284, 300, 302;—'s Corollary 147, 149, 152;—'s Lemmas 146, 147, 148, 149;—'s Proof 148 Brâhmaṇa 6; Śatapatha—7, 8 Brâhma-sphuṭa-siddhânta 4, 32 Brâhmî characters 14, 15 Brouncker 155

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v2.c18.32

Cantor 50 Cakravâla 162 Chasles 239 Clark, W. E. 93 Clere, E. 271 Coefficient 9 Colebrooke 33, 65, 141, 206, 255 Conjunct Pulveriser 135; generalised—137; alternative method 139 Constant Pulveriser 117 Cube-pulveriser 254 Cyclic method 161

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v2.c18.34

Datta, B. 1, 6, 9, 11, 14, 15, 30, 35, 36, 59, 60, 93, 131, 204, 205, 206, 207, 208, 209, 212, 221, 222, 223 Desboves 199 Devarâja 88 Dickson, L. E. 133, 199, 225, 227, 240, 270, 271 Diophantus 14, 209 Division 23, 27 Double equations;—in several unknowns 283;—of higher degrees 278;—of the first degree 258;—of the second degree 266, first type 266, second type 276 Dṛśya 12 Drummond 273 Dvicchedâgram 131 Dvidhâ 146 Dvivedi, Sudhakara 65

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Elimination of the middle term 69 Epanthema 50 Evolution and involution 23 Equations 11, 28; Classification of—35; common forms of—81; forming—28; higher—77; Indeterminate—of the first degree 87, *see* pulveriser; Indeterminate—of the second degree, *see* Square-nature; linear—44; linear—in one unknown 36; linear—with two unknowns 43; linear—with several unknowns 47, 125;—of higher degrees 76; plan of writing—30; preparation of —33; Quadratic—59; simultaneous quadratic—81 Euler 148, 166, 186, 262

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v2.c18.38

Fermat 150, 166 Fibonacci, Leonardo 214 Frénicle 166

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v2.c18.40

Gaccha 16 Gaṇeśa 69, 88, 90, 117, 208, 212, 240 Gaṅgâdhara 43 Ganguly, Sarda Kanta 51, 88, 93, 104, 139, 140 Gaṇita, 1, 3, 16; kuṭṭaka—1; avyakta—1; vyakta—1. Gaṇita-sâra-saṁgraha 38, 66, 123, 300 General indeterminate equations of the second degree: single equations 181 General problem of remainders 131 General solution of Square-nature 149 Genocchi 270 Ghana 10, 15, 35;—varga 10, 15;—varga-varga 10 Ghâta 10 Gulikâ 10 Gulikântara 40 Guṇadhana 78 Guṇaka 9 Guṇakâra 9 Guṇa-karma 3

v2.c18.41

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Harîtaka 18 Heath 50 Hewlett, John 186 Hrasva mûla 144 Hoernle 14, 15

v2.c18.43

v2.c18.44

Indeterminate equations 87, general survey 87, its importance 88, of the first degree 87, three varieties of problems 89, preliminary operations 91; simultaneous—of the first degree 127, Śrîpati's solution 127; single—of higher degrees 245, Bhâskara's method 246, Mahâvîra's rule 245, Nârâyaṇa's rule 248 Ibn-al-Haitam 133 Isosceles trapeziums 228; rational—228; pairs of—231 Isosceles triangles,—with a given altitude 223; with integral sides 222; pairs of rational—224 Iṣṭaguṇaghna 53 Iṣṭa-karma 39

v2.c18.45

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Jha, Murlidhara 19, 20 Jñânarâja 28, 65, 69, 93, 116, 128, 144, 148, 151, 154, 186, 189, 193 Jyeṣṭha pada 144

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v2.c18.48

Kâlaka 17 Kamalâkara 93, 116, 141, 143, 144, 148, 151, 154, 193, 194, 195, 196, 197, 198 Kâmika 9, 38 Kaniṣṭha pada 144 Karavindasvâmî 207 Kâtyâyana 59, 204, 206 Kaye 14, 48, 49, 50, 61, 93; 297 Koṇaśaṅku 64

v2.c18.49

Kṛṣṇa 27, 36, 65, 69, 90, 111, 118, 142, 148, 154, 163, 177 Kṛti-prakṛti 141 Kṣaya 12 Kṣepaka 144 Kṣetragata 3 Kummer 239 Kuṭṭaka 1, 89, 91; citra—miśra 52; dṛḍha—117;—gaṇita 1; origin of the name 90;—Śiromaṇi 88; sthira—117 Kuṭṭîkâra 89

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Laghubhâskarîya 284 Lagrange 148, 186 Laws of signs 20 Lemma 150; Brahmagupta's 146; Bhâskara's 162 Lîlâvatî 3, 88, 90, 117, 124, 139 Linear equations 36, 44; early solutions 36; in more than two unknowns 125;—in one unknown 36; rule of false position 37; solution of—40;—with several unknowns 47;—with two unknowns 43 Lohita 18

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Madhura 19 Madhyamâharaṇa 3, 35, 36, 69, 76 Maha-Bhâskarîya 89 Mahâvedi 6 Mahâvîra 20, 22, 23, 24, 25, 38, 44, 49, 50, 51, 52, 53, 56, 66, 67, 73, 74, 77, 78, 79, 82, 83, 84, 85, 87, 89, 91, 137, 138, 207, 208, 209, 210, 213, 214, 215, 216, 217, 218, 219 221, 222, 223, 224, 226, 227, 229, 231, 234, 236, 238, 242, 243, 244, 245, 301;—'s definitions 208;—'s rules 56, 86, 103, 300; rule of—124. Matsunago 199 Mazumdar, N. K. 93 Mehta, D. M. 88 Mikami, Y. 200 Mûla 15; varga—10; dvitîya-varga—11; n^th varga—11; prathama-varga—11; tritîya-varga—ghana 11. Multiple equations 283 Multiplication 22, 26

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Nârâyaṇa 5, 11, 14, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 41, 43, 50, 52, 53, 82, 83, 84, 93, 116, 119, 122, 143, 144, 148, 150, 151, 154, 164, 165, 168, 174, 176, 177, 178, 179, 181, 186, 202, 245, 248, 249, 260, 264, 266, 271, 274, 279, 284, 286;—'s rule 164, 248 Nîlaka 17 Nyâsa 30, 33 Nyûna 14

v2.c18.56

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Operations, fundamental—25; number of—25;—with an optional number 39 Origin of minus sign 14

v2.c18.58

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Padmanâbha 12, 70 Pairs of rectangles 219 Pakṣa 11 Palabhâ 64

v2.c18.60

Pañca gata 10 Pellian equation 5 Pîtaka 18 Power 10 Prâdeśa 7 Prakṛti 9 Principle of Composition 145, 147, 148, 150 Pṛthûdakasvâmî 1, 9, 11, 18, 20, 24, 29, 31, 32, 33, 34, 35, 40, 41, 55, 75, 102, 117, 121, 132, 134, 135, 143, 144, 145, 224, 227, 229, 234, 238, 251, 252, 297, 298, 300 Puruṣa 7

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Quadratic, two roots of 70, known to Mahâvîra 73. Quadrilaterals, rational—228; inscribed—having a given area 242

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Rahn, J. H. 225 Râmakṛṣṇa 65 Rangacarya 78, 104 Ranganâth 90, 212 Râśigata 4 Rational, inscribed quadrilaterals 235;—isosceles trapeziums 228;—quadrilaterals 228;—right triangles having a given hypotenuse 213;—right triangles having a given side 209;—scalene triangles 225;—triangles 204, early solutions 204, integral solutions 206, juxtaposit.on of—223, later rational solutions 207 Rodet 51, 93 Rule,—of concurrence 43;—of false position 37, 38; disappearance from later algebra 38 Rûpa 9, 12, 141

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Ṣaḍgata 10 Sadṛśi-karaṇa 11 Sama 11 Sama-karaṇa 11 Samaśodhana 33, 34 Samatva 11 Samîkaraṇa 11, 28; aneka-varṇa—35; avyaktavarga—35; asakṛt—181; ekavarṇa—35; sakṛt—181 Samślṣṭakuṭṭaka 136 Sâmya 11 Saṅkramaṇa 43, 44, 82, 84 Satpuruṣa 4 Schooten, Fras van 225 Sen Gupta, P. C. 93 Siddhânta-śiromaṇi 90 Śiva 5 Singh, A. N. 270, 271 Smith 14, 32, 38, 150 Śodhana 33 Special rules 129 Squaring 27 Square pulveriser 250 Square-root 28 Śrîdhara 12, 16, 38, 65, 67, 238;—'s rule 65 Śrîdhara Mahâpâtra 140 Śrîpati 5, 11, 18, 21, 22, 23, 24, 34, 40, 44, 64, 92, 137, 143, 145, 150, 155, 157, 207, 237, 302;—'s rule 67, 110, 127, 302 Sthânâṅga-sûtra 9, 35, 36 Subtraction 21; addition and—25 Śulba 6, 7, 36, 59, 204 Sûryadâsa 65, 69, 90, 162, 177, 211, 212, 215

v2.c18.67

Sûryadeva Yajvâ 91, 133 Sûryasiddhânta 64 Symbols 12;—for powers and roots 15;—for unknowns 16;—of operation 12

v2.c18.68

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Tattvârthâdhigama-sûtra 60 Technical terms 9, 143 Terminology 89 Thibaut, G. 11, 14 Thymaridas 50, 51 Trapeziums 228; rational—228; rational—with three equal sides 233 Triangles, having a given area 227;—and quadrilaterals having a given area 244 Triśatikâ 16, 65, 238