Mathematics in Ancient and Medieval India c12: Index

Mathematics in Ancient and Medieval India c12

Language: English

Index

‘Abd al- ‘Aziz ibn Shams, 300 Abu’l Khairu’llah, 307 Abul Qāsim, 310 Acyuta Piṣāraṭi, 47 *Ain-i Siyaq*, 305 Akbar, 300 Algebra, 175 *Amṛtasāgari*, 34 Anand Ram, 307 *Anuyogadvārasūtra*, 7 Āpastamba, 5 *Āpastamba Śulbasūtra*, 6 Arabic Literature, 299 Arabic Numerals, 66 *Ārca Jyautiṣa*, 7 Area circle, 155 cyclic Quadrilateral, 150 surface, 155 triangle, 148 Arithmetic, 8, 52 Āryabhaṭa I, 14-16, 78-83, 195-201 Āryabhaṭa II, 24-25, 207-208, 237-38 *Āryabhaṭīya*, 14-15, 140, 144 *Āryabhaṭīya-bhāṣya*, 39-40, 273, 291 *Āryasiddhānta* (*laghu*), 14 ‘Atāu’llah Qāri, 301 *Atharva Jyautiṣa*, 7

c12.3

c12.4

Bābur, 301 Bahā’ud-Dīn Âmulī, 303, 311 Bakhshālī Mathematics, 13-14, 97 Baudhāyana, 5 *Baudhāyana-śulbasūtra*, 5, 6 Bhadrabāhu, 8 *Bhagavatī sūtra*, 7 Bhāskara I, 17-19, 204-207, 231 Bhāskara II, 26-29, 99, 209-211, 217-23, 238-41, 288, 295 *Bījagaṇita*, 26, 28, 302, *Līlāvatī*, 26-29 *Karaṇakutūhala*, 26 *Siddhāntaśiromaṇi*, 26-29 *Bhaṭadīpikā*, 39 *Bīja*, 48 *Bījagaṇita*, 28, 302 *Bījagaṇita vatamsa*, 36 *Bījaprabodha*, 34 Binomial Theoram, 189-93 *Birūnī*, 87 Brahmagupta, 19-20, 207, 217, 257 *Brāhmasphuṭasiddhānta*, 19, 145, 224 *Brahmī*, 65 Bricks, 114-119 *Buddhivilāsinī*, 34

c12.5

c12.6

Calculus, 286-298 *Candracchāyāgaṇita*, 42 *Candracchāyāgaṇita-ṭīkā*, 42 *Chiu-chang suan shu*, 82 Chord of a circle, 158 Chronological list — Kerala astronomers, 45 Circumradius of a triangle, 154 Citrabhānu, 42 Commercial problems, 89 Cosine series, 271, 276

c12.7

c12.8

Dharma Nārāyaṇa, 304 Diagonals Quadrilateral, 153 Divākara, 33 *Dṛggaṇita*, 38, 40 *Dvirajjuvidhi*, 112-13

c12.9

c12.10

Early Medieval Period, 10-29 Eighteen siddhāntas, 8-9 *Ekarajjuvidhi*, 111 *Elements* of Euclid, 171

c12.11

c12.12

Factor, 93-96 Farīd'd-dīn Ma'sud, 302 Firūz Shāh, 300 Fraction, 156-58 Fundamental operations, 76-83 square root, 78-80 cubic root, 80-83

c12.13

c12.14

Gaṇeśa, 34 Gaṅgādhara, 34 *Gaṇitakaumudī*, 36, 141 *Gaṇitāmṛtalaharī*, 34 *Gaṇitāmṛta sāgarī*, 34 *Gaṇitāmṛtakūpīkā*, 34 *Gaṇitanuyoga*, 8 *Gaṇitasārasaṃgraha*, 23 *Gaṇita yuktibhāṣā*, 23 Geneology of astronomers, 33, 48 Geometrical propositions, 120-123 Geometrical figures, 146 Geometrical progressions, 186-87 Geometry, 103 *Goladīpikā*, 40 *Golasāra*, 43 *Govindakṛti*, 21 Govindasvāmin 21, 247, 251 *bhāṣya*, 21 *Grahagolatattva*, 50 *Grahasāraṇī*, 50

c12.15

c12.16

Ḥāji Kha'ullah, 303 Halāyudha, 189 Hindu Works, 8-10 Hiraṇyakeśī, 5

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c12.18

Inâmud-dīn Ḥusain, 306 Inderman, 307 Indeterminate equation first degree, 193-216 second degree 216-224 Indices, 54 Indo-Persian Arabic literature, 299

c12.19

Infinitesimal calculus, 286-298 Inscriptions Cambodia, 70 Champa, 70 Java, 70 Gurjara, 72 Khmere, 72 Malay, 72 Dinaya, 72 Po-nagar, 72 Bakul, 73 Instruments, 105-113 Integral Calculus, 294-298 Inverse rule, 87

c12.20

c12.21

Jaina School, 97 Jaina works, 7-8 Jayasimha, 305 Jñānarāja, 42 Jyautiṣa, 4 Jyeṣṭhadeva, 44-46 Jyotiṣa, 8 Jyotpatti, 50

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c12.23

*Kalpalatāvatāra*, 34 Kamalākara, 44, 241 *Karaṇāmṛta*, 42 *Karaṇapaddhati*, 46-47, 211-14, 241, 264-65, 273, 275, *Karaṇottama*, 47 *Kairāsyudāharaṇa*, 50 Karim Bakhsh, 308 *Karimadipikā*, 39 *Karmapradīpaka*, 40 Kaṭapayādi system, 35-36 Kātyāyana, 5 *Khaṇḍa*, 22 *Khaṇḍakhādyaka*, 19-20 *Khaṇḍitabījagaṇita*, 48 Kharoṣṭhī, 65 Khawāja Bahādur Husain Khān, 304 *Khulāṣatrul Hiṣāb*, 303 Khwajah Muhammad, 308 *Kriyākramakarī*, 42 Kṛṣṇa, 34 *Bījapallava* 34 *Kṣetrasamāsu*, 7 Kusumpura school, 8

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c12.25

*Laghubhāskarīya*, 18 *Laghuvivṛti*, 43 Lalla, 20-21, 236 Late Medieval Period, 29-35 *Līlāvatī*, 26, 28, 50, 301, 304 Commentaries, 29-32 Logarithm, 55-56 Lutfu'llah Muhandis, 303

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c12.27

M. Husain Isfahani Landani, 309 Mādhava, 37-38, 247, 253, 271 *Mahābhāskarīya*, 18 *Mahābhāskarīya bhāṣya*, 21 *Mahāsiddhānta*, 24-25, 27 Mahāvedi, 114 Mahāvīra, 23-24, 183, 185, 189 Maitrāyana, 5 Mānava, 5 *Manorañjanā*, 35 *Māsaka*, 5

c12.28

*Meruprastāra*, 190-91 Method of Interpolation, 257 Mīrzā Khairullāh Muhandis', 306 *Mitabhāṣinī*, 34 Muhammad Barkat, 307 Muḥmmad Zaman Fayyad, 306 Mūlachanda, 307 Mullâchând, 301 Munīśvara, 48, 49 Muṣliḥu'd-dīn al-lārī al Anṣārī, 301

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c12.30

Nand Rām, 304 Nârâyaṇa, 48 Nārāyaṇa Paṇḍita, 36-37, 101-2 Nawab Shamsu'ul Umara, 308 Newton-Stirling formula, 258 Nīlakaṇṭha, 40-42 *Niṣṛtārthaduti*, 44 Number, 23, 54, 83 Numerals, 58-66 Arabic, 66, 75-76 Chinese, 74 Egyptians, 61-63 Greeks, 63-64 Romans, 64 Indians, 64

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c12.32

Operations, 176-77

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c12.34

*Paitāmahasiddhānta*, 9 *Pañcasiddhāntikā*, 17 Paṇḍita Jagannātha, 50 Parameśvara, 38-40 *Parameśvarī*, 39 Pascal Triangle, 189-193 *Pāṭīgaṇita* of Lalla, 21 *Pāṭīgaṇita* of Śrīdhara, 23-24 *Paṭīsāra*, 41, 141 *Pauliśa siddhānta*, 9 Period of revival, 10 Permutation and Combination, 187-89 Persian literature, 299 Pie (π), 260-63 Pie series, 265 Plane figures, 164 Post vedic period, 7-10 *Praci*, 108 Progressive series, 180 Pṛthudaka Svāmī, 21-2? Commentary, 22 Ptolemy's sine table, 255-57 Pythagoras Theorem, 123, 165

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c12.36

Quadratic Equations, 179 Quadrilateral, 166

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c12.38

Rāma, 33 Rāmakṛṣṇa, 34 Rāmkṛṣṇadeva, 35 Raṅganātha, 34 Raushan Ali, 308 *Rekhāgaṇita*, 50, 171-73 Right angled triangle, 165 *Romaka Siddhānta*, 9 Rule of three, five etc., 87 Inverse rule, 87

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c12.40

Sadratnamālā, 51 Śaṃkara Vāriyar, 43 Śaṃkaravarman, 51 Saṃkhyāna, 8 *Samrāṭ Siddhānta*, 51 Sayyid Nuru'l Asfiyah, 309 Scalene triangle, 120, 161 Schools Aryabhaṭa I, 12 Kerala, 35 Mysore, 12 Ujjain, 12 Sh. Aḥmad b. M. Maghribi, 309 Sh. Muḥammad. 303 Shāhjahān, 302 *Siddhāntasārvabhauma*, 44, 51 *Siddhāntaśiromaṇi*, 26 *Siddhāntasundara*, 42 *Siddhāntasundarabīja*, 42 *Siddhāntatattvaviveka*, 49, 50 *Siddhāntatilaka* of Lalla, 21 Signs (mathematical), 83-85 Similar triangles, 147 Sine table, 246-53 Sine series, 271, 276 Skandasena, 21-22 Solid geometry, 169 *Somasiddhānta*, 9 Spherical trigonometry 259-60 Śrīdhara, 23-24 Śrīpati, 25 *Gaṇitatilaka*, 25 *Bījagaṇita*, 25 *Siddhāntaśekhara*, 25 Śulbakāra, 5 *Śulbasūtra*, 5 Śulbasūtras and later mathematics, 135-139 *Śunyabindu*, 71 Surd numbers, 96-102 *dvikaraṇī*, 96 *trikaraṇī*, 96 Sūryadāsa, 34 *Sūryaprajñapati*, 7 *Sūryaprakāśa* of Sūryadāsa, 34 *Sūryasiddhānta*, 9-10, 50, 247, 253-54 Symbols, 176

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c12.42

Taḥrīr-u-uqlidas, 50 Tan series, 275, 283 *Tantrasaṃgraha*, 40, 41, 271, 274 Taqrību't Taḥrīr, 307 *Tatstha*, 22 *Tattvārthādhigama sūtra*, 7 *Ta-yenli*, 215 Technical terms, 133, 142-46 Theon of Alexandria, 82 Theorem Baudhāyana, 123 Pythagoras, 125 Trigonometrical formulae, 234-42 functions, 230 series, 263-65 Trigonometry, 229

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*Ujalatān Rub*, 305 Ulugbeg, 306

c12.45

Umāsvātī, 7, 8 Units, 113-14 *Uparāgakriyākrama*, 47

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*Vādhula*, 5 Value pie (π), 260-63 root (√2), 5, 127 Vārāha, 5 Varāhamihira, 16-17, 231, 234-35 *Vārasaṃkalita*, 36 *Vasiṣṭhasiddhānta*, 9 *Vedāṅga Jyautiṣa*, 6-7 Vedic altars, 104 Vedic period sorces, 4-7 sūtra period, 4 *Veṇvāroha*, 37 *Vivaraṇa*, 39 Volume, 159 *Vyākhyā*, 39