[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [Mathematics in Ancient and Medieval India](https://indike.org/pramana/ins.science.bag-1979) › c12 # Mathematics in Ancient and Medieval India c12: Index Mathematics in Ancient and Medieval India c12 - **Language:** English ### Index ### [c12.1](https://indike.org/pramana/ins.science.bag-1979.c12.1) A ### [c12.2](https://indike.org/pramana/ins.science.bag-1979.c12.2) ‘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](https://indike.org/pramana/ins.science.bag-1979.c12.3) B ### [c12.4](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.c12.5) C ### [c12.6](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.c12.7) D ### [c12.8](https://indike.org/pramana/ins.science.bag-1979.c12.8) Dharma Nārāyaṇa, 304 Diagonals Quadrilateral, 153 Divākara, 33 \*Dṛggaṇita\*, 38, 40 \*Dvirajjuvidhi\*, 112-13 ### [c12.9](https://indike.org/pramana/ins.science.bag-1979.c12.9) E ### [c12.10](https://indike.org/pramana/ins.science.bag-1979.c12.10) Early Medieval Period, 10-29 Eighteen siddhāntas, 8-9 \*Ekarajjuvidhi\*, 111 \*Elements\* of Euclid, 171 ### [c12.11](https://indike.org/pramana/ins.science.bag-1979.c12.11) F ### [c12.12](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.c12.13) G ### [c12.14](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.c12.15) H ### [c12.16](https://indike.org/pramana/ins.science.bag-1979.c12.16) Ḥāji Kha'ullah, 303 Halāyudha, 189 Hindu Works, 8-10 Hiraṇyakeśī, 5 ### [c12.17](https://indike.org/pramana/ins.science.bag-1979.c12.17) I ### [c12.18](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.c12.20) J ### [c12.21](https://indike.org/pramana/ins.science.bag-1979.c12.21) Jaina School, 97 Jaina works, 7-8 Jayasimha, 305 Jñānarāja, 42 Jyautiṣa, 4 Jyeṣṭhadeva, 44-46 Jyotiṣa, 8 Jyotpatti, 50 ### [c12.22](https://indike.org/pramana/ins.science.bag-1979.c12.22) K ### [c12.23](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.24](https://indike.org/pramana/ins.science.bag-1979.c12.24) L ### [c12.25](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.26](https://indike.org/pramana/ins.science.bag-1979.c12.26) M ### [c12.27](https://indike.org/pramana/ins.science.bag-1979.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](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.29](https://indike.org/pramana/ins.science.bag-1979.c12.29) N ### [c12.30](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.31](https://indike.org/pramana/ins.science.bag-1979.c12.31) O ### [c12.32](https://indike.org/pramana/ins.science.bag-1979.c12.32) Operations, 176-77 ### [c12.33](https://indike.org/pramana/ins.science.bag-1979.c12.33) P ### [c12.34](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.35](https://indike.org/pramana/ins.science.bag-1979.c12.35) Q ### [c12.36](https://indike.org/pramana/ins.science.bag-1979.c12.36) Quadratic Equations, 179 Quadrilateral, 166 ### [c12.37](https://indike.org/pramana/ins.science.bag-1979.c12.37) R ### [c12.38](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.39](https://indike.org/pramana/ins.science.bag-1979.c12.39) S ### [c12.40](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.41](https://indike.org/pramana/ins.science.bag-1979.c12.41) T ### [c12.42](https://indike.org/pramana/ins.science.bag-1979.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 ### [c12.43](https://indike.org/pramana/ins.science.bag-1979.c12.43) U ### [c12.44](https://indike.org/pramana/ins.science.bag-1979.c12.44) \*Ujalatān Rub\*, 305 Ulugbeg, 306 ### [c12.45](https://indike.org/pramana/ins.science.bag-1979.c12.45) Umāsvātī, 7, 8 Units, 113-14 \*Uparāgakriyākrama\*, 47 ### [c12.46](https://indike.org/pramana/ins.science.bag-1979.c12.46) V ### [c12.47](https://indike.org/pramana/ins.science.bag-1979.c12.47) \*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 ### [c12.48](https://indike.org/pramana/ins.science.bag-1979.c12.48) W ### [c12.49](https://indike.org/pramana/ins.science.bag-1979.c12.49) Word numbers, 98 ### [c12.50](https://indike.org/pramana/ins.science.bag-1979.c12.50) Y ### [c12.51](https://indike.org/pramana/ins.science.bag-1979.c12.51) \*Yājuṣa Jyautiṣa\*, 7 \*Yuktibhāṣā\*, 44-45, 274, 219, 296-98 ### [c12.52](https://indike.org/pramana/ins.science.bag-1979.c12.52) Z ### [c12.53](https://indike.org/pramana/ins.science.bag-1979.c12.53) Zero symbol, 67 Zīj-ī Muhammad Shāhī, 30., 306, 307 --- Source: [https://indike.org/pramana/ins.science.bag-1979.c12](https://indike.org/pramana/ins.science.bag-1979.c12) · Pramāṇa