History of Hindu Mathematics: A Source Book v1.c10: Index

History of Hindu Mathematics: A Source Book v1.c10

Language: English

Index

Ababa, 12 Abbuda, 12 Abenragel, 99 Abhyâsa, 130, 134 Abja, 13 Abû Sahl Ibn Tamim, 98 Addition, 130; direct process, 131; inverse process, 131; terminology, 130; the operation, 130 Aghana, 175, 177, 178, 179, 180 Ahaha, 12 Akkhobhinî, 12 Akṣarapallî, 33, 34, 72, 74 Akṣiti, 10 Al-Amûnî Saraf-Eddin, 99 Al-Battani, 83 Al-Bîrûnî, 39, 55, 98, 99, 100, 128, 210 Alexander de Villa Die, 95, 103 Al-Fazârî, 89 Al-Haṣṣâr, 143 Al-hindî, 143 Alibin Abil-Regal Abul-Hasan, 99 Alkalasâdî, 99, 143 Al-Kharki, 50 Al-Khowârîzmî, 90, 143, 153, 154 Al-Masûdî, 97, 100 Al Nadîm, 98 Al Nasavî, 90, 143, 153, 154, 174 Alphabetic Notations, 63; akṣarapallî, 72; explanation, 67; kaṭapayâdi system, 69; other letter systems, 75; system of Âryabhaṭa I, 64 Al-Qass, 90 Al-Sijzî, 90 Aṁśa, 185, 186, 188 Ananta, 10 Aṅkapallî, 33 Anta, 9 Antya, 10, 13, 163 Anuyogadvâra-sûtra, 11, 12, 83, 169 Apavartana, 189 Arbuda, 9, 13 Archimedes, 11 Arithmetic, 123; exposition and teaching, 126; fundamental operations, 128; general survey, 123; sources, 125; terminology and scope, 123 Arjuna, 10 Arkhand, 97 Arthaśâstra of Kauṭilya, 6, 7, 21, 187, 218 Âryabhaṭa I, 12, 69, 71, 87, 125, 128, 134, 135, 137, 150, 155, 156, 162, 163, 173, 197, 198, 204, 211, 219, 232, 234 Âryabhaṭa II, 71, 72, 130, 132, 136, 152, 172, 177, 184, 204, 205, 212, 240 Âryabhaṭîya, 65, 67, 69, 71, 80, 82, 86, 125, 126, 130, 134, 150, 170, 171, 175, 197, 204, 211, 217, 219, 239 Asaṅkhyeya, 12 Aśvaghoṣa, 2

v1.c10.3

Atata, 12 Athanasius Gamenale, 96 Atharvaveda, 18, 57 Avarga, 65, 66, 67, 69 Avesta, 101 Avicenna, 184 Ayuta, 9, 10, 12, 13

v1.c10.4

v1.c10.5

Bahula, 10 Bakhshâlî Manuscript, 47, 61, 65, 77, 81, 86, 134, 137, 151, 186, 192, 204, 239 Bapudeva Sastri, 245 Barnet, L.D., 6, 72 Barter and exchange, 226 Barth, 65 Bayley, 29, 30, 124 Behâ Eddin, 100, 149, 184 Bhâga, 185, 186, 188, 190 Bhâga-bhâga, 191 Bhâgahâra, 124, 150, 198 Bhâgajâti, 196 Bhâgamâtâ, 190, 192, 193, 195 Bhâgâpavâha, 191, 195 Bhagavatî-sûtra, 4, 7 Bhâjaka, 150 Bhâjana, 150 Bhâjya, 150, 177, 178 Bhâṇḍa-pratibhâṇḍa, 124, 226 Bhandarkar, 17, 19 Bhâsa, 2 Bhâskara I, 66, 67, 80, 82, 86, 87, 125, 130, 134, 170, 197, 204, 211, 239 Bhâskara II, 10, 13, 125, 128, 129, 131, 132, 136, 137, 146, 149, 152, 157, 159, 161, 162, 164, 167, 172, 184, 188, 195, 205, 208, 209, 212, 230, 234, 235, 241, 242, 243, 245, 246 Bhaṭṭotpala, 55 Bhinna, 188 Bihârî, 81 Bîjadatta, 184 Bîjagaṇita, 8, 235, 239, 241, 242, 245 Bindu, 12, 81 Bodhisattva, 10 Boethius, geometry, 93; question, 92 Bower manuscript, 74 Brahmagupta, 8, 87, 89, 124, 125, 128, 134, 135, 137, 147, 149, 150, 156, 159, 160, 163, 169, 170, 176, 188, 189, 196, 198, 199, 205, 211, 212, 217, 220, 222, 232, 239, 241, 242, 243, 245 Brâhmaṇa, Aitereya, 58; Pañcaviṁśa, 10; Śatapatha, 57, 186; Taittirîya, 57 Brâhma-sphuṭa-siddhânta, 8, 59, 89, 156, 228, 241 Brâhmî numerals, 25; early occurrence and forms, 25; period of invention, 37; relation with letter forms, 33; résumé, 37; theories about their origin, 28 Bṛhat-kṣetra-samâsa, 79 Bṛhat-saṁhitâ, 55, 59 Bṛnda, 163 Brockkhaus, 65 Buddha, 2, 36, 187 Bühler, 16, 17, 19, 21, 23, 24, 30, 33, 35, 37, 45, 47, 49, 60, 74 Burnell, 30, 75

v1.c10.6

v1.c10.7

Caire, 97 Cajori, 88 Capella, 92 Caraka, 2

v1.c10.8

Carra de Vaux, 97, 100, 101, 102 Cataneo, 175 Catur, 13 Chandaḥ-sûtra, 58, 75, 76, 77, 86 Chatterjee, C.D., 53 Châyâ, 124 Checks on operations, 180 Chedana, 150 Chid, 212 Chuquet, 175 Citi, 124 Clark, W.E., 64, 65, 66, 67, 170, 171, 175, 197 Coedis, G., 43 Colebrooke, 134, 135, 145, 147, 156, 164, 177, 211, 233, 245 Commercial Problems, 218; barter and exchange, 226; interest in ancient India, 218; interest in Hindu gaṇita, 218; other problems, 220; other types of, 227; problem involving a quadratic equation, 219 Cowell, E.B., and Neil, R.A., 7 Cube, 162; minor methods of, 166; terminology, 162; the operation, 163 Cube-root, 175; terminology, 175; the operation, 175 Cullaniddesa, 4 Cunningham, 28, 29

v1.c10.9

v1.c10.10

Dantidurga, 40 Darius, 23 Darius Hystaspes, 101 Daśa, 9, 12, 13 Daśagîtikâ, 64, 65, 66, 71 Daśaguṇâḥ saṁjñâ, 13 Daśaguṇottara saṁjñâ, 10 Daśa-koṭi, 13 Daśa-lakṣa, 13 Daśa-sahasra, 13 Datta, B., 7, 61, 65, 81, 84, 85, 123, 155, 170, 184, 185, 218, 243 Deccke, W., 16 Decimal place-value system, 38; epigraphic instances, 40; forms, 39; important features, 38; inventor unknown, 49; place of invention of the new system, 48; their supposed unreliability, 44; time of invention, 49 Delambre, 184 Devendravarmaṇa, 40 Dharma-sûtra, 17 Dhûlî, 8; karma, 8, 123, 129 Digges, 210 Dîgha-Nikâya, 7 Division, 150; terminology, 150; the method of long, 151; the operation, 150 Divyâvadâna, 7 Djâhiz, 97 Dramma, 227 Dvivedi, S., 59, 129, 131, 156, 168, 178, 183, 241

v1.c10.11

v1.c10.12

Ekâdaśa-râśika, 124 Ekânna-catvâriṁśat, 14 Ekânna-viṁśati, 14 Ekîkaraṇa, 130 Ekona, 14 El-jowharee, 100 Elliot, 100 End, 101, see hend Eneström, G., 149 Euting, J., 23

v1.c10.13

v1.c10.14

Fihrist, 98 Firdausî, 100

v1.c10.15

Firouzâbâdi, 100, 101 Fleet, 52, 60, 65, 67, 124 Flügel, G., 98 Fractions, 185; addition and subtraction, 196; cube and cube-root, 199; division, 197; early use, 185; lowest common multiple, 195; multiplication, 196; reduction in combinations, 190; reduction to common denominator, 189; reduction to lowest terms, 189; square and square-root, 199; terminology, 188; the eight operations, 195; unit fractions, 199; writing of, 188 Frisius, Gemma, 175

v1.c10.16

v1.c10.17

Gaṇaka, 127 Gaṇeśa, 136, 145, 146, 211, 230, 244 Gaṅgâdhara, 131, 133, 147 Ganguli, 65 Gaṇita, 4, 5, 6, 7, 8, 83, 128, 130; avyakta, 123; vyakta, 123 Gaṇita-kaumudî, 125 Gaṇita-mañjarî, 136, 144, 145 Gaṇitânuyoga, 4 Gaṇita-sâra-saṁgraha, 80, 125, 219, 223, 227, 230, 240 Gaṇita-tilaka, 125 Gerbert, 93, 94 Ghana, 8, 124, 162, 177, 178, 179; pada, 175 Ginsburg, J., 95 Gomûtrikâ, 135, 147, 148 Gotama-sûtra, 218 Guṇaka, 135 Guṇakâra, 135, 198 Guṇana, 124, 134; iṣṭa, 136, 149; phala, 135; tastha, 146; tiryaka, 145; Guṇya, 135

v1.c10.18

v1.c10.19

Halifax, John of, 95 Hall, F., 81 Halle, 104 Halsted, G.B., 38, 39 Hanana, 134, 139 Handasa, 102 Handasi, 101, 102 Hara, 150 Haraṇa, 150 Hârya, 150 Heath, 50 Hemcandra, 12 Hend, 101 Hetuhila, 11 Hetvindriya, 11 Hind, 100, 101 Hindasa, 101, 102 Hindasî, 101 Hindi, 100, 101, 102 Hindisah, 98, 101 Hindu Numerals in Arabia, 88; Arabic reference, 96; definite evidence, 93; European references, 102; in Europe, 92; miscellaneous references, 95; Syrian reference, 95; the terms hindasa, etc., 101 Hisâb-al-ghobâr, 98, 124 Hunter, G.R., 19, 29

v1.c10.20

v1.c10.21

Ibn Albanna, 99 Ibn Hawkal, 100 Ibn Seedeh, 100 Ibn Târik, 89 Ibn Wahshiya, 96 Icchâ, 198, 204-208; pakṣa, 211, 213 Idânî, 186 Ilm-hisâb-altakhta, 123

v1.c10.22

Indraji, Bhagvanlal, 6, 26, 35-37 Infinity, 243 Inscription, Ahar Stone, 42, 52; at Po Nagar, 44; Belhari, 40; Buchkalâ—of Nâgbhaṭa, 41; Deogarh Jaina—of Bhojadeva, 42; Dholpur, 60; from Dhauli, 33; from Girnâr, 33; from Kanheri, 41, 42; Ghatiyala—of Kakkuka, 41; Gurjara—45; Gwalior—of Allah, 42; Gwalior—of the reign of Bhojadeva, 42, 82; Hâthîgumphâ, 6; Hindu, 60; Junâr, 47; Kanheri, 40; Kharoṣṭhî, 21; Kṣatrapa, 34; Nânâghât, 25, 26; of Aśoka, 16, 20, 21, 23, 28, 34; of Bauka, 41; of the Kuṣânas, 22, 34; of Rudradaman, 47; of the Parthians, 21; of the Śakas, 21; of Sâmanta Devadatta, 41; of Sambor, 44; of Śrîvijaya, 44; of Yaśovarmaṇa, 43; Pehava, 42; Sanskrit and old Canarese, 43; Siyadoni stone, 43; stone, 45; word numerals in, 59 Isidorus of Seville, 102 Iṣṭa, 135 Iṣṭakarma, 230 Istakri, 100 Itarhi, 186

v1.c10.23

v1.c10.24

Jacobi, H., 7 Jadhṛ, 170 Jaivardhaṇa II, 40, 82 Jaladhi, 13 Jarez de le Frontera, 94 Jâti, 188 Jinabhadra Gaṇi, 61, 79 John, 96 Jones, Sir W., 16 Jyotiṣa, 8

v1.c10.25

v1.c10.26

Kâccâyana's Pali Grammar, 11 Kaiyyaṭa, 63 Kâkiṇî, 206 Kalâ, 185, 188 Kalâsavarṇana, 8 Kalhaṇa, 50 Kâlidâsa, 2 Kalpasûtra, 6, 7 Kâṇḍa, 18 Kaṅkara, 10 Kapadia, H.R., 80, 151 Kapâṭasandhi, 134, 135, 136, 137, 143, 144, 145 Karahu, 11 Karaṇa, 50 Karaṇa-kutûhala, 184 Karaṇî, 170 Karpinski, 97; see Smith Karṣa, 206 Kaṭapayâdi system, 69; first variant, 70; second variant, 71; third variant, 72; fourth variant, 72 Kathâna, 12 Kâtyâyana, 58, 63 Kauṭilya, 2; Arthaśâstra of, see Arthaśâstra Kâyastha, 50 Kaye, G. R., 44, 45, 46, 47, 48, 59, 60, 65, 85, 101, 102, 156, 168, 170, 171, 175, 190 Keith, see Macdonell Kerala system, 72 Kern, 65 Kha-cheda, 243; -hara, 242, 243, 244; -guṇa, 242 Khalif al-Mansûr, 89 Khalif Walid, edict of, 89 Khaṇḍa, 135

v1.c10.27

Khaṇḍa-khâdyaka, 89 Khâravela, 6 Kharoṣṭhî numerals, 21; early occurrence, 21; forms and origin, 22; lipi, 21 Kharva, 13; mahâ, 13 Khâta, 124 Kopp, 16 Koṭi, 10, 11, 12, 13 Koṭi-koṭi, 11, 12 Koṭippakoṭi, 12 Krâkacika, 124 Krama, 131 Kṛṣṇa, 243, 244 Kṛti, 155, 169 Kṣetragaṇita, 7, 8 Kṣipra, 186 Kṣiti, 13; mahâ, 13 Kṣobha, 13; mahâ, 13 Kṣobhya, 10 Kṣoṇi, 13; mahâ, 13 Kumuda, 12 Kuṣṭha, 185 Kuṭṭaka, 8

v1.c10.28

v1.c10.29

Labdha, 150 Laghu-Bhâskarîya, 59 Lahiri, 65 Lakkha, 11 Lakṣa, 11, 13 Lalitavistara, 10, 37, 187 Lalla, 61, 87, 125 Langdon, 25, 29 La Roche, 175 Lâṭyâyana, 58 Lekhapañcâśikâ, 50 Lekhaprakâśa, 50 Leonardo Fibonacci of Pisa, 94, 103 Lespius, 16 Lîlâvatî, 125, 131, 132, 133, 134, 136, 137, 144, 145, 146, 147, 211, 213, 227, 229, 230, 235, 241, 245; Gaṇeśa's commentary, 144, 145, 146 Lowest Common Multiple, 195

v1.c10.30

v1.c10.31

Macdonell and Keith, 9 Madhya, 9, 13 Mahâ-Bhâskarîya, 59, 80 Mahâbja, 13 Mahâkathâna, 12 Mahâsaroja, 13 Mahâvîra, 5, 13, 55, 56, 57, 77, 80, 136, 137, 145, 151, 156, 157, 161, 162, 164, 166, 167, 168, 172, 188, 191, 192, 195, 196, 198, 199, 205, 208, 212, 220, 222, 224, 230, 233, 235, 237, 238, 240, 241 Mahmûd bin Qajid al-Amûni Saraf-Eddin, 99 Maitrâyaṇî Saṁhitâ, 9, 18, 185 Majjhima Nikâya, 4 Malayagiri, 79 Mâna, 204, 205 Manorañjana, 132, 137 Marre, A., 100, 184 Marshall, 19 Martin, Ohm, 246 Mâṣâ, 218 Mathematics, appreciation of, 3; decay of, 127; Hindus and, 3; in Hindu education, 6; of zero, 238; scope and development of Hindu, 7 Maximus Planudes, 104, 144, 184 Mazumdar, R.C., 59 Measures, see weights Megasthenes, 21, 37 Mihir Yast, 101 Milindapañho, 7

v1.c10.32

Mille, 9 Miscellaneous problems, 230; problems involving solution of quadratic equations, 234; problems involving the square of the unkown, 238; problems involving the square-root, 235; problems on mixture, 233; regula falsi, 230; the method of inversion, 232 Miśraka, 124; vyavahâra, 219, 233 Miśraṇa, 130 Mitra, Rajendra Lal, 10, 97, 187 Mohammad, 88 Mohammad Ben Musa, 102 Mohenjo-daro, 19; and Harappa, 19, 23, 29; and the Indus Valley civilization, 17; discoveries at, 1; finds of, 20 Montucla, J.F., 99 Mudrâ, 7 Mudrâbala, 11 Muhûrta, 186 Mukerjee, Sir Asutosh, 17 Mûla, 169, 170, 220, 234; aṁśa, 237; dviragra śeṣa, 236; ghana, 124, 175; jâtî, 235; miśra, 237; śeṣa, 235; varga, 124, 169 Multiplication, 134; algebraic methods, 149; Brahmagupta's method, 136; by separation of places, 146; cross-multiplication method, 145; direct process, 138; door-junction method, 136; gelosia method, 144; inverse method, 139; methods of, 135; parts-method, 148; terminology, 134; transmission to the west, 143; zigzag method, 147

v1.c10.33

Munîśvara, 213 Myriad, 9

v1.c10.34

v1.c10.35

Nâgabala, 10 Nâgarî script, 39 Nâgârjuna, 2 Nahuta, 12 Naiṣadha-carita, 85 Nallino, 83 Nârada, 4 Nârâyaṇa, 13, 137, 152, 161, 162, 167, 168, 183, 184, 205, 240 Nau, F., 95 Nava, 13;—daśa, 15;—viṁśati, 15 Nava-râśika, 124 Neil, R.A., *see* Cowell Nikharva, 10, 13 Nîlakaṇṭha, 67, 170 Ninnahuta, 12 Nirabbuda, 12 Niravadya, 11 Niruddha, 195 Niṣka, 213, 214, 215, 216 Niyuta, 9, 10, 12 Notation, abjad, 89; decimal place-value, 3; difference from other, 27; epigraphic instances of decimal place-value, 40; Greek alphabetic, 50; places of, 12; scale of, 9 Numeral, ghobâr, 89, 90, 91, 93, 94; Hieratic and Demotic, 28; Hindu, 38; Kharoṣṭhî and Semitic, 28 Numeral notation, 1; Brâhmî, 25; earliest, 19; in spoken language, 13; Kharoṣṭhî, 21; terminology, 9 Numerical, Aśokan—figures, 37; development of symbolism, 16

v1.c10.36

Nyarbuda, 9, 10, 13

v1.c10.37

v1.c10.38

Ojha, 17, 24 Oldenburg, 4 Operations, checks on, 180

v1.c10.39

v1.c10.40

Pacioli, 146 Pada, 155, 169, 170, 177 Padma, 13; mahâ, 13 Paduma, 12 Paṇa, 206, 216, 218, 227, 229 Pañca, 13 Pañca-râśika, 124 Pañca-siddhântikâ, 59, 78, 79, 239 Pâṇini, 2, 18, 33, 63, 218 Paṅkti, 173 Pannavanâ-sûtra, 37 Papyrus Blacas, 24 Parameśvara, 67, 155, 197 Parârdha, 9, 13 Parasparakṛtam, 134 Pargiter, 58 Parikarma, 8 Paṭala, 18 Pâṭana, 132 Patañjali, 2, 63, 85 Pâṭî, 8, 124, 126, 129, 138, 139, 140, 141, 148, 152, 157, 158, 159, 173, 174, 177, 178, 180 Pâṭîgaṇita, 8, 82, 123, 126, 128, 151, 184, 187, 195, 222, 226, 227, 233, 235, 239, 240 Pâṭîsâra, 125, 213 Paṭṭa, 123 Paṭṭopâdhyâya, 50 Peurbach, 175 Phala, 198, 204, 205, 206, 208, 212, 216, 220, 223, 228 Phalaka, 123 Phoenician forms (of numerals), 24 Phoenician script, 17 Piṅgala, 75, 76, 77 Place-value, date of invention of the notation, 86; in Hindu literature, 83; in Jain canonical works, 83; in literary works, 85; in works on philosophy, 85; invention of system, 51; new notation, 53; principle, 39; the decimal notation, 40; the decimal system, 43 Plate, Cambay—of Govinda, 43; Chargaon—of Huviṣka, 47; Ciacole, 40; Daulatabad—of Saṅkargaṇa, 41; Dhiniki Copper, 40; Grant of Avanîvarmaṇa, 42; Grant of Balavarmaṇa, 42; Gurjara Grant, 40, 45, 48; Kadab, 60; Pâṇḍukeśvara—of Lalitasuradeva, 41; Ragholi, 40, 82; Sangli—of Râṣṭrakûṭa Govindarâja, 43; Torkhedi, 41 Prabhâga, 190 Prakṣepa karaṇa, 233 Prâkṛta, 170 Prakṣepaṇa, 130 Pramâṇa, 198, 204, 205, 223; râśi, 198; pakṣa, 211, 213 Pratiloma, 151 Pratyutpanna, 135, 139, 140 Prayuta, 9, 12, 13 Princep, James, 33 Pṛthudakasvâmî, 77, 124, 129, 148, 156, 163, 228 Puliśa, 61, 79 Puṇḍarîka, 12 Purâṇa, 2, 84, 86, 206, 228; Agni, 58, 59, 62, 84, 86; Vâyu, 84; Viṣṇu, 84

v1.c10.41

Pûrva, 164

v1.c10.42

v1.c10.43

Rabbi ben Ezra, 96, 103, 217, 230 Radix, 170 Râjataraṅgiṇî, 50 Rajju, 8 Ramanujacaria, 156, 168 Râmâyaṇa, 2 Rangacarya, 151, 226 Râśi, 8, 124; rupâṁsaka, 199 Ray, H.C., 17 Ray, Sir P.C., 85 Regula falsi, 230, 238 Reinaud, 97, 98 Ṛgveda, 9, 15, 17, 18, 20, 57, 185 Rhys Davids, 7 Riese, 149 Rodet, 65, 66, 170, 175 Rosen, 102 Rule of Three, 203; appreciation of, 208; as a particular case, 216; compound proportion, 210; illustration, 213; inverse, 207; proportion in the west, 210; terminology, 203; the method, 204, 211 Rûpa, 6 Rûpa-vibhâga, 136

v1.c10.44

v1.c10.45

Sachau, E.C., 98, 99 Sadguruśiṣya, 71 Sadratnamâlâ, 70 Sahasra, 9, 12, 13 Sakala, 199 Salila, 10 Samacaturaśra, 155 Samâpta-lambha, 11 Samavâyâṅga-sûtra, 6, 37 Saṁkalana, 130 Saṁkalita, 124, 130, 196 Saṁkhyâ, 238 Saṁkhyâna, 4, 6, 7 Sammelana, 130 Samudra, 9, 10 Saṁyojana, 130 Sanatkumâra, 4 Śaṅkarâcârya, 85 Śaṅkha, 13 Sâṅkhyâyana śrauta sûtra, 10 Saṅkramaṇa, 221, 222 Śaṅku, 13 Śapha, 185 Sapta, 13 Sapta-râśika, 124 Saritâpati, 13 Sarvabala, 11 Sarvadhana, 132 Sarvajñâ, 11 Sarvânukramaṇî, 71 Sastri, Madhava, 184 Sastri, Sambasiva, 67 Śata, 9, 12, 13; koṭi, 13 Sâtavâhana, 25 Śatottara gaṇanâ, 10; saṁjñâ, 10 Savarnaṇa, 194 Script, Indian, 16; Nâgarî, 39; North Semitic, 17; Phoenician, 17; South Semitic, 16, 17 Sebokht, 89, 93, 95, 96 Sefer ha-Mispar, 103 Sefer Yesîrâh, 98 Senart, E., 26 Sengupta, 175, 197 Śeṣa, 132 Shamasastri, R., 6, 19, 187, 218 Siddhânta, 3, 125, 128, 135, 150; Brâhma-sphuṭa, 8, 59, 89, 156, 228, 241; Mahâ, 125, 181, 183, 184, 240; Parâśar, 3; Pitâmaha, 3, 125; Puliśa, 59, 62, 79, 86; Romaka, 125; Śekhara, 125, 136; Sûrya, 3, 59, 62, 125; Tattva-viveka, 125; Vasiṣṭha, 3, 125 Siddhasena Gaṇi, 80, 171 Śilâditya VI, 52 Silberberg, Moritz, 103 Sindhind, 97 Singh, A.N., 170, 171, 172, 173, 175 Śîrṣaprahelikâ, 12 Sitanath, Sri, 76 Skandasena, 188 Smith, 144, 146, 149, 150, 153, 154, 175, 210, 217, 230, 232, 233; and Karpinski, 11, 27, 30, 48, 80, 83, 88, 89, 90, 95, 103 Śodhana, 132 Śodhya, 177, 178 Sogandhika, 12 Square, 155; minor methods of squaring, 160; terminology, 155; the operation, 156 Square-root, 169; terminology, 169; the operation, 170 Śrauta-sûtra, 58 Średhî, 124 Śrîdhara, 8, 13, 134, 136, 145, 155, 156, 157, 160, 161, 162, 163, 167, 168, 172, 177, 188, 190, 191, 192, 193, 196, 198, 199, 205, 207, 212, 230, 240 Śrîdharâcârya, see Śrîdhara Śrîharṣa, 85 Śrîpati, 128, 136, 137, 138, 144, 145, 150, 167, 172 Stambhoddeśa, 230 Sthâna, 12, 161, 166;—khaṇḍa, 146, 148 Sthânâṅga-sûtra, 8, 204 Subandhu, 81, 82, 85 Subtraction, 132; direct process, 133; inverse process, 133; terminology, 132; the operation, 132 Śulba 130, 134, 155, 170, 185, 188 Sumatiharṣa, 184 Śûnya, 38, 54, 77;—bindu, 81, 85 Sûryadâsa, 133, 197, 208, 211 Sûryadeva, 67, 71 Suśruta, 2 Suter, H., 51, 99, 102, 143, 174 Sûtra, 4 Śvetavarṇî, 129

v1.c10.46

v1.c10.47

Taccheda, 241 Taittirîya Saṁhitâ, 9, 14, 15; Brâhmaṇa, see Brâhmaṇa Talkhis, 99 Tallakṣaṇa, 11 Tântric, 19 Tarik al-hindî, 143 Tastha, 136, 145; guṇana, see guṇana Tattvârthâdhigama-sûtra, 80, 151, 171 Taylor, 16, 29, 132, 147, 245 Theon of Alexandria, 171 Theophanes, 89 Theory, Indraji's, 35 Thibaut, 155 Tiṭilambha, 11 Trairâśika, 124, 203, 204; vyasta, 124, 207, 210 Tri, 13; pâda, 185 Tripraśna, 5 Triśatikâ, 59, 125, 151, 187, 205, 227, 229 Tropfke, 80

v1.c10.48

v1.c10.49

Umâsvâti, 2, 80, 151, 189 ûna-viṁśati, 15; triṁśat, 15

v1.c10.50

Upaniṣad, Chândogya, 3, 58; Muṇḍaka, 4 Uppala, 12 Utkrama, 131 Utsaṅga, 10 Uttara, 163 Uttarâdhyayana-sûtra, 4

v1.c10.51

v1.c10.52

Vâdava, 10 Vadha, 134 Vâjasaneyî saṁhitâ, 9, 15 Vajrâbhyâsa, 145, 146 Vajrâpavartana-vidhi, 196 Vallikâ-kuttîkâra, 233 Vâlmîki, 2 Varâhamihira, 61, 79, 209, 239 Varâṭaka, 206 Varga, 8, 65, 66, 67, 69, 124, 155, 156, 235; mûla, see mula;—varga, 8 Varṇa, 63, 229 Vâsavadattâ, 81, 85 Vaśiṣtha, 17 Vedâṅga, 7, 19;—jyotiṣa, 7, 58 Vediśrî, 25 Vibhûtâṅgama, 11 Vidyâ, aparâ, 4; Brahma, 4; nakṣatra, 4; parâ, 4; râśi, 4 Vikalpa, 8 Vinaya Piṭaka, 4, 7 Vinimaya, 204, 205 Visamjñâ-gati, 11 Vivâha, 10 Vivara, 10 Viyoga, 132 Viyojaka, 132 Viyojya, 132 Vṛnda, 13 Vyâsabhâṣya, 85 Vyavahâra, 8;—sûtra, 84 Vyavakalita, 124 Vyavasthâna-prajñapti, 11 Vyutkalana, 132 Vyutkalita, 124, 132

v1.c10.53

v1.c10.54

Wahshiya, 97 Warner, A.G., and Warner, E., 100 Wäschke, 104 Weber, 16, 17, 37, 58 Weights and Measures, 186 Whish, 65 Widman, 149 Woepcke, F., 90, 102, 143, 174, 184 Wolack, Gottfried, 83 Woods, J.H., 85 Word-numeral, 53; date of invention, 62; explanation of the system, 53; in inscriptions, 59; list of, 54; origin and early history, 60; without place-value, 57; with place-value, 58; Wright, W., 96 Writing in ancient India, 16