Adhvaryu, 5. Agni, height of, 7. Agnicit, construction of, 7. Agnidhriya altar, 6, 8, 86, 107, 128, 130, 137, 139, 172, 177, 184, 240, 276. Ahavaniya fire-altar, 5, 7, 8, 170, 272. Ahavaniya from the garhapatya, placement of, 80, 104, 121, 126, 169, 173, 237, 266. Akṣa, 77, 106, 121, 127, 135. Akṣṇayā, 120, 121, 148, 265. Alajacit, 6. Angula, 77, 113, 124, 128. Apastamba, 2, 3, 8, 9, 10. Apastamba, date, 4. Apyaya, 117, 255. Aratni, 77, 106, 113, 124, 125, 128, 135, 136. Ardhadaśama, 12. Ardhanavama, 12. Ardhāṣṭama, 12. Area measures in Baudhāyana-śulbasūtra. 77. Arthaśāstra, 1. Aśvamedha fire-altar, 5, 82, 83, 105, 119, 137, 178, 239. Athenaeus, 10. Bahu, 77. Băla, 128, Bamboo rod, measurement with, 107, 108, 129, 241, 274. Baudhayana, 2, 3, 8, 9, 10, 11. Baudhayana, date, 4. pakşeştakā, 117, 118. pañcadaśabhagiyā, 118, 242. pañcami, 88, 90, 92, 185, 188, 197, 204, 242. pañcami-ardhyā, 91. pañcami-pādya, 91, 99. prādeśa, 242. prāṇabhṛt, 131. 132, 133. prauga, 227. ṛtavya, 130, 131, 132, 134. sapādā, 91, 197. şaṣṭhi, 95, 96, 185, 220. ṣoḍaśī, 96, 99, 116, 117, 118, 232. sulapadya, 93, 197, 211, 213. svayamātṛṇņa, 90, 93, 131, 132. trayodaśī, 248. triangular, 198, 211, 248. turiya, 130. ubhayata prauga, 227. ubhayï, 91, 198. urvasthi, 110, 244. vaiśvadevī, 130, 132. vāyavyā, 132. virāja, 132. Bühler, Georg, 2, 3, 4. Bürk, 2, 12, 13, 152, 157. Cajori, 151. Caland, 12. Cantor, 162. Bharadvāja, 4. Bhaskara II, 154. Brāhmaṇacchamsa (hearth), 130, 139, 276. Bṛhaddevată, 3. Brick, clefts to be avoided, 83. Brick, height of, 85, 109. Bricks for the construction of chariot-wheel, 111. Brick-types, adhyardha, 88, 91, 188, 197, 204, 242. aņūka, 110, 118, 244. apasyā, 132. aratni, 110, 244. ardhya of pañcami, 88, 188, 197, 204, 242. bṛhati, 93, 96, 97, 124, 132, 211, 213,220. caturaśra-adhyardhã, 204. caturaśra-padyā, 204. caturbhagiyà, 113, 242, 244. caturthi, 95, 96, 98, 99, 185, 190, 220, 229. caturthi-adhyardha, 98. caturthi-ardhya, 89, 190, 229. caturthi-padyā, 89, 99. chanda, 132. dirghapādyā, 93, 197, 211, 213. dvādaśī, 248. hamsamukhi (swan-beaked), 89, 90, 99, 191, 229. nakula, 139. padya of pañcami, 88, 188, 197, 204. pakṣāgriyā, 117. pakşamadhyiyā, 117. Caturbhagona, 12. Caturtha-saviseṣārdha, 12. Caturtha-saviśeșa-saptama, 12. Câtvāla, 8, 82, 112, 134, 177. Centre of segment (pradhi-madhyamā), 233. Chakrabarty, 162. Chandaścit, 6, 184. Chao Chun Chhing, 154. Chariot measure, 106, 121, 127, 135, 273. Chou Pei Suan Ching, 11, 154. Cicero, 10. Circle, transformation into a square, 80, 103, 123, 162, 236, 268. Circumference-diameter ratio, 82, 136. Cubic measure, 135. Dakṣināgni fire-altar, 5, 7, 8, 170, 237, 266, 272. Dakṣinagni, placement of, 80, 104, 121, 126, 136, 169, 173. Darśapūrṇamāsa (dārśapaurṇamāsa) vedi, 5, 6, 175. Dārśiki vedi, 272. Datta, 152, 154, 174. Dharmasūtras, 3. Dharmasūtras, history of, 4. Dhiṣṇyas, 8, 82, 86, 107, 133, 139, 172, 177, 184, 240, 277. Dhisnyas, different types, 172. Diagonal of a rectangle, 3, 4, 5; 12, 5, 13; 15, 8, 17, 105.INDEX OF INTRODUCTION, TRANSLATION AND COMMENTARY Diagonal of a rectangle, square area of, 78, 101, 121. Diagonal of a right triangle, relationship with sides, 121, 135. Diagonal of a square, area of, 9-10, 78, 101, 121. Drenckhahn, 162. Droṇacit, 6. Dvārakānātha, 12, 157, 158, 161, 184, 225. Dvikaraṇī, 78, 102, 122, 150, 235. East-west line, 77, 78, 101, 104, 120, 126, 136, 264, 272. Eggeling, 3. Ekadasini altar, 128, 270, 271. Ekadasini altar, use of in the construction of malāvedi and aśvamedha vedi, 178. Ekato’nimaddirghacaturaśra, 226. Euclid, Theorem, 47, 11, 154. Euclidian tradition, 10. Filliozat, 3. Fire-altar, āhavaniya, 5. areas of in the Satapatha Brāhmaṇa, 8. dronacit in the form of a circle, 96, 142, 221-25, 268, 281. enlargement of, 179-181. garhapatya, 5. height of, 83, 181. perpetual (nitya), 5, 7, 8. rectilinear, placement of bricks in, 109, 110. Fire-altar in the form of alaja bird, 92, 118, 139, 140, 208-210. chariot-wheel, circular segments, 94, 215-16, 249, 281. chariot-wheel, construction of, 94. chariot-wheel, with spokes, 94-95, 143, 216- 19. isosceles triangle (prauga), construction of, 93, 123, 142, 211-12, 247-49, 268, 281. falcon in square, construction of, 86, 87, 185, 240, 244-47, 275, 276. falcon in square (another type), 88, 188, 279. falcon with curved wings and extended tail, construction of, 90, 113, 116, 139, 140, 190-195, 196-202, 251-256, 281. kite (kankacit), construction of, 91,118, 140, 141, 202-207. pyre (śmaśānacit), construction of, 97, 142, 225-227. rhombus (ubhayata prauga), 93, 111, 123, 142, 213-14, 249, 281. tortoise (kūrmacit), construction of, 98, 228- 33. tortoise with rounded limbs, 99, 232-33. tortoise with twisted limbs, 228-232. trough, construction of, 95, 112, 123, 220- 21, 249-250. Fire-altar for aśvamedha (sacrifice), 100. Fire-altar for the first time, area of, 82. Fire-altar paricāyya, construction of, 97. Fire-altar samuhya, construction of, 97, 112, 142. Fire-altar upto 101-fold, 83, 107, 124, 247. Fire-altar with characteristics of an animal, 84. Fire-altar with wings and tail, Brāhmaṇa teach- ing, 83. Fire-altar without wings and tail, 83. Fire sacrifice (agnihotra), 1. Fractions, 11, 12. 291 Garbe, Richard, 4. Garhapatya fire, circular, square, 85, 107, 138, 182, 183, 279. Gārhapatya fire, measurement of, 85, 86, 107, 133. Garhapatya fire, placement of, 80, 104, 121, 169, 173, 237, 266. Garhapatya fire-altar, 5, 8, 125, 129, 170, 240, 272, 276, 277. Garhapatya fire-altar, in Rgveda, 5. Garhapatya fire-altar in Taittirīya Samhitā 5. Gayatra measure, 138. Guriar, 162. Havirdhāna (shed), 8, 82, 127, 128, 134, 172, 173, 177, 274. Heath, 151, 152. Heron, 10. Hiranyakeśin, 2, 4. Hotriya altar, 6. Irrational number √/2, 8, 11. Irrational number in Babylonian cuneiform texts, 11. Iṣā, 77, 106, 121, 127. Isosceles trapezium, 6, 79, 226, 239, 268. Isosceles triangle (prauga) into a square, trans- formation of, 124, 226. Jānu, 77. Kahun papyrus, 11. Kalpasūtras, 1, 2. Kāmasastra, 1. Kāmya agni, 5, 111, 247. Kamya agni, list of, 6. Kane, P.V., 4. Kankacit, 6. Kapardisvāmi, 12, 151, 161, 243, 245, 246. Karaṇī, 121. Karavindasvāmī, 12, 161, 168, 169, 181, 243, 245, 246, 250, 251, 256. Kathaka-kapisthala school, 2. Kātyāyana, 2, 3, 4, 8, 9. Katyayana, date, 3. Kaukili vedi, 128. Keith, 3. Kṛṣṇala, 128. Kṣetrajñāna, 267. Laertius, Diogenes, 10. Laugākṣi, 2. Lokampṛṇa brick, 85. Macdonell, 3. Madana Pathaka, 12. Mahābhāṣya, 3. Mahārņava, 2. Mahāvedi, 8. Mahāvedi, measurement of, 81, 105, 170, 177, 237. Mahidhara, 13, 178. Maitrāyani Samhita, 7. Maitrāyaṇi school, 2. Māna, 128. 292 INDEX OF INTRODUCTION, TRANSLATION AND COMMENTARY Mānava, 2, 3, 8, 9. Mānava, date, 4. Mārjālīya, 6, 8, 82, 86, 130, 172, 177, 184, 276. Măruti altar, 127, 273. Masaka, 2. Method of addition (ekaḥ samāsaḥ), 122. Method of combination (samãsa) (of squares), 155. Method of deduction (nirhāsa), 123. Method of difference (nirhāra) (between squares), 156. Method of one cord (ekarajju vidhi), 237. Method of two cords (dvirajju vidhi), 238. Milhaud, Gaston, 10. Müller, 162, 163. Nākasat brick, 84, 109, 130, 133 134 181. Natyaśastra 1. Needham 154. Neugebauer 11. Nirņāma, bending of wings, 192, 196, 209, 252. Nirudapaśubandha vedi, 239. Niska, 128. North-south line (udīcī), 120, 264. Nyañcana, nirañchana, 77, 78, 120, 127, 136, 137, 148, 265. Pada, 77, 106, 124. Paitṛki vedi, 5, 8, 121, 152, 240, 273. Paitṛki vedi, measurement of, 81, 106, 175. Pakṣanamani (bending of wings), 117. Pañcacoḍā brick, 84, 109, 130, 134, 181. Pañcăngi cord, 129, 136, 274, 279. Panini, date, 3, 4. Paravan, 125. Paricayya fire-altar, 6, 113, 224. Parsvamani, 121. Paśubandha vedi, 8, 81, 127, 175, 273. Pasuki vedi, 127, 273. Patanjali, 3. Pentagon, construction of, 124. π, value of, 8, 11, 161, 179, 278. Prăci (east-west line), 78, 104, 120, 136, 265. Prādeśa, 77, 113, 128, 135. Prådeśakṣetra, 243. Pradhi-madhyama (centre of segment), 233. Pragvamsa (sacrificial chamber), 81, 177, 266, 274. Prakrama, 77, 105, 135. Pramāņa 78 102 122 137 148. Prauga (isosceles triangle) 6. Proclus 10 154. Pṛṣṭhya (east-west line) 77, 78, 101, 126. Pṛthâ, 77. Purușa, 77, 113, 124, 128. Pythagoras, 10, 11, 154. Pythagorean theorem in China, 11. Pythagorean theorem in other culture areas, 154. Ramgopal, 3, 4. Rathacakracit, 6. Rectangle, construction of, 77, 120, 148, 149, 265. Rectangle into rhombus, transformation of, 160. Rectangle into square, transformation of, 79, 102, 122, 159-60, 268. Rectangle into triangle, transformation of, 160. Renou, 3. Rhombus into square, transformation of, 124, 269. Right rectilinear figure, construction of, 101. Right triangle, properties of, 278, 279. Root five, √/5, value of, 174, 175. Root three, V/3, value of, 164. Root two, √2, irrationality of, 168. Root two, √/2, value of, 80, 101, 121, 164, 165, 174, 175, 234. Root two, 1/2, value of, Datta’s proof, 167-68. in other culture areas, 168. Rodet’s proof, 165-66 Thibaut’s proof, 165. Rope-stretcher (harpedonap’tae), 1. Sacrificial altars, fires in Samhitās and Brāh- manas, 5-8. Sacrificial chamber (prāgvamsa), 81, 120, 127. Sacrificial fires, 77. Sacrificial ground, plan of, 169-173. Sadas (tent), 6, 82, 106, 120, 127, 128, 172, 177, 240, 274. Sakatamukha, 120, 266. Samaveda school, 2. Śamyā, 77, 106, 121. Sarton, George, 10. Satapatha Brāhmaṇa, 7, 170, 173, 180, 181. Satyāṣāḍhā, 4. Saumikyā vedi, 104, 105, 137, 170, 279. Sautrāmaņi vedi, 5, 8, 105, 122, 176, 239. Sautrāmaņi vedi, measurement of, 81. Sayă, 128. Sikhaṇḍini vedi, 125, 128, 224. Śivadāsa, 275. Śmaśānacit, 6. Soma-carts, 172. Soma sacrifice, 1. Source materials, 12-13. Square, construction of, 77, 101, 102, 120, 148, 234, 235, 241, 265, 272. Square, enlargement of, 236, 237. Square, n-times a given square, 270, 271. Square, theorem of, 10, 101, 135, 151-54, 234, 267, 278. Squared relationship between diagonal and sides of rectilinear figure, 9-10, 78, 101. Square into circle, transformation of, 79, 103, 123, 135, 160-61, 236, 268, 278. Square into double isosceles triangle, transforma- tion of, 79. Squares into isosceles triangle, transformation of, 79, 160. Square into rectangle, transformation of, 79, 103, 122, 156-58, 236, 268. Square into rhombus, transformation of, 160. Squares, combination of, 78, 102, 122, 155, 267. Squares, difference of, 79, 102, 122, 155, 268. Srautasutras, 1, 2, 3, 4, 9. Sulba, meaning of, 1. Sulbasūtras, place and time of authors, 2-5. Sulbasūtras, special importance of, 1. Sulbavid, 1, 2, 8, 134, 277. Sulba-vijñāna, 2. Saraja, 12, 151, 157, 243, 245, 246, 250. Suparṇaciti, construction of, 133. Suparņa garutman, 6, 7. Surds, surd numbers, 11, 150, 235. Syenacit, 6. INDEX OF INTRODUCTION, TRANSLATION AND COMMENTARY 293 Taittiriya Samhita, 7. Taittiriya school, 2. Tatkaraṇī, 121, 267. Thibaut, 2, 4, 12, 13, 152, 157, 162. Tila, 77. Tiryaǹmāni, 78, 120, 121, 137, 148, 158, 265, 266. Trapezium, 226. Triangle (sakaṭamukha), construction of, 120, 269. Triangle into square, transformation of, 269. Tṛkaraṇī, 78, 102, 122, 151, 235, 267. Tṛtiyakaraṇī, 78, 102, 122, 151 235 267. Tunda, 128. Ubhayata prauga (rhombus), 6. Upacayya fire-altar, 113. Uparava, 8, 82, 106, 173, 177, 240. Unit, enlargement of, 270. Units and measures, Apastamba, 113, 240. Baudhayana, 77, 147. Katyāyana, 124, 125, 267. Mánava, 128, 135, 274, 278. Utkara, placement of, 80, 126, 173, 266. Uttara vedi, 5, 6, 8, 128, 175, 240. Uttara vedi, measurement of, 81, 82, 106, 108, 173. Uttarayuga, 77. Vādhula, 2, 4. Vaikhanasa, 4. Vājasaneya Samhità, 6. Van Gelder, 12, 13. Vårāha, 2, 4. Varuna, 127, 273. Vedāngas as appendages of the Vedas, 1. Vitasti, 124, 125, 128, 129. Vogt, 151. Volume, measurement of, 277. Vyama, 77. Vyāyāma, 77, 113, 128. Wings, bending of, in falcon-shaped fire-altar, 89, 117, 192, 196. Wings, bending of, in kańkacit, 92. Yuga, 77, 106, 121, 127, 135. Yajamânamātrī, 80. Yajurveda, 2. Yava, 128. Zeuthen, 151.