[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [The Science of the Shulba: A Study in Early Hindu Geometry](https://indike.org/pramana/ins.science.datta-1932) › c24 # The Science of the Shulba: A Study in Early Hindu Geometry c24: Index The Science of the Śulba: A Study in Early Hindu Geometry c24 - **Language:** English ### Index ### [c24.1](https://indike.org/pramana/ins.science.datta-1932.c24.1) \*Abhyantara-viśeṣa\*, 197n. \*Agni\*, 27, 30 \*et seq.\*, 39-40, 60n-61n, 120, 152; Enlargement of, 158 \*et seq.\* (See \*Kāmya Agni\*, and \*Ekaśata-vidha Agni\*). \*Agni-cayana\*, 28, 29. \*Agni-cit\*, 28, 28n. \*Āgnīdhrīya\*, 34, 42. \*Āhavanīya\*, 21, 27, 203 \*et seq.\*; Altar of, 21, 31. \*Alaja\*, 23. Algebra, Early history, 165; Geometrical, 165 \*et seq.\*; Problems of, in ancient India, 2. Al-Khowārizmī, 111n. Allman, 111. Altar, 2, 20 \*et seq.\*; Science of construction, 164; date of the science, 29; geometry traced in, 30. (See Falcon-shaped Altar, Fire Altar, and Vedic Altar). \*Aṁsa\*, 212. Āpastamba, Authority mentioned, 26-27; Bürk’s edition, 20; Commentaries of, 10, 13, 19; \*Śrauta-sūtra\* of, 1, 13, 25n, 29; \*Śulba-sūtra\* of 3-4, 13, 25; -\*Sūtra-paribhāṣā\*, 13. \*Āpastambīya Śulba-bhāṣya\*, 10. \*Āraṇyaka\*, 25. \*Ardha-daśama\*, 213. \*Ardha-navama\*, 213. \*Ardhyā\*, 44. Area, combination, 71 \*et seq.\*; To draw a square equal to, \*n\* times a given square, 71-74; \*n\*th part of a given square, 74-76; sum and difference of two given squares, 76-80; two given pentagons. 80-82; two given triangles, 80; Definition of, 95; Problems of, in ancient India, 2; Transformation of, 83 \*et seq.\*; square, from isosceles triangle, 92-93, from rectangle, 83-85, from rhombus, 94, into rectangle, 85-90, square and rectangle, into isosceles trapezium, 90-92, into rhombus, 93-94, into triangle, 92. (See also Measures.) Āryabhaṭa I, 16, 18. \*Āryabhaṭīya\*, 16. \*Aṣṭadaśa-karaṇī\*, 188. \*Aṣṭa-vidha\*, 170. \*Aśvamedha-vedi\*, 34, 152 \*et seq.\*, 162 \*et seq.\* \*Aśvamedhika Agni\*, 172-73. \*Aśvamedhikī-vedi\*, 107, 188. \*Atharva-veda\*, schools of, 1n. ### [c24.2](https://indike.org/pramana/ins.science.datta-1932.c24.2) Babylonian mathematician, 213. Bakhshālī Manuscript, 208. Baudhāyana, commentaries, 10; His sources, 25, 26; \*Śrauta-sūtra\* of, 1; \*Śulba-sūtra\* of, 2-3, 25 \*et seq.\* \*Bāhya-viśeṣa\*, 197n. \*Bhāga\*, 212. \*Brāhmaṇa\*, 25 \*et seq.\*, 29 \*et seq.\*; Primary functions, 29; Source of geometry in, 25-27. (See also \*Maitrāyaṇīya Brāhmaṇa\*, \*Śatapatha Brāhmaṇa\*, and \*Taittirīya Brāhmaṇa\*.) \*Bhāradvāja Gṛhya Sūtra\*, 13. Bhāskara (Second), 12; \*Bījagaṇita\* of, 165. Brahmagupta, 17. Bürk, 86 \*et seq.\*; 107 \*et seq.\* ### [c24.3](https://indike.org/pramana/ins.science.datta-1932.c24.3) Caland, 86n. Cantor, 111. \*Caturasra-śyenacit\*, 109-110, 112, 120, 152. \*Caturbhāgona\*, 213. \*Catur-guṇa\*, 212. \*Caturtha-saviśeṣārdha\*. 213. \*Caturtha-saviśeṣa-saptama\*, 213. \*Catuṣkaraṇī\*, 188. Chinese mathematicians, 218. ### [c24.4](https://indike.org/pramana/ins.science.datta-1932.c24.4) Circle; Area of, 95; Division, equal, 42-43; Doubling, 21; Magnitudes, 201; Squaring and vice versa, 18-19, 21, 27, 40, 143-51. (See also, Postulates, Quadrature, Segment, and Square.) Commentators, 10-11, 13, 16-19. Compass, Possibility of, 34 Congruence theorems, 44. Constructions, 52-70; Parallelogram, 67-70; Perpendicular, 42-55; Rectangle, 62-63; Square, 55-62; Trapezium, isosceles, 63-66. (See Altar.) Cylinder, Volume of a, 101. ### [c24.5](https://indike.org/pramana/ins.science.datta-1932.c24.5) Dakṣiṇa, 21, 120, 203. Dakṣiṇāgni, 27, 31, 203 \*et seq.\* Darśapaurṇamāsa-sūtra, 13. Dārśapaurṇamāsikī-vedi, 30, 34. Darśa Sacrifice, 21. Demonstration, 50-51. Dhiṣṇiya, 42, 150. Diagonal, bisects a rectangle and mutually, 43, 45. (See also Postulates, Pythagorean Theorem, Rectangle and Rhombus.) Dimension. (See Spatial Dimensions.) Double-producer, 71. Droṇa, 23. Droṇa-cit, 150, 214. Dvādaśa, 212. Dvārakanātha Yajvā, 10, 18-19, 87 \*et seq.\* Dvi-guṇa, 212. Dvi-karaṇī, 188. Dvirajvāvihāraṇa, 64. Dvi-saptama, 213. ### [c24.6](https://indike.org/pramana/ins.science.datta-1932.c24.6) Eggeling, 158n. Egyptian mathematician, 213. Ekādaśinī-vedi, 162 \*et seq.\* Ekarajvāvihāraṇa, 64. Ekaśata-vidha, 169 \*et seq.\* Ekaśata-vidha, Agni, 160. Ekavidha Agni, 171. Ekaviṃśa-vidha, 172 \*et seq.\* Equation, Solution of. (See Quadratic equation, Simple Equation.) ### [c24.7](https://indike.org/pramana/ins.science.datta-1932.c24.7) Factorisation, 218-20. Figures, construction of similar, 24; Division of, 24; Rectilinear, 222. (See also Similar Figures.) Fire altar, 152 \*et seq.\*; Enlargement of, 158 \*et seq.\*, 174 \*et seq.\*, 203 \*et seq.\*; Falcon-shaped, 22-23, 67, 183 \*et seq.\*, 215-216; bending the wings, 37-38; construction of, 154 \*et seq.\*, 158n; enlargement of, 166 \*et seq.\*; form of, 134; magnitude, 34; measurement, 34-37. (See Altars, Āhavanīya, Dakṣiṇa, Gārhapatya.) Fraction, 212-17; Division of, 214; Fraction of a, 213; General fraction, 213; Operations with, 213-17; Squaring of a, 216; Terminology of, 212-13; Unit fraction, 212 \*et seq.\* ### [c24.8](https://indike.org/pramana/ins.science.datta-1932.c24.8) Garbe, 25. Gārhapatya, 21, 27, 203 \*et seq.\*; Altar of, 21, 31, 150. Gārhapatya-citi, 31. Gārhapatya-vedi, 180-81. Geometry, Hindu, before 300 B.C., 6-7; Before 3000 B. C., 27 \*et seq.\*; Esoteric, 2n; Growth of, 20; Influence upon Greek Geometry, 9; Manuals of, 1n; Name of 1, 7, 88n; Origin, 2-6, 20, 25 \*et seq.\*, 30; Practical, 2n; Problem of, in Śulba-sūtra, 2; Propositions of, in the Śulba, 21, 22, 24; (q. v.). Gopāla, 10. Gṛhya-sūtra, 1n. ### [c24.9](https://indike.org/pramana/ins.science.datta-1932.c24.9) Haṃsamukhī, 82 Hankel, 50-51, 104, 106, 107. Health, 111. Hemādri, 13. Hindu Geometers, 50. Hindu Geometry. (See Geometry,) Hiraṇyakeśī Śulba, 2, 29. Horse Sacrifice, 173. Hotrīya, 34. ### [c24.10](https://indike.org/pramana/ins.science.datta-1932.c24.10) Indeterminate Equations, 180-86. Indeterminate problems, 178 et seq. Irrationality, of √2. (See Surds.) Irrationals, first discovery by the Hindus, 115 et seq. Iṣṭi-yajña, 21. ### [c24.11](https://indike.org/pramana/ins.science.datta-1932.c24.11) Jainas, Canonical works of the, 201-2. Jānu, 101. Junge, 106. ### [c24.12](https://indike.org/pramana/ins.science.datta-1932.c24.12) Kalpa-sūtra, 1, 1n. Kāmya Agni, 22, 24, 38, 120, 121. Kapardisvāmī, 10, 13, 19. Kapiṣṭhala Saṃhitā, 28. Kaṅka, 28. Karaṇī, 188. (See Surds.) Karavindusvāmī, 10, 14-17. Karma-dīpikā, 11. Kalā, 212. Kāṭhaka Saṃhitā, 28. Kātyāyana, 1, 4-5, 10-11, 26. Koṭihoma-vedi, 152. Kṛṣṇa-yajur-veda, 2. Kuṇḍakṛti, 11. Kūrma, 23. ### [c24.13](https://indike.org/pramana/ins.science.datta-1932.c24.13) Lakṣahoma-vedi, 152. Leonardo Febonacci of Pisa, 180. Līlāvatī, 12. Line, 222; Angular units of, 69. (See also Straight Line.) ### [c24.14](https://indike.org/pramana/ins.science.datta-1932.c24.14) Magnitudes, 2-3. (See also Circle, Spatial Relations and Magnitudes.) Mahādeva, King of Devagiri, 13. Mahā-vedi, 22, 64, 96-97, 98, 153. (See also Saumiki-vedi) Mahāvīra, 180. Mahīdhara, 10; Works of, 11. ### [c24.15](https://indike.org/pramana/ins.science.datta-1932.c24.15) Maitrāyaṇa, Brāhmaṇa, 25; Śrauta-sūtra of, 2; Sulba-sūtra of, 6; Sulba, 12; Saṃhitā, 98, 28n. Mānava, Śrauta-sūtra of, 2; Śulba-sūtra of, 5-6; commentary of Sivadāsa, 12. Mantramahodadhi, Age of, 11. Mārjālīya, 34, 43. Maśaka, 2. Mathematics, Jaina school of, 201n; Problems of Hindu, 2. Measures, Areas and Volumes of, 95 et seq.; kinds of, 8. Mensuration, 95. ### [c24.16](https://indike.org/pramana/ins.science.datta-1932.c24.16) Nata, 67. Nemicandra, 201. Nirūdhapaśubandha, 21; -vedi, 137. Nitya, 20. Nitya Agni, 21. Nyañchana, 58. ### [c24.17](https://indike.org/pramana/ins.science.datta-1932.c24.17) Oldenberg, 27. ### [c24.18](https://indike.org/pramana/ins.science.datta-1932.c24.18) Pādya, 14. Paitṛki-vedi, 22, 75, 113. Pākayājñikī-vedi, 152. Pakṣeṣṭaka, 67-68. Pañcadaśa-bhāga, 22. Pañcaguṇa, 212. Pañcakarṇa : vide Pentalateral. Pañcama (Pañcama-bhāga), 212. Pañcamī, 44n. Pañcāgni, 62. Parallelogram, Construction of, 67-70; Measurement of area of, 96. Paricāyya, 23. Paricāyya-cit, 150. Pārśvamāni, 221. Paśu-yajña, 21. Pātīnī, 62. Paurṇamāsa sacrifice, 21. Pentagon, 80-82. Pentalateral, 80-82. Perpendicular, Construction of, 52-55. Pitr-yajña, 98. ### [c24.20](https://indike.org/pramana/ins.science.datta-1932.c24.20) Postulates, 41 \*et seq.\* ; Circle, divisibility, 42; Circle, maximum square described within a, 49; Diagonals, mutual bisection; 44; Diagonals of a rhombus, perpendicular bisection, 45; Rectangle, bisection by diagonal, 43; Rectangle, relation with a parallelogram, p. 48; Rectangle, relation with the rhombus inscribed, 48; Square, relation with the square inscribed, 47; Square, relation with the triangle inscribed, 47; Straight line, equal divisibility, 41; Triangle, bisection of an isosceles, 46; Triangle, equal and similar division. 42. (See also \*Śulba.\*) ### [c24.21](https://indike.org/pramana/ins.science.datta-1932.c24.21) \*Prācī\*, 221. ### [c24.22](https://indike.org/pramana/ins.science.datta-1932.c24.22) \*Prāgvaṃśa\*, 22. ### [c24.23](https://indike.org/pramana/ins.science.datta-1932.c24.23) \*Pramāṇa\*, 196. ### [c24.24](https://indike.org/pramana/ins.science.datta-1932.c24.24) \*Praüga\*, 23. ### [c24.25](https://indike.org/pramana/ins.science.datta-1932.c24.25) \*Praüga-citi\*, 121. ### [c24.26](https://indike.org/pramana/ins.science.datta-1932.c24.26) Prism, Volume of a, 101. ### [c24.27](https://indike.org/pramana/ins.science.datta-1932.c24.27) Proclus, 178. ### [c24.28](https://indike.org/pramana/ins.science.datta-1932.c24.28) Progression, Arithmetical, 217-18. ### [c24.29](https://indike.org/pramana/ins.science.datta-1932.c24.29) Problems, Geometrical, 22-23; Solutions of, 52 \*et seq.\* (See Constructions, and Indeterminate Problems.) ### [c24.30](https://indike.org/pramana/ins.science.datta-1932.c24.30) \*Pṛthvī\*, 221. ### [c24.31](https://indike.org/pramana/ins.science.datta-1932.c24.31) \*Puruṣa\*, 102. ### [c24.32](https://indike.org/pramana/ins.science.datta-1932.c24.32) \*Puruṣābhāsa\*, 157. ### [c24.33](https://indike.org/pramana/ins.science.datta-1932.c24.33) Pyramid, Volume of the Frustum of, 101-3. ### [c24.34](https://indike.org/pramana/ins.science.datta-1932.c24.34) Pythagorean Theorem, 24, 71, 104, \*et seq.\*; Arithmetical character \*vs.\* Geometrical character, 107-8; Bhāskara's proof, 118; Chinese origin, 118; Converse, 105-6; Early History, 119-22; Early knowledge and employment, 32-33; Geometrical proof of the Hindus, 115-19; Hindu \*vs.\* Greek origin, 106 \*et seq.\*, 118. ### [c24.35](https://indike.org/pramana/ins.science.datta-1932.c24.35) Q. E. F., Corresponding term in Hindu constructions, 50. ### [c24.36](https://indike.org/pramana/ins.science.datta-1932.c24.36) Quadratic Equation, 165 \*et seq.\*: Solutions of complete, 166 \*et seq.\*; Discrepancies, 168 \*et seq.\*; Solutions of pure, 165; ax²+bx=c, 165; x²=1+m/972, 165; x²=1+2m/15, 166; 7x²+½x=7½+m, 166 \*et seq.\* ### [c24.37](https://indike.org/pramana/ins.science.datta-1932.c24.37) Quadrature, of a circle, 40. ### [c24.38](https://indike.org/pramana/ins.science.datta-1932.c24.38) Quadrilateral, 47, 48. (See also Square.) ### [c24.39](https://indike.org/pramana/ins.science.datta-1932.c24.39) \*Rāma\*, 10-12. ### [c24.40](https://indike.org/pramana/ins.science.datta-1932.c24.40) \*Rāmacandra\*, 13. ### [c24.41](https://indike.org/pramana/ins.science.datta-1932.c24.41) \*Rathacakra\*, 23. ### [c24.42](https://indike.org/pramana/ins.science.datta-1932.c24.42) \*Rathacakra-citi\*, 120, 150. ### [c24.43](https://indike.org/pramana/ins.science.datta-1932.c24.43) Rational Rectangle, 109, 123 \*et seq.\*, 178 \*et seq.\*; Derivation, Āpastamba's formula, 136; by the Hindus, 136; Early History of, 138-39; Euclid's formula, 135-36; Hindu discovery, 124-27; Hindu knowledge of general rules, 127-39; Number of, known to the Hindus, 127; Plato's formula, 134-36; Pythagoras's discovery, 127; Pythagoras's formula, 133-36. (See also Rational Rectangle.) ### [c24.44](https://indike.org/pramana/ins.science.datta-1932.c24.44) Rational Right-angled Triangle, 178-80. ### [c24.45](https://indike.org/pramana/ins.science.datta-1932.c24.45) Rectangle, construction, given sides, 22, 62-63; Equal to a square, 23; Diagonical bisection, 43; Measurement of, 95, 96 \*et seq.\*; Square on the diagonal equal to sum of the squares on the sides, 24; Transformation into isosceles trapezium, 90-92; rhombus, 93-94; square, 83-85, 206; triangle, 92. (See also Construction, Postulates, Rational Rectangle, Rhombus and Square.) ### [c24.46](https://indike.org/pramana/ins.science.datta-1932.c24.46) Rectilinear figure, measurement of, 95; construction, having given area, 98. ### [c24.47](https://indike.org/pramana/ins.science.datta-1932.c24.47) \*Ṛg-Veda\*, \*Saṃhitā\*, 27 \*et seq.\*; Schools of, 1n. ### [c24.48](https://indike.org/pramana/ins.science.datta-1932.c24.48) Rhombus, Construction, equal to square, 23; Diagonals bisect mutually, 45; Formation by joining the middle points of the sides of a rectangle, 48. (See also Postulates, Rectangle and Square.) ### [c24.49](https://indike.org/pramana/ins.science.datta-1932.c24.49) Right-angle. (See Straight Line.) Right-angled Triangle, 105; Construction, Kapardisvāmi's, 13, Karavindasvāmi's, 14-16; Rāma's, 11. Rodét, 208. Root, Hindu name of, 188. Rule of Three, Bhāskara's (Second), 12; Līlāvatī's, 12. Ruler, use in construction, 33. ### [c24.50](https://indike.org/pramana/ins.science.datta-1932.c24.50) Sacrifice, Darśa, 21; Iṣṭi, 2; Nirūḍhapaśubandha, 21; Obligatory, 20; Optional, 20, 23; Paśu, 21; Paurṇamāsa, 21; Soma yajña, 21; Vedic, 20 et seq. Sadas, 34. Ṣaḍguruśiṣya, 18. Samara-sāra, 11. Samara-sāra-saṃgraha, 11. Śmaśāna, 23. Sāma-Veda, Schools of, 1n. Saṃhitā: see Kapiṣṭhala Saṃhitā, Kāṭhaka Saṃhitā, Maitrāyaṇīya Saṃhitā, Ṛg-Veda Saṃhitā, Taittirīya Saṃhitā, Vājasaneya Saṃhitā. Samūhya 23. Samūhya-cit, 150. Śankarabhaṭṭa, 12. Śāṅkhyāyana Gṛhya-paddhati, 11. Saptama-karaṇī 188. Sapta-ridha, 170. Śaradā-tilaka Tantra, 11. Sarvābhyāsa, 157. Śatapatha Brāhmaṇa, 27n, 28 et seq., 28 n. Saumikī-vedī, 22, 64-67. (See Mahā-vedī.) Sautrāmaṇī-vedī, 22, 75, 98, 107, 152 et seq., 186. Saviśeṣa, 188, 196-202. Sāyaṇa, 12. Scalene triangle, Source of discovery by the Hindus, 45. Schopenhauer, 107. Segment of a circle, Hindu method of finding area, 17. Series, Early reference, 217; Progressive, 217-18. Similar Figures, 40, 152 et seq.; Construction, given a side, 162. (See also Trapezium.) ### [c24.51](https://indike.org/pramana/ins.science.datta-1932.c24.51) Simple Equation, solution of, 177. Śivadāsa, Commentator of Mānava Sulba, 12. Śmaśāna-cit, 101 et seq. Ṣoḍaśī, 197n. Soma-yajña, 21. Spatial dimensions, 215. Spatial relations and magnitude, 2 et seq.; 25 et seq. Square, 27, 40; Area, on its diagonal is double its area, 22, 109 et seq.; History of the theorem, 40, 105 et seq., 114-15; Area, on the diagonal of a rectangle equal to sum of squares on sides, 24, 27. (See Pythagorean Theorem.) Area, double of a triangle on the same base and with equal altitude, 47. To construct area equal to 108 sq. padas, 98-99; equal to a simple multiple or submultiple of another, 23; equal to the sum or difference of two equal, 23; To construct, a circle equal in area of a, 21, 140-43; and vice versa, 21, 140-43; To construct, having given the side, 21, 33, 55-62; To construct a triangle or rhombus equal to a, 23. Enlargement of a, 176; Mensuration of a, 176 et seq.; Relation with the quadrilateral formed by joining the middle points, 97; Size, maximum, within a circle, 49; To transform, into an isosceles trapezium, 90-92; from an isosceles triangle, 92-93; into a rectangle, 23, 85; from a rectangle, 23; into a rhombus, 93, from a rhombus, 94, into a triangle, 92; (See also Areas, combination of, Circle, Construction, Postulates, Pythagorean Theorem, Rectangle and Rhombus.) Śrauta-sūtra, 1-2. Śruti, source of Geometry in, 26-27. Straight line, to draw at right angles to another, 52-55; Equal division of a, 40-41. (See Postulates.) Śulapāṇi, 13. Śulba, Definition of, 7-8; Early origin of matter in, 39; Postulates of, 41 et seq.; -proof vs. ### [c24.52](https://indike.org/pramana/ins.science.datta-1932.c24.52) Euclidian proof, 50; Technical terms of, 221-26. (See \*Śulba-sūtra.\*) \*Śulba-dīpikā\*, 10. \*Śulba-mīmāṁsā\*, 10 \*Śulba-Pradīpa\*, 10. \*Śulba Pradīpikā\* 10. \*Śulba-sūtra\*, of Āpastamba, 3-4; of Baudhāyana, 2-3; Classification of, 6-7; Commentators of, \*q.v.\*; Definition of, 1-7; Number of, 1, 1n; π evaluated according to, 18; Problems of Geometry in, 2, 2n; Study of, 12; Time of, 6-7. \*Śulba-sūtra-vivaraṇa\*, 10. \*Śulba-sūtra-vṛtti\*, 10. \*Śulba-vārttika\*, 11. \*Śulba-vyākhyā\*, 10. Sundararāja, 10, 87 \*et seq.\*; Age of, 17-18. \*Suparṇa-citi\*, 34n. \*Suparṇa Garutman\* (or \*Suparṇa\*), 34. Surds, 185 \*et seq.\*; Evaluation of some, 205; Formula, approximate, 206-11; Hindu knowledge of, 185; Hindu knowledge of the irrationality of √2, 195-203; Rationalisation of simple, 185; \*Śulba\* name of, 188; Value of √2, 188-89; Hindu origin of, 189-94; Value of √3, 194-95. \*Śyena\*, 34. \*Śyena-cit\*, 22-23. (See Altar, falcon-shaped; \*Caturasra-Śyena-cit\*, \*Vakrapakṣa-Śyena-cit\*). Symmetry, Line of, 221. ### [c24.53](https://indike.org/pramana/ins.science.datta-1932.c24.53) \*Taittirīya Brāhmaṇa\*, 25. \*Taittirīya Saṁhitā\*, 25-26, 28-31. Terminology, 212-13. Terms, Technical, 221-26. Theorem, Geometrical, 21-22, 24; Pythagorean, 24, 104 \*et seq.\* Thibaut, 86 \*et seq.\*, 108 \*et seq.\* \*Tiryaṅmānī\*, 221. Transformation, Geometrical, 23. Trapezium, Area of, to find the, 22; Isosceles, to construct an, face, base and altitude given, 22, 31-32, 63-67; similar and equal to a third of another, 153; similar and double its area, 154; similar and n times its area, 154; similar and equal to multiple or sub-multiple of another, 22; similar to a given one and having a given altitude, 163; Isosceles, having an area of 324 sq. padas, 99-101; Measurement of, 95-96; Isosceles, to transform a square or rectangle into an, 90-92. (See also Construction, Rectangle and Square.) \*Trayodaśa\*, 212. Triangle, area of a, is half the square on the same base and equal altitude, 47; To construct a, equal to a square, 92; Division of a, into equal and similar parts, 46; Isosceles, to bisect an, 46-47; Measurement of, 95, 96. (See also Postulates, Rectangle, Right-angled Triangle, Scalene triangle and Square.) \*Tri-aṣṭama\*, 213. \*Triguṇa\*, 212. \*Trī-karaṇī\*, 109, 188. \*Triśatikā\*, Age of, 11. \*Tṛtīya-karaṇī\*, 109, 188. ### [c24.54](https://indike.org/pramana/ins.science.datta-1932.c24.54) \*Ubhadataḥ praüga\*, 23. \*Ubhayı̄\*, 45. \*Uparava\*, 34. \*Uttara vedi\*, 33, 34. ### [c24.55](https://indike.org/pramana/ins.science.datta-1932.c24.55) Vādhula, 2. \*Vājasaneya Saṁhitā\*, 28. \*Vakrapakṣa-Śyena-cit\*, 38, 112 \*et seq.\* \*Vakrapakṣa-Vyastapuccha-Śyena\*, 23. \*Vakrapakṣa-Vyastapucchā-Śyena-cit\*, 197n Varāha, 2, 6. Vedāṅga, Meaning of, 1. \*Vedārtha-dīpikā\*, 13. Vedi, Configuration of, 221; Enlargement of, 158 \*et seq.\*; Line of symmetry, 221; Relative position, 30; Time of existence, 39. Vedic Altars, 20 \*et seq.\* ### [c24.56](https://indike.org/pramana/ins.science.datta-1932.c24.56) Vedic Sacrifices, 20 \*et seq.\* Venkateśvara Dīkṣhita, 10. \*Viśeṣa\*, 196-202. (See also \*Abhyantara-Viśeśa\*, \*Vāhya-viśeṣa\* and \*Saviśeṣa\*. \*Viṣṇubhakti-Kalpalatā-prakāśa\*, 11. Volume, measurement of, 101-8. ### [c24.57](https://indike.org/pramana/ins.science.datta-1932.c24.57) \*Yajur-Veda\*, 28; Schools of, 1n. ### [c24.58](https://indike.org/pramana/ins.science.datta-1932.c24.58) π, 18, 148-49. √2, 11, 12, 188-89, 202-3 (See also Surds.) √3, 194-95. 1/√3, 19. √5, 203-6. √29, 205-6. √61, 205-6. --- Source: [https://indike.org/pramana/ins.science.datta-1932.c24](https://indike.org/pramana/ins.science.datta-1932.c24) · Pramāṇa