The Science of the Shulba: A Study in Early Hindu Geometry c24.51

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.