Geometry in Ancient and Medieval India c8.s2.3

c8.s2.3

trapezium must have been a familiar geometrical figure in their literature from very early times. In the Jyotiṣkaraṇḍaka (10th Prābhṛta V. 190-91) we find a simple rule for calculating the diameter at any height of a mountain shaped like the frustum of a cone. The rate of increase of the diameter is given by $(diameter at base—diameter at top)/height$ Hence the height at which the diameter is required should be multiplied by this ratio and added to the diameter at the top to get the diameter at that height. The geometrical fact that corresponding elements in similar figures are proportionate, known to the authors of the *Sulbasūtras* and the *Brāhmaṇas*, who increased the size of the *vedis* without altering their shape or the proportions of their parts, is apprehended in a more comprehensive and scientific way here. The *Tiloyapaṇṇatti*, which from the quotations from and the references to it in other works must be an early work, has a fuller treatment of trapezia and trapezoidal solids and a fuller application of the properties of similar figures. But since the extant version of the *Tiloyapaṇṇatti* belongs to a much later period, the work is reserved for treatment in a later chapter.