Mathematics in Ancient and Medieval India c6.s7.7

c6.s7.7

Various rules of construction and transformation occurring in the *Śulbasūtras* are : 1) the so-called Pyathagorian theorem, 2) the properties of similar figures, 3) the circle squaring, 4) construction of right triangle, 5) calculation of areas, through different division and transformation of figures. The first two of these topics enter largely in the later Hindu Mathematics and astronomy which will be seen in our subsequent discussion on geometry of Āryabhaṭa I, Brāhmagupta, Bhāskara II etc. That the later Hindu mathematicians did not lose their interest as regards circle squaring can be found from our discussion on the method of construction of a right triangle. It is mainly found in the works of Brahmagupta, Mahāvīra and others. The item 5) does not appear in the later Hindu works on mathematics in the particular manner in which they occur in the *Śulbasūtras*. But that the later mathematicians were interested in finding the area of triangular, tetragonal and circular plots and the volume of a right prism, sphere, can also be seen from our discussion of geometry of Āryabhaṭa I, Brahmagupta, Mahāvīra and others. The history of development of arithmetic and algebra of the post-Vedic mathematics also shows that they were not unaware of the work of the *Śulbasūtras*. But in this connection, it must be clear that the first two items were used more significantly than others. Whitney's remark may be noted in this connection, “The two main principles, by aid of which the greater portion of all Hindu calculations are made, are, on one hand, the equality of the square of the hypotenuse in a right angled triangle to the sum of the square of the other two sides, and on the other hand, the proportional relation to the corresponding parts of similar triangles.”²