Mathematics in Ancient and Medieval India c6.s9.22

c6.s9.22

a) *Similar triangle* : In the *Śulbasūtras*, many similar figures were drawn, though there is no mention of the actual proportional relationship of the corresponding parts of the two similar figures. In the *Sūryasiddhānta* (c. 400 A. D.) and other astronomical treatises we meet with such proportional relationship between two similar figures.¹ The result like, “*Ksitijyā* (earth sine) multiplied by the *Vyāsārdha* (radius) and then divided by the *dina-vyāsadala* (day-radius) gives the *caradala* (ascensional difference)” is the direct application of this proportional relations of the similar triangles. Āryabhaṭa I (c. 476 A. D.) used this proportional relationship of the corresponding sides in case of similar triangles to solve shadow problems.² Similar application of many other astronomical and geometrical problems was found in the works of Brahmagupta³ and other later scholars.⁴