The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t31.13

c8.t31.13

**6.7.** *Construction of a square equal to n times the given square.* This method undoubtedly hints at the construction of a square which is equivalent to n times a given square. Let n number of equal squares each of side a are to be combined. *Śulbakāras* used isosceles triangles for different constructions. Here also Kātyāyana possibly considered an isosceles triangle ABC, in which {cl} & BC=(n-1)\ a, / & AB+AC=(n+1)\ a, / Since & BD=DC, AB=AC, / & BD=\cfrac{n-1}\ a, and AB=\cfrac{n+1}a, According to this rule, the altitude AD will produce the sum of n equal squares. Now AD²[t] &=AB²-BD² / &=((n+1)/2a)²-((n-1)/2a)² / &=na²