The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t1.33

c8.t1.33

**1.9-1.11.** Here Baudhāyana states that in a square *ABCD*, AC²=2 AB² [since AB=BC] or AC=√2 AB, where *AC* is known as the *dvikaraṇī* of the measure *AB*. If AB=a, AC=√2 a, where *a* is the measure. The result is sometimes considered by scholars as a particular case of the more generalized rule given by Baudhāyana in *Bśl.* 1.10. But Baudhāyana gave no such hint. On the other hand, he has tried to establish a more generalized result on the basis of this statement. According to him, when the measure of the side of a square is *a*, its diagonal is √2 a. Then again the measure of the diagonal of a rectangle having sides *a* and √2 a, is √3 a, for a²+(√2 a)² = (√3a)²; √3a is known as the *tṛkaraṇī*. This result has been extended