The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t1.15

c8.t1.15

*Second Method.* Let *XS*, the given measure (*pramāṇa*) be *a* and *XY*, the increased cord, 2*a* (Fig. 2(a)). *S* is the mark at the middle of *XY*; then *XS* measures the length for *prācī*. *T* is the *nyañcana* mark, so that *ST*=½*a*—¼*a*=¼*a*. *U* is another mark at the middle of *SY*. *XT*, the diagonal (*akṣṇayā*) = a+¼a=5/4a *TY*, the breadth (*tiryaṅmānī*) = 2a-5/4ι=¾a Clearly, a²+(¾a)²=(5/4ι)² In other words, XY²+YT²=XT².