The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t1.29
The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t1.29
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- English
c8.t1.29
Let *XS* be the cord of given measure *a* [Fig. 4(a)] ;
XY=1½a=3/2a ;
SY=½ a;
*T* the *nyañcana* mark.
∴ XT=a+(⅓·½ a-⅙·½ a)=a+1/12 a=13/12 a
and TY=½ a-1/12a=5/12 a
The relation a²+(5/12 a)² = (13/12 a)² holds,
i.e., XY²+YT²=XT².