The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t37: Chapter 12: Diagonal of a Right Triangle
The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t37
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- English
Chapter 12: Diagonal of a Right Triangle
c8.t37.2
This chapter deals with the method of calculating the diagonal of a right triangle when its other sides are known. Sometimes out of three sides any two are known, when the third can be calculated. The length is known as measure or *pramāṇa* or *pārśvamānī*, breadth *veśeṣa* or *tiryaṅmānī*, and diagonal *akṣṇayā*.
c8.t37.3
(i) If length=a, breadth=a2-a12=512 a,
c8.t37.4
diagonal produces a square equal to (1312 a)²
c8.t37.5
(ii) If length=a2, diagonal=a2+a24=1324 a,
c8.t37.6
then breadth produces a square equal to (524 a)².
c8.t37.7
By applying this, two fold producer (√ 2a), three fold producer (√ 3a), twenty-one fold producer (√21 a) used for the *aśvamedha vedi*, and 101 fold producer are obtained.
c8.t37.8
This also justifies that $1²+(√10)²=11.$