The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t1.46

c8.t1.46

(iv) According to Datta,e the construction of the *paitṛki vedi* established the theorem of square on the diagonal. The altar is mentioned in the *Śatapatha Brāhmaṇa* (XIII.8.1.5) as a square with its corners pointed towards the cardinal directions. It is referred to by Baudhāyana (*Bśl.* 3.11) and also by Kātyāyana (*Kśl.*2.2), where the method of its construction in detail has appeared. The square *EGWH* obtained by joining the middle points of a square *ABCD* (of area 2 sq. *puruṣas*) is the *paitṛki vedi* and is half (in area) of the original square (Fig. 29). The original square *ABCD* is a square on its east-west line *EW*. *EW* is again the diagonal of the newly formed square *EGWH*. This is undoubtedly a convincing proof (since *EW*²=2 *EG*²).