The Science of the Shulba: A Study in Early Hindu Geometry c17.79

c17.79

We have so far considered the construction of figures, particularly isosceles trapeziums, similar to a given one and differing from it in area by a specified amount. It is sometimes also necessary to construct a figure, similar to another and having a given side. For instance, the *Ekādaśinī-vedi* is stated to be similar to the *Mahāvedi* and is indeed an enlarged form of it.² It is so called because it must have, according to the injunction of the scriptures, eleven (*ekādaśa*) sacrificial posts (*yūpa*) in front. It is further prescribed that the two posts on either sides of the middle one must be at a distance of one akṣa (=104 aṅgulis) and four aṅgulis from it and the rest are an akṣa distant from each other. Each post has a diameter of one pada. Hence the east side of the *Ekādaśinī-vedi* is 10 akṣas 11 padas 8 aṅgulis long. Thus it is required to construct an isosceles triangle similar to the *Mahāvedi* and having its face equal to this length. Again, according to Baudhāyana, the shape of the *Aśvamedha-vedi* is similar to the *Mahāvedi* and has 21 yūpas on the east side, that is, has a face of 20 akṣas 21 padas 8 aṅgulis long.