The Science of the Shulba: A Study in Early Hindu Geometry c6.19

c6.19

The *Śulba-sūtra* of Manu is a small treatise composed in both prose and verse. It is divided into seven *khaṇḍas* (or "parts," "sections"). In the first section is given a description of the measuring tape, the gnomon, measures, four methods of determining the cardinal directions and also a method of constructing a square on a given straight line. It may be noted that we do not find in the Āpastamba and Baudhāyana *Śulba-sūtras* any method of determining the cardinal directions, though it is essentially necessary for the proper construction of the sacrificial altars to have an accurate knowledge about them. They proceed on the assumption that the cardinal directions are already known. Kātyāyana teaches three methods for the same, while Manu teaches as many as four. The sections ii-vi treat of the relative positions, spatial magnitudes and also the methods of the construction of the the different *vedis*. Here we find mention of certain *vedis*, *e.g.*, the *Pākayājñikī*, *Māruti* and *Vārunī vedis* which are not included in the abovementioned manuals. The last section of the *Mānava Śulba-sūtra* furnishes us with some hints about the sacrificial fees. It also describes the method of the construction of the *Suparṇa-citi*. This *citi* is not found in other *Śulba-sūtras*. But for the head, its spatial magnitudes are the same as those of the most primitive *citi*, the *Saptavidha-sāratni-prādeśa-caturasra-śyena-cit*, described by Baudhāyana and others.