Geometry in Ancient and Medieval India c8.2

c8.2

**3.1.** To the period of mathematical development represented by the *Śulbasūtras*, probably belongs the mathematical knowledge of the Jainas too. Dating their canonical literature is as difficult as the dating of the Vedic literature. For long Vardhamāna Mahāvīra, of about the same period as the Buddha, was held to be the founder of Jainism. But Mahāvīra is actually the last of the *Tīrthaṁkaras* and some of the earlier *Tīrthaṁkaras* and *Cakravartins* like Ṛṣabha and Bharata are well known in Hindu Purāṇic literature also. Hence it is more likely that this dissident faith, revolting against sacrificial killing, was quite an old rival to the Vedic faith or that it had taken root in India even before the Vedic faith. The mathematical knowledge contained in the Jaina religious writings should therefore have been more or less parallel to that in the Vedic literature. Whereas the practical necessity of building the altars turned the sacrificing Vedic tribes to mathematics, to geometrical constructions, the Jainas were impelled to indulge in mathematical calculations by an abstract love of precision. Still the connection between the two is easily noticed. The trapezium, the shape of the *Mahāvedi* of the Vedic religion, which in the speculations of the *Brāhmaṇas* attained cosmic significance, reappears in Jaina cosmography as the shape of the universe, the shape of the mountains, and the shape of the *varṣas* (the continents). Along with this geometrical figure, the circle and its parts also came to assume great importance, since the earth and the orbits of the heavenly bodies were given a circular shape. And so the geometry or rather mensuration of the circle and the trapezium constitutes the geometry of the Jaina religious literature.