History of Dharmashastra (Ancient and Mediaeval Religious and Civil Law in India) v6.c82.797

v6.c82.797

As incidental to the colossal figures of the years of Kalpas and Yugas, a few words on numerals, their antiquity and the methods of writing numerals would not be out of place, In the Ṛgveda numerals from 1 to 10 are frequently used. ‘Sahasra’ (thousand) and ‘ayuta’ (ten thousand) occur in Ṛg. IV. 26. 7, VIII. 1 5, VIII 21 18 One of these says¹⁰⁹⁶ ‘O wielder of thunderbolt! O immensely rich (Indra)! I shall not give thee away even for a big price, not for a thousand, not for ten thousand, nor for hundreds’. In Ṛg VIII 46. 22 a poet says ‘I secured 60000 and several tens of thousands of horses, 20 hundreds of camels, one thousand dark-coloured mares and ten thousands of cows bright in three parts of their bodies’ In Ṛg I. 53 9 Indra is said to have struck down sixty thousand and 99 enemies. Vide Ṛg. I. 126 3 (for sixty thousand cows), VIII 4. 20 and VIII 46 29 for 60000 and VI. 63 10 for one hundred thousand horses. In some of these the larger numbers are mentioned first and the smaller ones next (as in Ṛg I. 53 9, VIII. 46 22); in others it is the reverse No conclusion can therefore be drawn that the smaller numbers come first in the Ṛgvedic times In Tai. S IV 4 11 3–4 reference is made to bricks in numbers from one, one hundred, thousand, ayuta (ten thousand), niyuta, prayuta, arbuda, nyarbuda, samudra, madhya, anta and parārdha, while in Tai S VII 2 11–19 various numbers from one to one tions of man There is a good deal of literature on this subject which is passed over here as not material for our purpose One of the latest works on this system is ‘From Zero to Infinity’ by Constance Reid (Routledge and Kegan Paul, London, 1956). Zero is the first of ten symbols with which one can represent an infinitude of numbers and it is also the first of the numbers. This work says that the zero escaped even the greatest Greeks, Pythagoras, Euclid and Archimedes (p 4) The Egyptians¹¹⁰² had a decimal system of numerals but no sign for zero and therefore no positional notation, which even the Greeks did not know, ancient Babylonians also had no definite symbol for zero and there is no example of zero signs at the end of numbers even in their latest astronomical writings It is difficult to say when exactly a symbol or word for zero was employed in India But it must have been several centuries before the beginning of the Christian era Pingala’s work on metres is a *vedāṅga* Pingala’s sūtra on metres makes use of zero (śūnya) in VIII 28-31. Even the Śatapatha Br. (XI. 4 3 20) seems to be aware of Vedāṅgas. But it may be argued that there is nothing to show that Pingala’s work was known to it It is most probably mentioned as Chandoviciti in the Āpastamba-dharmasūtra ¹¹⁰³ Śabara¹¹⁰⁴ (about 200 A D. and not later than 400 A D.) speaks of Piṅgala's work as on the same level with Pāṇini's sūtra It is unnecessary to offer further proofs of the antiquity of Piṅgala's sūtra.