Pramāṇa · Search · About · API

Mathematics in Ancient and Medieval India c5.s1: Numbers

Mathematics in Ancient and Medieval India c5.s1

Language
English

Numbers

c5.s1.1

The Sanskrit names for the counting of numbers used in Vedic India from one to nine are : *eka*, *dvi*, *tri*, *catur*, *pañca*, *ṣaṭ*, *sapta*, *aṣṭa*, *nava*. Besides 10, multiples of 10 upto 100, separate names for numbers were recognised and named as follows : *daśa* (10), *viṁśati* (2× 10), *triṁśat* (3× 10)...etc. For larger numbers, ten and multiples of ten had formed the basis of numeration. While the Greeks had no terminology for denomination above myriad ( 10⁴ ) and the Romans above the mill ( 10³ ), the ancient Indians dealt freely with upto twelve denominations. The *Yajurveda Saṃhita* thus gives : *eka* ( 1 ), *daśa* ( 10 ), *śata* (10²), *sahasra* (10³), *ayuta* (10⁴), *niyuta* (10⁵), *prayuta* ( 10⁶ ), *arbuda* ( 10⁷ ), *nyarbuda* ( 10⁸ ), *samudra* ( 10⁹ ), *madhya* ( 10¹⁰ ), *anta* ( 10¹¹ ) and *parārdha* ( 10¹² ). The same list occurs in the *Taittirīya Saṃhita*, *Maitrāyaṇī Saṃhita* and others.¹ For expressing compound numbers lying between 10 and multiples of 10 upto 100, addition of simple numbers (from 1 to 9) was made to the required multiples. For example, *ekādaśa* (=1+10=11) *saptaviṃśati* ( =7+2 × 10=27 ), *aṣṭatriṃśat* ( =8+3 × 10=38 ) etc. Compound numbers above 100 were expressed as follows : *ṣaṣṭiṃ sahasrā sapta śatāni navatiṃ nava* (=60 × 10³ +7 × 10²+9 × 10 +9=60799 ). In certain special cases, the principle of subtraction was also in evidence. Thus number 19, 29 etc. were expressed as *ekānnaviṃśati* ( =20 – 1=19 ), *ekānna triṃsat* ( 30 – 1=29 ) respectively. In the *Sūtra* period, *ekānna* was changed to *ekona*. The principles explained above were also followed in the *Śulba-sūtras* and later works. In one instance, 972 is expressed as *aṣṭaviṃśatyūnaṃ sahasram*=1000–28 ( *Āpastamba-śulba*, 5. 7 ). The Babylonians ( c. 1600 B. C. ) introduced earlier sexagesimal scale of notation.² There is no evidence that the decimal scale of the Indians was derived from the Babylonians, though the principle might be the same. The decimal scale, as it could be seen afterwards, is in fact far more convenient and simple and is a natural way of expressing numerical value which has been adopted subsequently all over the world as the ideal system.

c5.s1.2

¹ *Yajurveda Saṃhitā*, 17. 2; *Taittirī ya Saṃhitā*, 4. 40. 11. 4 and 7. 2. 20. 1; *Maitrāyanī Saṃhitā*, 2. 8. 14; *Kāṭhaka Saṃhitā*, 17. 10; vide also *History of Hindu Mathematics* by Datta and Singh, Part I, Motilal Banarasi Das, Lahore, p. 9, 1935.

c5.s1.3

² Cajori, F. *A History of Mathematics*, 2nd revised and enlarged edition, p. 4.

Linked texts (4)