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Indian Epigraphy c15.t3: 3. Numbers expressed by Letters

Indian Epigraphy c15.t3

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3. Numbers expressed by Letters

c15.t3.1

The celebrated astronomer Āryabhaṭa, who wrote his Āryabhaṭīya at Pāṭaliputra in the Kaliyuga year 3600 (499 A.D.), used a system of representing numbers by letters of the alphabet.¹ The 25 consonants from *ka* to *ma* indicated respectively the numerals 1 to 25. The 8 letters from *ya* to *ha* similarly indicated the numbers 30, 40, 50, 60, 70, 80, 90 and 100 respectively. The vowels *i*, *u*, *ṛ* and *ḷ* (short or long) and the diphthongs *e*, *ai*, *o* and *au* were added to the letters to indicate the multiplication of a number by 10² to 10¹⁶, i.e. the addition of two, four, six, eight, ten, twelve, fourteen and sixteen zeroes after a number indicated by a consonant. Thus *ga*=3, *gi*=300, *gu*=30000, *ya*=30, *yi*=3000, *yu*=300000, *ri*=4000, *giri* (or *gri*)=4300 (300+4000), etc.

c15.t3.2

¹ Cf. Filliozat, op. cit., p. 188. See above, p. 222.

c15.t3.3

A system developed in South India was called Kaṭapayādi. In this, the 10 letters from *ka* to *ña* had the value respectively of the numbers 1 to 9 and 0. The same was the case with the following 10 letters from *ṭa* to *na*. The five letters from *pa* to *ma* indicated the numbers 1 to 5, and the 9 letters from *ya* to *la* had the value of the numbers 1 to 9 respectively. In the formation of chronograms, vowels were added to the consonants without affecting the numerical value of the letters and two or more consonants could be combined in conjuncts in which only the last consonant of a ligature had the numerical value. But the principle of *vāma-gati*, i.e. the turning round of the sum, was observed in the determination of the value of a word. Thus *ga*=3 and *ja*=8; but the word *gaja*=83 and not 38. The chronogram *khago=ntyān=meṣam=āpa* would give *kha*=2, *ga*=3, *ya*=1, *ma*=5, *ṣa*=6, *ma*=5 and *pa*=1, i.e. 1565132.¹

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¹ See Bühler, op. cit., p. 87; Ojha, op. cit., 122 ff. See above, p. 222.

c15.t3.5

The Nannādi system popular in Kerala was based on the following lines : *na-nna-nya-ṣka-jhra-hā(ha)-gra-pra-dre-ma* | *tha-li(la)-pia-ba-tra(tru)-tri-ca-ṇa-ña* ||²

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² Cf. *JRAS*, 1896, p. 790; *Trav. Arch. Ser.*, Vol. II, pp. 132. ff.

c15.t3.7

The 10 letters of the first line had the value respectively of the numbers from 1 to 10 while the others in the second line represented 20, 30, 40, 50, 60, 70, 80, 90 and 100. This system was generally employed in paginating manuscripts.

c15.t3.8

In a simpler system prevalent in South India, the letters of the alphabet from *ka* to *ḷa* represented respectively the numbers 1 to 34, *kā* to *ḷā* the numbers 35 to 68, *ki* to *ḷi* the numbers 69 to 102, and so on.

c15.t3.9

There was a similar system of paginating manuscripts prevalent in Ceylon. According to this *ka*, *kā*, *ki*, *kī* *ku*, kū, kṛ, kṛ, kl, kl, ke, kai, ko, kau, kaṃ and kaḥ had the value respectively of 1 to 16. Similarly 16 akṣaras formed by kha khā, etc., had the value of the numbers from 17 to 32. The 16 akṣaras associated with ḷa, the last consonant of the alphabet, thus represented the numbers 529 to 544. Numbers beyond 544 could be expressed by beginning again as 2 ka, 2 kā, and so on. In Burma, the same system was used with the omission of ṛ, ṝ, ḷ and ḹ, so that ka to kaḥ would indicate the numbers 1 to 12.

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