Indian Palaeography from about B.C. 350 to about A.D. 1300 c9.s1: § 33. — The numerals of the Kharoṣṭhī; Plate I

Indian Palaeography from about B.C. 350 to about A.D. 1300 c9.s1

Language: English

§ 33. — The numerals of the Kharoṣṭhī; Plate I

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¹ Compare E. C. BAYLEY, the Genealogy of the Modern Numerals, *J.RAS*, N.S., 14, 335 ff.; 15, 1 ff.

In the Kharoṣṭhī inscriptions of the Śakas, of Gondopherres, and of the Kuṣanas, from the 1st century B. C. and the 1st and 2nd centuries A. D., as well as in other probably later documents, we find a system of numeral notation (plate I, col. XIV)² which DOWSON first explained with the help of the Taxila copper-plate.³

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² The signs of col. XIV. have been drawn according to S.NEI, 3, pl. 1 (JA. 1890, I, pl. 15); *J.ASB.* 58, pl. 10; FLEET'S photograph of the Taxila copper-plate (EI. 4, 56); and a gelatine copy of the Wardak vase, kindly presented by S. VON OLDENBURG.

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³ *J.RAS.* 20, 228.

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Its fundamental signs are: — (*a*) One, two and three vertical strokes for 1, 2, 3. (*b*) An inclined cross for 4. (*c*) A sign, similar to the Kharoṣṭhī *A*, for 10. (*d*) A double curve, looking like a cursive combination of two 10 (BAYLEY), for 20. (*e*) A sign, resembling a Brāhmī *ta* or *tra*, for 100, to the right of which stands a vertical stroke, whereby the whole becomes equivalent to IC.

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The numbers lying between these elements are expressed by groups, in which the additional ones invariably are placed on the left. Thus, for 5 we have 4 (+) 1; for 6, 4 (+) 2; for 8, 4 (+) 4; for 50, 20 (+) 20 (+) 10; for 60, 20 (+) 20 (+) 20; for 70, 20 (+) 20 (+) 20 (+) 10. Groups formed of the signs for 10 (+) 1 to 10 (+) 9, and 20 (+) 1 to 20 (+) 9, and so forth, are used to express the numerals 11 to 19, and 21 to 29, &c.

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The higher numerals beyond 100 are expressed according to the same principle; thus, 103 is 100 (+) 3 or IC III. The sign for 200 consists of 100, preceded on the right by two vertical strokes. And the highest known number is IIC XX XX XX X IV, which means 274.⁴

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⁴ Thus CUNNINGHAM. SENART, op. cit., 17, reads 84, doubting the existence of 200 (which however is plain in the autotype of J.ASB. 58, pl. 10), while BARTH reads 284. There is at least one unpublished inscription with 200, and, according to a communication from BLOCH, also one with 300.

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The few numeral signs in the Aśoka edicts of Shāhbāzgarhī and Mansehra (plate I, col. XIII)⁵ show that in the 3rd century B. C. the Kharoṣṭhī system of numeral notation differed from the later one at least in one important point. Both in Shāhbāzgarhī, where the signs for 1, 2, 4, 5 occur, and in Mansehra, which offers 1, 2, 5, the inclined cross for 4 is absent, and 4 is expressed by four parallel vertical strokes, and 5 by five. It is as yet not ascertainable, how the other signs looked in the 3rd century B. C.

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⁵ Drawn according to BURGESS' impression of Shāhbāzgarhī edicts I—III, XIII.

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BURNELL and others⁶ have stated long ago that the Kharoṣṭhī numerals are of Semitic origin. And it may now be added that probably they have been borrowed from the Aramaeans.

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⁶ B.ESIP. 64; J.ASB. 32, 150.

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and that, with the exception of the cross-shaped 4, they have been introduced together with the Aramaic letters. According to [74] Euting's table of the ancient Aramaic numerals,¹ 1 to 10 are marked, as in the Aśoka edicts, by vertical strokes, which however, contrary to the Indian practice, are divided into groups of three. The Kharoṣṭhī 10 comes close to that of the Teima inscription, 𐡚, and the 20 resembles the sign of the Satrap coins, 3, which is also found in the papyrus Blacas² (5th century B. C.), and somewhat modified in the papyrus Vaticanus. Both the Aramaeans and the Phoenicians used the signs for 10 and 20 in the same manner as the Hindus, in order to express 30, 40, and so forth.

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¹ Nabatäische Inschriften, 96 f.

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² Corp. Inscr. Sem., P. Aram. 145 A (pointed out by Euting).

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For the Kharoṣṭhī 100, Euting's table offers no corresponding Aramaic sign, and that given in his edition of the Saqqārah inscription³ is, as he informs me, not certain. Hence, there remain only the Phoenician symbols 𐤕, 𐤐, which are suitable for comparison. But the close relationship of Phoenician and Aramaic writing makes it not improbable that the latter, too, possessed in earlier times a 100, standing upright. The Kharoṣṭhī practice of prefixing the signs for 1 and 2 to the 100 is found in all the Semitic systems of numeral notation.

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³ Palaeographical Society, Or. Ser., plate 63.

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The inclined cross, used to express the 4 in the later Kharoṣṭhī inscriptions, is found only in Nabataean inscriptions incised after the beginning of our era, and is used there only rarely for the expression of the higher units. The late occurrence of the sign both in Indian and in Semitic inscriptions makes it probable that both the Hindus and the Semites independently invented this cursive combination of the original four strokes.