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Indian Palaeography from about B.C. 350 to about A.D. 1300 c9.s2.t2: B. — The decimal notation

Indian Palaeography from about B.C. 350 to about A.D. 1300 c9.s2.t2

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B. — The decimal notation

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For the decimal notation, now occasionally called *aṅkapallī*, the Hindus used originally the *aṅkas* or the units of the ancient system, together with the cipher or naught,³ which originally consisted of the *śūnyabindu*, the dot (marking a blank, see below, § 35, E), called by abbreviated names *śūnya* and *bindu* (see BW.). Very likely this system is an invention of the Hindu mathematicians and astronomers, made with the help of the Abacus (BURNELL, BAYLEY). If HOERNLE'S very probable estimate of the antiquity of the arithmetical treatise, contained in the Bakhshālī MS., is correct,⁴ its invention dates from the beginning of our era or even earlier. For, in that work the decimal notation is used throughout. At all events, it was known to Varāhamihira (6th century A. D.), who employs the word *aṅka*, "the decimal figures," in order to express the numeral 9 (Pañcasiddhāntikā, 18, 33; compare below, § 35, A). Its most important element, the cipher or naught, is mentioned in Subandhu's Vāsavadattā, which Bāṇa (about A. D. 620) praises as a famous book. Subandhu compares the stars with "ciphers (*śūnyabindavaḥ*) which the Creator, while calculating (the value of) the universe, on account of the absolute worthlessness of the Saṁsāra marked with his chalk, the crescent of the moon, all over the firmament which the darkness made similar to a skin blackened with ink."⁵ The cipher, known to Subandhu, of course consisted of a dot, like that of the Bakshālī MS. (plate IX, B, col. IX.).

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³ Compare HOERNLE'S explanation, Seventh Oriental Congress, Aryan Section, 132; IA. 17, 35.

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⁴ IA. 17, 36.

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⁵ Vāsavadattā (ed. F. E. HALL), p. 182.

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The earliest epigraphic instance of the use of the decimal notation occurs in the Gurjara inscription of the Cedi year 346, or A. D. 595,¹ where the signs (plate IX, B, col. I) are identical with the numeral symbols of the country and of the period (compare the Valabhī column of plate IX, A).² The same remark applies to the 2 in the date of the month of the Cicacole plate mentioned on page 78 above, in which document we find also the later circular cipher and [79] a decimal 8 in the shape of a cursive sign derived from *pu*. Another inscription of the 8th century, the Sāmāṅgaḍ plates of Sakasaṁvat 675, or A. D. 754, offers only strongly modified cursive signs (plate IX, B, col. II.).

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¹ Compare facsimiles at EI. 2, 19 ff. ; and see Fleet in GI (CII. 3), 209, note 1.

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² The apparent difference in 6 is due to a fault of the impression.

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In the specimens³ (plate IX, B, cols. III—VIII, XIII) from inscriptions of the 9th and later centuries, when the use of the decimal figures is the rule, we have likewise only cursive signs, which in the 11th and 12th centuries (compare cols. VII, VIII, and XIII) show local differences in the west, east and south. But all their figures have been derived either directly from the letter-numerals of the older system, or from letters with the same phonetic value. The last remark applies to the 9 of cols. III, V, VI ff., which is identical with the signs for *O* used in later inscriptions in the word *Oṁ* (compare, *e.g.*, IA. 6, 194 ff., Nos. 3—6).

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³ Preparation of Plate IX, B, cols. III—XIII (for cols. I, II, see the text, above) ; all hand-drawn : — Col. III ; from facsimiles of Rāṣṭrakūṭa inscriptions at Kanheri, Nos. 15, 43 A, B. Col. IV ; from facsimile of the Rāṣṭrakūṭa copper-plate from Torkheḍe, EI. 3, 53. Col. V ; the 3 and 6 from an impression of the Haḍḍālā copper-plate (IA. 12, 190) ; the 4, 7, 9, 0, from facsimile of the Asnī inscription, IA. 16, 174 ; the 5 and 8 from facsimile of the Morbī copper-plate, IA. 2, 257. Col. VI ; from facsimile of the Sāvantvādī copper-plate, IA. 12, 266. Col. VII ; from facsimile of the Chaulukya copper-plate, IA. 12, 202. Col. VIII ; the 1, 3, 8, from the Gayā inscription, IA. 10, 342 ; the 5 from C.MG. pl. 28, A. Cols. IX, X ; Hoernle’s Bakhshālī figures. Cols. XI, XII ; from Bendall’s table of numeral in Catalogue of the Cambridge Sanskrit Buddhist MSS. Col. XIII ; from B.ESIP. pl. 23, Telugu and Kanarese numerals, 11th century.

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Among the specimens from MSS. (plate IX, B, cols. IX—XII), the decimal figures of the Bakhshālī MS. show the ancient letter-numerals for 4 and 9.

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The Tamil numerals, which greatly differ from the usual ones and preserve the old signs for 10, 100 and 1000, have been given by Burnell, ESIF. plate 23 (compare *id.* page 68). Those from Kābul are contained in the table accompanying E. C. Bayley’s paper, Numismatic Chronicle, 3rd Series, 2, 128 ff.

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