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Indian Palaeography from about B.C. 350 to about A.D. 1300 c9: VI. Numeral Notation

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

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VI. Numeral Notation

§ 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.

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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.

§ 34. — The numerals of the Brāhmī; Plate IX

A. — The ancient letter-numerals

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⁴ Compare Bhagvanlal, IA. 6, 42 ff.; B.ESIP. 59 ff., and pl. 23; E. C. Bayley, On the Genealogy of the modern Numerals, J.RAS, N.S., 14, 335 ff.; 15, 1 ff.

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In the Brāhmī inscriptions and coin-legends we find a peculiar system of numeral notation, the explanation of which is chiefly due to J. Stevenson, E. Thomas, A. Cunningham, Bhāū Dājī and Bhagvānlāl Indrājī.⁵ Up to the year A. D. 594-95 it is used exclusively, and later together with the decimal system.⁶ It appears also exclusively in the Bower MS. and in the other MSS. from Kashgar,⁷ as well as together with the decimal system, — chiefly in the pagination, — in the old MSS. of the Jainas of Western India and of the Bauddhas of Nepāl as late as the 16th century.⁸ And the Malayālam MSS. have preserved it to the present day.⁹

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⁵ J.BBRAS, 5, 35, and pl. 18; P.IA. 2, 80 ff.; C.ASR, 1, XLII, and J.ASB. 33, 38; J.BBRAS. 8, 225 ff.; the results of the last article belong chiefly to Bhagvānlāl Indrājī, though his name is not mentioned.

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⁶ Compare below, § 34, B. The latest epigraphic date in letter-numerals is probably the Nevār year 259 in Bendall's Journey in Nepāl, 81, No. 6; compare also Fleet, GI (CII. 3), 209, note 1.

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⁷ See Hoernle, "The Bower MS. ;" WZKM. 7, 260 ff. The Bower MS. occasionally has the decimal 3.

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⁸ Compare Bhagvānlāl's table, IA. 6, 42 f.; Kielhorn, Report on the Search for Sanskrit MSS., 1880-81, VIII. ff.; Peterson, First Report, 57 f., and Third Report, App. I, passim; Leumann, Śīlāṅka's Commentary on the Viśeṣāvaśyaka (especially table 35); Cowell and Eggeling, Cat. Sanskrit Buddhist MSS., 52 (J. RAS. 1875); Bendall, Cat. Cambridge Sanskrit Buddhist MSS., LII ff., and table of numerals. In Bendall's Nos. 1049 and 1161, the letter-numerals are also used for dates. The latest date in letter-numerals from Nepāl (Bendall's table of numerals) is A. D. 1583. Letter-numerals are usually only found in Jaina palm-leaf MSS. up to about A. D. 1450; but the Berlin paper MS. No. 1709 (Weber, Verzeichniss d. Skt. und Prāk. Hdschrft., 2, 1, 268; compare D.WA, 37, 250) shows some traces of them.

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⁹ Bendall, J.RAS. 1896, 789 ff.

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In this system, 1 to 3 are expressed by horizontal strokes or cursive combinations of such; 4 to 9, 10 to 90, 100, and 1000, each by a separate sign (usually a Mātṛkā or a ligature); the intermediate and the higher numbers by groups or ligatures of the fundamental signs. In order to express figures consisting of tens and units, or of hundreds, tens and units, and so forth, the symbols for the smaller numbers are placed either unconnected to the right of, or vertically below, the higher ones. The first principle is followed in all inscriptions and on most coins, the second on a few coins¹ and in the pagination of all manuscripts. In order to express 200 and 2000, one short stroke is added to the right of 100 and 1000. Similarly, 300 and 3000 are formed by the addition of two strokes to the same elements. [75] Ligatures of 100 and 1000 with the signs for 4 to 9 and 4 to 70, stood for 400 to 900 and 4000 to 70000 (the highest known figure), and the smaller figures are connected with the right side of the larger ones.

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¹ Compare J.RAS. 1889, 128.

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The Jaina MSS. offer, however, an exception in the case of 400. In the pagination of their MSS., both the Jainas and the Bauddhas use mostly the decimal figures for 1 to 3 (plate IX A, cols. XIX—XXVI), more rarely the Akṣaras *E* (*eka*), *dvi*, *tri*, or *sva* (1), *sti* (2), *śrī* (3),² the three syllables of the well-known Maṅgala, with which written documents frequently begin. Occasionally the same documents combine the naught and other figures of the decimal system³ with the ancient numeral symbols. Similar mixtures occur also in some late inscriptions. Thus, the year 183 of Dēvēndravarman's Cicacole plates is given first in words and next expressed by the symbol for 100, the decimal 8, and the syllable *lo*, *i.e.* *loka* = 3 (see below, § 35, A), while the day of the month, 20, is given only in decimal figures.⁴

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² IA. 3, 44; KIELHORN, Report for 1880-81, X; PETERSON, First Report, 57.

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³ KIELHORN, loc. cit.; BENDALL, Catalogue, LIII.

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⁴ Compare facsimile in EI 3, 133, and see the Additions and Corrections of that volume; the signs have been given in pl. IX, col. XV, under 2, 3, 8 *b*, 100 *a*. For other cases of mixtures, see FLEET, GI (CII. 3), 292, and IA. 14, 351, where the date is, however, 800 4 9 = 849.

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In the MSS., the signs of this system are always distinct letters or syllables of that alphabet in which the manuscript is written. They are however not always the same. Very frequently they are slightly differentiated, probably in order to distinguish the signs with numeral values from those with letter values. In other cases there are very considerable variants, which appear to have been caused by misreadings of older signs or dialectic differences in pronunciation. The fact that these symbols really are letters is also acknowledged by the name *akṣarapallī*, which the Jainas occasionally give to this system, in order to distinguish it from the decimal notation, the *aṅkapallī*.⁵ A remark of the Jaina commentator Malayagiri⁶ (12th century), who calls the sign for 4 the *ṅkaśabda*, "the word *ṅka*," indicates that he really pronounced, not *catur*, but *ṅka*.

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⁵ Oral information.

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⁶ IA. 6, 47.

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The phonetical values of the symbols in plate IX, A, cols. XIX—XXVI,⁷ and of some others, given by BENDALL (B.), BHAGVĀNLĀL INDRĀJI (Bh.), KIELHORN (K.), LEUMANN (L.), and PETERSON (P., see note 8 on page 77 above), are: —

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⁷ Preparation of Plate IX, A, cols. XIX—XXVI: — Col. XIX; from facsimiles in HOERNLE's "The Bower MS." Cols. XX—XXIII, and XXVI; cuttings from BENDALL's Table of Numerals, Nos. 1049, 1702, 856, 1643, 1688. Col. XXIV; drawn according to the tables of BHAGVĀNLĀL, KIELHORN, and LEUMANN. Col. XXV; drawn from the same sources; but 8, 9, 100, are cuttings from ZACHARIAE's photograph of the Sāhasāṅkacarita of the Royal Asiatic Society. Col. XXVI; see above, under cols. XX—XXIII.

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4 = *ṅka* (XIX; compare L., p. 1); with intentional differentiation, *rṅka* (L., p. 1.) and *rṅkī* (XXV); with *ṇa* for *ṅa* and additions, *ṇka* (XXVI; B., Bh.), *rṇka* (XXIV; compare K.), or *pka* (XX, XXI), or *ḥka* (XXIII; B.).

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5 = *tṛ* (XIX, XXI, XXV, XXVI; B., Bh., K.); with intentional differentiation, *rtṛ* (Bh., K); with a mistaken interpretation of the top-stroke as *ō*, *rtṇā* (XXIV); with a misinterpretation of the curved *ta* (compare the sign of B.'s No. 1464), also *hṛ* (compare the sign of B.'s No. 1645 ff.) or *hva* (XXIII).

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6=phra (XIX, XXI, XXVI;¹ B., Bh.) or *phu* (K.): and with intentional differentiation, *rphu* or *rphru* (XXIV; K.); with a misinterpretation of an old *pha*, also *ghra* (XXII); and with dialectic softening of the *tenuis*, *bhra* (XXIII; compare B., p. LIV).

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¹ For this *pha*, compare plate VI, 33, V.

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7=gra (XIX, XXI, XXVI; Bh.) or *grā* (XXV; B., Bh., K); with intentional differentiation and misinterpretation of the *ra*-stroke, *rgghā* (XXIV; P.); with misinterpretation of *ga*, *bhra* (XX; compare B., p. LIV) or *ṅa* (XXIII; compare B., LIV).

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8=hra (XIX, XXI, XXIII, XXVI; B., Bh.; partly with irregular addition of the *ra*-stroke to the hook of *ha*) or *hrā* (XXV; B., Bh., K.); and with intentional differentiation, *rhra* (K.) or *rhrā* (XXIV; K.).

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9=O (XIX, XXI, XXIII, XXIV, XXVI; B., Bh.) or *Oṁ* (XXV; K.).

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10=ηṛ (XIX), formed out of the ancient *thu* (cols. IV—VI) through the opening of the circle of *tha*; or *dā* (XX, XXIII; B., Bh.), the Nepalese representative of older *ḷa* (cols. X, XI; compare IA 6, 47), which likewise is a derivative from *thu*; or, especially in Nāgarī MSS., *ḷ* (XXI, XXV, XXVI; Bh., K.), through a misinterpretation of *ḷa*; and with intentional differentiation, *rḷ* (XXIV; K.).

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20=th² or *thā* (XIX—XXI, XXIII, XXIV, XXVI; B., Bh., K.); or with intentional differentiation, *rtha* and *rthā* (XXV; K.).

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² Common also in the Bower MS. Peterson's *gha* is due to a misreading of the *clītha*.

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30=la or *lā* (XIX—XXI, XXIII, XXIV, XXVI; B., Bh., K., P.); or with intentional differentiation, *rla* and *rlā* (XXV; K.).

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40=pla and *ptā* (XX, XXI, XXIII, XXIV, XXVI; B., Bh., K.); or with intentional differentiation, *rpta* and *rptā* (XXV; K.).

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50=Anunāsika (? Bhāgvānlāl), but corresponding only in col. XXIV. to an actually traceable form of this nasal (IA. 6, 47); occasionally turned round (XX; B.: XXIII; K.).

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60=cu, frequent in Nepalese MSS. (XX, XXI, XXIII.), or *thu*, regular in Nāgarī MSS. (XXV, XXVI; Bh., K); and with intentional differentiation, *rthu*³ (XXIV; K.).

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³ Peterson's *rghu* is a misreading.

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70=cu, frequent in Nepalese MSS. (XX, XXI, XXIII; B., Bh.) or *thū*, regular in Nāgarī MSS. (XXV, XXVI); and with intentional differentiation, *rthū* (XXIV; K.).

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80=Upadhmānīya with one central bar (XXIII, XXVI; B., Bh.: compare plate IV, 46, III), or later modified forms of that sign (XXI, XXIV; Bh., K.), which appear also in MSS. (K.) and in inscriptions (plate IV, 46, XXIII).

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90=Upadhmānīya with two cross-shaped bars (XXI, XXIII, XXVI; compare plate VII, 46, V, VI), and cursive forms of that sign (XXIV), or perhaps Jihvāmūlīya (XXV; Bh.) derived from the *ma*-like sign of plate VII, 4″, III, XIII.

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100=su in Nāgarī MSS. (XXIV, XXV; Bh., K.); or *A* in Nepalese MSS., owing to a misinterpretation of *su* (XX, XXIII, B., Bh.); or *lu* in Nepalese and Bengālī MSS., the result of another misinterpretation (XXI XXVI; B., Bh.).

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200=su in Nāgarī MSS. (XXIV, XXV; Bh., K.), or A in Nepalese MSS. (XX, XXIII; B., Bh.), or *lū* in Nepalese and Bengālī MSS. (XXVI; Bh., B.).

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300=su-ā in Nāgarī MSS. (XXIV, XXV; Bh.: read *stā* by K.), or *A-ā* in Nepalese MSS. (XX).

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400=su-o (XXV; read *sto* by K.) in Nāgarī MSS.

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In the inscriptions, the phonetical values of the signs often differ from those in the MSS. and vary very considerably, and almost every one of the vertical and horizontal columns (plate IX, A, I—XVIII)¹ shows at least some, occasionally a great many, cursive or intentionally modified forms, which possess hardly any resemblance to letters :—

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¹ Preparation of Plate IX, A, cols. I—XVIII : — Col. I ; the 4, cutting from Burgess' facsimile of the Kālsī edict XIII, EI. 2, 435 ; the 6, 50, 200, drawn according to facsimiles of the Sahasrām and Rūpnāth edicts, IA. 6, 155 ff. Col. II; cuttings from facsimile of the Siddāpura edict, EI. 3, 138. Col. III ; cuttings from facsimiles of Nānāghāṭ inscriptions, B.ASRWI. 5, pl. 51. Col. IV ; cuttings from facsimiles of Nāsik inscriptions, B.ASRWI. 4, pl. 52, Nos. 5, 9, 18, 19; pl. 53, Nos. 12—14 : the 70 drawn according to the Girnār Praśasti, B ASRWI. 2, pl. 14. Col. V ; drawn according to facsimiles of Kṣatrapa coins, J.RAS. 1890, plate at 639. Col. VI, VII; cuttings from facsimiles at EI. 1, 381 ff. ; 2, 201 ff. Col. VIII ; cuttings from facsimiles at B.ASRSI. 1, pl. 62, and EI. 1, 2 ff. Cols. IX, X; cuttings from facsimiles at F.GI(CII. 3), Nos. 2, 3, 5, 7, 9, 11, 19, 23, 23, 59, 63, 70, 71. Col. XI ; cuttings from facsimiles at F.GI (CII. 3), Nos. 38, 39; IA. 6, 9 ff, and other Valabhī inscriptions. Col. XII ; drawn according to facsimile at J.BBRAS. 16, 108. Cols. XIII, XIV ; drawn according to facsimiles at IA. 9, 154 ff. Col. XV; drawn according to facsimiles at IA. 13, 120 ff; EI. 3, 127 ff. Col. XVI ; cutting from facsimiles at F.GI(CII. 3), Nos. 40, 41, 55, 53, 81. Col. XVII ; cutting from facsimiles at IA. 15, 112, 141. Col. XVIII ; drawn according to facsimile at J.ASB. 40, pl. 2. Cuttings reduced by one-third.

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4 = *ka* (I), *ki* (III, in 400, 4000; IV, A; V, A; VI, B), *kri* (V, B; IX, A), *pka* (III, A; VI, A; VIII, A; IX, B), *ṅka* (X, A), *tka* (facsimile IA. 5, 154), *yka*.

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5 = *tra*, mostly with irregular addition of the *ra*-stroke to the vertical of *ta* (V, A; VIII, A, B; IX, B; X, A; XV, A), *trā* (VII, A), *tu* (IX, A), *nu* (IV, B), *na*, *nā* (XI, A, B), *tṛ* (XIII, A), *hr* (XIII, B; XIV, A; XVII, A), *hra* (XVI, A), together with two cursive signs without phonetic value in V, A, B.

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6 = *ja*, *sa*² (I, II; compare plate II, 15, III; 39, VII), *phra* (III, in 6000; IV, V), *phrā* (IX, XI), *phā* (XIII), *pha* (XIV), together with four cursive signs (VI—VIII, XV), among which the first is probably derived from *ja*, the second from *sa*, and the other two from *phra*.

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² Probably to be read thus ; not as a modification of *phra* or *phu*.

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7 = *gra* or *gu* (III—VI, IX—XI, XIII, XV), *ga* (VII) with a cursive sign (XII) derived from a *gra* like that in XIII.

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8 = *hra* with irregular addition of the *ra*-stroke to the end of *ha* (IV, A, B; VI, A), *ha* (VI, B), *hā* (VII, A; X), *hrā* (XI, XVII, XVIII) or in eastern inscriptions *pu* (VIII, B; XV, A; XVI) probably a cursive derivative from *hra*, together with five cursive signs without phonetic value (V, A; VIII, A; IX, A, B; XV, B), among which the second and the fifth are derived from *pu*, the first from *hra*, the third from *hrā*, and the fourth from *hā*.

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9 = O; really occurring letter-forms in col. V (compare plate IV, 6, IX), in col. VI (compare *AU*, plate VII, 7, X), in col. IX (compare plate VI, 13, I), in cols. XI, XII (compare plate V, 47, IX), in col. XIV (compare plate V, 9, XV), in col. XVII (compare plate VI, 13, V ff.), different from the most ancient form (III, IV) in cols. VII. and XIII, cursive in cols. X. and XVI.

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10 = *ṭhū*³ (III, in 10000; IV, A, B; V, A; VI, A), hence a cursive sign, derived by the opening of the circle of *ṭha* (V, B; VI, B; VII A; VIII, IX), which later is converted into *a* (X, XI, A, B), or into *rya* (XVI, A), or, as in the MSS., into *l* (XIII, A, B; XVII, A), or into *kha* and *ce* (XV, A, B).

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³ Thus Bayley, doubtfully ; for the *ū* of the sign in IV, B, compare *nū*, plate III, 25, 6.

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20 = *ṭha* (III, in 20000; XV), or, as in the MSS., *tha*, *thā*, of the type of the period.

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30 = *la*, as in the MSS.; occasionally with small modification.

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40 = *pta*, as in the MSS., for which occasionally a cursive cross (V, A) or a *sa* through a transposition of the *ta* (V, B; XI, B; XV).

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50 = [77] Anunāsika (? Bhagvānāl), as in the MSS., facing either the right or the left, occasionally with small modification.

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60 = *pu* (IX), together with four different cursive signs without phonetic value.

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70 = *pū* (IV—VI; IX; XI, A), or *prā* (XII), together with a cursive cross (VII) and another cursive sign (XI, B), both possibly derived from *pū*.

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80 = Upadhmānīya with a diagonal bar, and cursive forms of the Upadhmānīya exactly as in the MSS.

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90 = Upadhmānīya with the central cross, as in the MSS.

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100 = either *su* (I, in 200; III; IX, A, B; X; XIII, in 300; XIII, in 400; XIV, in 400), for which, through a misreading, appears *A* in the Nepāl inscriptions of the 7th and 8th centuries (XIII, A, B; XIV, in 300), and *lu* in eastern inscriptions¹ of the 6th and later centuries (X, in 200; XVIII, in 200), or *śu* (probably owing to the dialectic permutation of *śa* and *sa*) in the western² and Kalinga inscriptions (IV; V; XI; XII, in 400; XV, A, B), for which, through a misreading, *O* (XVII, A, B) appears in late northern inscriptions.

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¹ Earliest instance in the inscription of Mahānāman, F.GI (CII. 3), No 71; 200 in col. X.

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² Compare also the date of the Gujarāt Calukya inscription, Seventh Oriental Congress, Aryan Section, 211 ff.; and the facsimile at J.BBRA S, 16, 1 ff.; and the Valabhī form at EI. 3, 320, 1. 14, where a *ś* of the period, mutilated on the left, is used; and the date of the Kota inscription, IA. 14, 351, with a distinct *śa* of the 9th century. The form *su* occurs in a western inscription, lately found at Udepur by G. H. Ojha, in the numeral *sū-u* or *sū-ā*, = 300.

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200 and 300 are formed by the addition of respectively one and two horizontal bars to the right of the *akṣara* for 100; but in the Rūpnāth sign (I) by the prolongation of the vertical of *sa*. A distinct *ū*, as in the MSS., appears only in the 200 of col. XVIII.

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400 = *su-ki* (III), or *su-pka* (X; XIII; XIV), but *śu-pka* (XI). 500 = *śu-tra* (IV). 600 = *śu-phra* (XII). 700 = *su-gra* (III).

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1,000 = *ro* (III), or *cu* (probable in IV, distinct in XV, in 8,000), or *dhu* (IV, in 2,000; IV, in 70,000). 2,000 and 3,000 = *dhu* with one or two horizontal strokes (IV). 4,000 = *ro-ki* (III), or *dhu-ki* (IV). 6,000 = *ro-ṇhra* (III). 8,000 = *dhu-hra* (IV), or *cu-pu* (XVI).

c9.s2.t1.66

10,000 = *ro-thū* (III). 20,000 = *ro-ṭha* (III). 70,000 = *dhu* with the cursive sign for 70.

c9.s2.t1.67

The above details show: — (1) That the inscriptions of all periods, even the Aśoka edicts in the case of 100, differ from the MSS. by offering, side by side with distinct letters, numerous cursive or intentionally modified forms, and that, in the case of 50 and 60, just the older inscriptions show no real Akṣaras.

c9.s2.t1.68

(2) That, excepting 7, 9, 30, 40, 80, 90, the phonetical value of the letters varies already since the earliest times, and that in many cases, as in those of 6, 10, 60, 70, 100, 1000, the variations are very considerable.

c9.s2.t1.69

(3) That occasionally, as in the case of 10, 60, 70, the distinct letters, used in the later inscriptions and the MSS., are derived in various ways from cursive signs without a phonetical value.

c9.s2.t1.70

These facts, as well as the incompleteness of our knowledge of the most ancient forms, make an explanation of the origin of the system for the present very difficult. Bhagvānāl Indrājī, who first attempted the solution of the problem, conjectured that the numeral symbols of the Brāhmī are of Indian origin, and due to a peculiar use of the Mātṛkās and certain ligatures for numeral notation. But he declared himself unable to find the key of the system.

c9.s2.t1.71

In 1877, I agreed with him, and KERN¹ likewise concurred, but explained the 4 and 5 as combinations of four and five strokes, arranged in the form of letters. But BURNELL differed entirely. He denied that the older "cave-numerals," with the exception of rare cases, resemble letters, and dwelt strongly on the impossibility of finding a principle, according to which the Akṣaras of the MSS. have been converted into numerals. He further pointed out the general agreement of the principles of the Indian system with those of the Demotic notation of the Egyptians. From this fact, as well as from the resemblance [78] of the Demotic signs for 1 to 9 to the corresponding Indian symbols, he inferred that the "cave-numerals" have been borrowed from Egypt, and after further modifications have been converted into Akṣaras. Finally, E. C. BAYLEY tried to show in his lengthy essay, quoted above, that, though the principles of the Indian system have been derived from the hieroglyphic notation of the Egyptians, the majority of the Indian symbols have been borrowed from Phoenician, Bactrian, and Akkadian figures or letters, while for a few a foreign origin is not demonstrable.

c9.s2.t1.72

¹ IA. 6, 143.

c9.s2.t1.73

BAYLEY'S explanation offers great difficulties, *inter alia* by the assumption that the Hindus borrowed from four or five different, partly very ancient and partly more modern, sources. But the comparative table of the Egyptian and Indian signs given in his paper, and his remarks about the agreement of their methods in marking the hundreds, induce me to give up BHAGVĀNLĀL'S hypothesis, and to adopt, with certain modifications, the view of BURNELL, with whom also BARTH concurs.² It seems to me probable that the Brāhma numeral symbols are derived from the Egyptian Hieratic figures, and that the Hindus effected their transformation into Akṣaras, because they were already accustomed to express numerals by words (compare below, § 35, A).

c9.s2.t1.74

² B. ESIP, 65, note 1.

c9.s2.t1.75

This derivation, the details of which, however, still present difficulties and cannot be called certain, has been given in Appendix II. to the 2nd edition of my Indian Studies No. III. But two other important points may be considered as certain: — (1) That the varying forms in the Aśoka edicts show these numerals to have had a longer history in the 3rd century B. C.; and (2) that the signs have been developed by Brahmanical schoolmen, since they include two forms of the Upadhmānīya, which without doubt has been invented by the teachers of the *Śikṣā*.

B. — The decimal notation

c9.s2.t2.1

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.).

c9.s2.t2.2

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

c9.s2.t2.3

⁴ IA. 17, 36.

c9.s2.t2.4

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

c9.s2.t2.5

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.).

c9.s2.t2.6

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

c9.s2.t2.7

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

c9.s2.t2.8

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).

c9.s2.t2.9

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.

c9.s2.t2.10

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.

c9.s2.t2.11

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.

§ 35. — Numeral notation by words and letters

A. — The word-numerals

c9.s3.t1.1

[80] In many manuals of astronomy, mathematics and metrics, as well as in the dates of inscriptions and of MSS., the numerals are expressed by the names of things, beings or ideas, which, naturally or in accordance with the teaching of the Śāstras, connote numbers. The earliest traces of this custom have been discovered by A. Weber in the Śrautasūtras of Kātyāyana and Lāṭyāyana.⁴ A few examples are found in the Vedic Jyotiṣa and in the arithmetic of the Bakhshālī MS. More numerous instances occur in Piṅgala’s manual of metrics, and from about A. D. 500 we find, first in Varāhamihira’s Pañcasiddhāntikā, a system of this description, which, gradually becoming more and more perfect, extends to the cipher or naught, and to nearly all the numbers between 1 and 49. During this latter period any synonym may be used for the words expressing numbers, and in some cases the same word may be used for different numbers. If the words are compounds, they may be represented by their first or second part.

c9.s3.t1.2

⁴ W.IS, 8, 166 f.

c9.s3.t1.3

This system of numeral notation, of course, has been invented in order to facilitate the composition of metrical handbooks of astronomy and so forth. The most important words, used to express numbers, are as follows :¹—

c9.s3.t1.4

¹ The abbreviations mark the sources from which the words have been collected, as follows: — Bakh. = the Bakhshālī MS., HOERNLE, 130. Ber. = Berūnī's India, SACHAU, 1, 178. Bro = C. P. BROWN's list, as quoted by BURNELL, ESIP. 77 f. Bur. = BURNELL's additions, ESIP. 77 f. Jyo. = the Jyotiṣa, WEBER's edition, 6 Piṅg. = Piṅgala, WEBER, Indishe Studien, 8, 167 f. Var. = Varāhamihira's Pañchasiddhāntikā, THIBAUT's edition. A few other instances are given from manuscripts and inscriptions. The numerous synonyms, being unnecessary for Sanskritists, have been mostly omitted; but such omissions have been indicated by "&c."

c9.s3.t1.5

The cipher, 0, is expressed by (*a*) *śūnya* (Var., Ber.), "a void ;"² (*b*) *ambara*, *ākāśa*, &c., " the (empty) space of heaven" (Var., Ber., Bro.), *ananta* (Bro.).

c9.s3.t1.6

² *Śūnya* may either mean "the empty place on the Abacus," or be an abbreviation of *śūnyabindu* (see above, § 34, B).

c9.s3.t1.7

1 is expressed by (*a*) *rūpa* (Jyo., Bakh , Piṅg., Var.) "one piece;" (*b*) *indu*, *śaśin*, *śītaraśmi*, &c. (Var., Ber., Bro.), or abbreviated into *raśmi* (Ber.), "the moon;" (*c*) *bhū*, *mahī*, &c. (Var, Ber, Bro., Bur.), "the earth ;" (*d*) *ādi* (Ber.), "beginning ;" (*e*) *pitāmaha* (Ber.), "Brahman;" (*f*) *nāyaka* (Bro.), "the hero" (of a play); (*g*) *tanu* (Bro.), "the body."

c9.s3.t1.8

2 is expressed by (*a*) *yama*, *yamala* (Var., Ber.), "twins;" (*b*) *aśvin*, *dasra* (Var., Ber.), "the two Aśvins;" (*c*) *pakṣa* (Var., Ber.), "the two wings, or the halves of the body;" (*d*) *kara*, &c. (Var., Bur.), "the hands;" (*e*) *nayana*, &c. (Var., Ber., Bur.), "the eyes;" (*f*) *bāhu* (Bro.), "the arms;" (*g*) *karṇa* (Bro.), "the ears;" (*h*) *kuṭumba* (Bro.), "the family," *i. e.*, husband and wife; (*i*) *ravicandrau* (Ber.), "sun and moon."

c9.s3.t1.9

3 is expressed by (*a*) *agni*, *hotṛ*,³ &c. (Var., Ber., Bro., Bur.), "the sacrificial fires;" (*b*) *rāmāḥ* (Var., Bro), "the three Rāmas" (of epic poetry); (*c*) *guṇa* (Var.), *triguṇa* (Ber.), "the qualities of matter;" (*d*) *trijagat*, *loka* (Ber.), "the three worlds;" (*e*) *trikāla* (Ber.), "the three times;" (*f*) *trigata*⁴ (Ber.), "sounds, &c., with three meanings;" (*g*) *sahodarāḥ* (Bro.), "the three uterine brothers ;"⁵ (*h*) *trinetra*, &c. (Bro.), "the three eyes of Śiva."

c9.s3.t1.10

³ See Pañcasiddhāntikā, 8, 6. This is equivalent to *agni*, because Agni is the Hotṛ-priest of the gods.

c9.s3.t1.11

⁴ See BRW. *sub hac voce*.

c9.s3.t1.12

⁵ Yudhishṭhira, Bhīma and Arjuna (CARTELLIERI).

c9.s3.t1.13

4 is expressed by (*a*) *aya*, *āya* (Jyo.), *kṛta*,⁶ (Var., Ber), "the (four) dice;" (*b*) *veda*, *śruti* (Piṅg., Var., Ber.), "the Vedas;" (*c*) *abdhi*, *jaladhi*, &c. (Piṅg., Var., Ber., Bur.), abbreviated *jala* (Var.), *dadhi* (Ber.), "the oceans;" (*d*) *diś* (Ber.), "the cardinal points;" (*e*) *yuga* (Bro.), "the (four) ages of the world;" (*f*) *bandhu* (Bro.), "the (four) brothers;"⁷ (*g*) *koṣṭha* (Bro.), (?); (*h*) *varṇa* (manuscript), "the (four) principal castes."

c9.s3.t1.14

⁶ Thus BRW. *sub hac voce*; possibly *kṛta* may stand for *kṛtādi yuga*.

c9.s3.t1.15

⁷ Rāma, Lakṣmaṇa, &c.

c9.s3.t1.16

5 is expressed by (*a*) *indriya*, &c. (Piṅg., Var., Bur.), "the organs of sense;" [81] (*b*) *artha*, *viṣaya*, &c. (Var., Ber.), "the objects of the senses;" (*c*) *bhūta* (Piṅg., Var., Ber.), "the elements;" (*d*) *iṣu*, &c. (Var., Ber., Bur), "the arrows of Kāma;" (*e*) *pāṇḍava* (Ber.), abbreviated (*pāṇḍu*)-*suta*, *putra* (Bro.), "the (five) Pāṇḍu sons;" (*f*) *prāṇa* (Bro.), "the vital airs;" (*g*) *ratna*⁸ (Ber.) "the (five) jewels."

c9.s3.t1.17

⁸ See APTE, Sanskrit Dictionary, *sub hac voce*.

c9.s3.t1.18

6 is expressed by (*a*) *rasa* (Bakh., Piṅg., Var., Ber.), "the (six) flavours;" (*b*) *ṛtu* (Piṅg., Var., Ber.), "the seasons;" (*c*) *aṅga* (Ber.), "the auxiliary sciences of Vedic studies;" (*d*) *māsārdha* (Ber.), "one half of the (twelve) months;" (*e*) *darśana*, &c. (Bro.), "the (six) philosophical systems;" (*f*) *rāga* (Bro.), "the (six) principal tunes;" (*g*) *ari* (Bro.), "the (internal) foes (of men);" (*h*) *kāya*⁹ (inscription), "the bodies" (?).

c9.s3.t1.19

⁹ Compare EI. 1, 324, line 48,

c9.s3.t1.20

7 is expressed by (*a*) *ṛṣi*, *muni* (Piṅg., Var.), "the (seven) seers;" or by *atri*, the first among them (Bro); (*b*) *svara* (Piṅg., Var., Bro.), "the notes" (of the octave); (*c*) *aśva* (Var., Bro.), "the horses" (of the sun); (*d*) *aga*, &c. (Var., Ber., Bur.), "the (primeval) mountains;" (*e*) *dhātu* (Bro.), "the elements" (of the body); (*f*) *chandas* (Bro.), "the (classes of the) metres;" (*g*) *dhī* (Ber.), (?); (*h*) *kalatra* (Bro.), (?).

c9.s3.t1.21

8 is expressed by (*a*) *anuṣṭubh* (Piṅg.), a metre with octo-syllabic Pādas or lines; (*b*) *vasu* (Piṅg., Var.), "the Vasu gods;" (*c*) *ahi*, &c. (Ber., Bur.), "the (eight classes of) snakes;" (*d*) *gaja*, &c. (Ber., Bur.), "the elephants (guarding the eight points of the horizon);" (*e*) *maṅgala*, *bhūti* (Ber., Bro.), "the (eight kinds of) auspicious things;"¹ (*f*) *siddhi* (manuscript), "the supernatural powers."

c9.s3.t1.22

¹ Compare *aṣṭamaṅgala*.

c9.s3.t1.23

9 is expressed by (*a*) *aṅka* (Var., Bro.), "the decimal figures;" (*b*) *nanda* (Var., Ber.), "the (nine) Nandas;" (*c*) *chidra*, &c. (Ber.), "the cavities of the body;" (*d*) *go*, *graha* (Ber., Bro., Bur.), "the planets;" (*e*) *nidhi* (Bur.), "the treasures (of Kubera);" (*f*) *pavana* (Ber.), (?).

c9.s3.t1.24

10 is expressed by (*a*) *diśaḥ*, &c. (Piṅg., Var., Ber.), "the (ten) points of the horizon;" (*b*) *rāvaṇaśiras* (Ber.), "the heads of Rāvaṇa;" (*c*) *avatāra* (Bro.), "the incarnations (of Viṣṇu);" (*d*) *karman* (Ber.), "the (ten Gṛhya)-ceremonies;" (*e*) *khendu* (Ber.), cipher (0) and moon (1), *i.e.* 10.²

c9.s3.t1.25

² STEN KONOW, Deutsche Litt. Int., 1897.

c9.s3.t1.26

11 is expressed by (*a*) *rudra* (Piṅg., Var., Ber.), "the (eleven) Rudras," or by *īśa*, *śiva*, &c. (Var., Ber.), the first of the eleven Rudras; (*b*, *c*) *akṣauhiṇī*, *lābha* (Bro.), (?).

c9.s3.t1.27

12 is expressed by (*a*) *āditya*, *arka*, &c. (Piṅg., Var., Ber.), "the (twelve) sun-gods," or "suns;" (*b*) *vyaya* (Bro.), (?).

c9.s3.t1.28

13 is expressed by (*a*) *viśvedevāḥ*, abbreviated *viśva* (Var., Ber.), "the (thirteen) all-gods;"³ or by *kāma*, the most famous among them (Bro.); (*b*) *atijagatī* (Var.), a metre with thirteen syllables in each Pāda; (*c*) *aghoṣa* (Jagaḍūcarita),⁴ "the surd consonants."

c9.s3.t1.29

³ Compare F. E. HALL, Viṣṇupurāṇa, 3, 192.

c9.s3.t1.30

⁴ SB. WA. 126, 5, 58.

c9.s3.t1.31

14 is expressed by (*a*) *manu* (Var., Ber.), "the (fourteen) Manus;" (*b*) *indra* (Var., Ber.), "the (fourteen) Indras;" (*c*) *loka* (Bro.), "the (fourteen) worlds."

c9.s3.t1.32

15 is expressed by (*a*) *tithi* (Var., Ber.), "the lunar days (of a half-month);" (*b*) *ahan* (Bro.), "the solar days (of a half-month);" (*c*) *pakṣa* (Bro.), "half a month (fifteen days)."

c9.s3.t1.33

16 is expressed by (*a*) *aṣṭi* (Var., Ber.), a metre with sixteen syllables in the Pāda; (*b*) *bhūpa*, &c. (Var., Ber.), "the (famous sixteen) kings;"⁵ (*c*) *kalā* (Bro.), "the digits of the moon."

c9.s3.t1.34

⁵ Described in the *ṣoḍaśarājakīya-parvan* of the Mahābhārata, 7, 65–71 (CARTELLIERI).

c9.s3.t1.35

17 to 19 are expressed by *atyaṣṭi* (Ber.), *dhṛti*, *atidhṛti* (Var., Ber.), metres with seventeen to nineteen syllables in the Pāda.

c9.s3.t1.36

20 is expressed by (*a*) *kṛti* (Var., Ber.), a metre with twenty syllables in the Pāda; (*b*) *nakha* (Var., Ber.), "the nails (of the hands and feet)."

c9.s3.t1.37

21 is expressed by (*a*) *utkṛti* (Ber.);⁶ (*b*) *svarga* (Bro.), "heaven."

c9.s3.t1.38

⁶ Probably a mistake for *prakṛti*, a metre with twenty-one syllables in the Pāda.

c9.s3.t1.39

22 is expressed by *jāti* (Bro.), (?).

c9.s3.t1.40

24 is expressed by *jina* (Var., Ber.), "the (twenty-four) Tīrthaṃkaras of the Jainas."

c9.s3.t1.41

25 is expressed by *tattva* (Ber.), "the principles of the Sāṅkhya philosophy."

c9.s3.t1.42

26 is expressed by *utkṛti* (Var.), a metre with twenty-six syllables in the Pāda.

c9.s3.t1.43

27 is expressed by *bhasamūha* (Jyo.), *nakṣatra* (Bro.), "the lunar mansions."

c9.s3.t1.44

32 is expressed by *danta*, &c. (Var., Bro.), "the teeth."

c9.s3.t1.45

33 is expressed by *sura*, &c. (Var., Bro.), "the gods."

c9.s3.t1.46

40 is expressed by *naraka* (Var., Pañcasiddhāntikā, 4, 6), "the hells."

c9.s3.t1.47

49 is expressed by *tāna* (Bro.), "the notes."

c9.s3.t1.48

[82] In the Jyotiṣa and in the arithmetic of the Bakshālī MS., only single words are used to indicate numbers.

c9.s3.t1.49

In Piṅgala's and other metrical manuals, the words with numeral meanings often form (sometimes together with ordinary numerals) Dvaṁdva compounds, which must be dissolved by "*or*." Thus, *vedartusamudrāḥ* means "4 or 6 or 4."

c9.s3.t1.50

In the works of Varāhamihira and other astronomers, we find, in addition, longer Dvaṁdva compounds, consisting of such word-numerals (be it alone, or associated with ordinary numerals), which have to be dissolved by "*and*," and then yield long rows of figures to be read from the right to the left.¹ Thus, in the Pañcasiddhāntikā, 4, 44, we have:—

c9.s3.t1.51

¹ According to BURNELL, in some modern inscriptions the word-numerals are placed in the usual order of the decimal figures.

c9.s3.t1.52

0 & 0 & 4 & 4 & 1
*kha-kha-veda-samudra-śītaraśmayaḥ* = 14, 400;

c9.s3.t1.53

and in 9, 9 of the same work, we have; —

c9.s3.t1.54

0 & 0 & 16 & 2
*kha-kh-aṣṭi-yamāḥ* = 21,600.

c9.s3.t1.55

Such Dvaṁdva compounds, which presuppose the existence of the decimal notation, are used also for the dates of inscriptions. Dates expressed in this manner, are found in the Kamboja and Campā inscriptions of the 7th century.² In Java they occur in the 8th century.³ And about the same time appears the first trace of such a notation in an Indian document, the Cicacole copper-plate inscription mentioned on page 78 above, where *lo*, = 3, is an abbreviation of *loka*. Next follow the dates of the Kaḍab plates of A. D. 813,⁴ and of the Dholpur stone inscription of A. D. 842,⁵ which are expressed in word-numerals; and, in the next century, the plates issued by the Eastern Calukya Amma II. in A. D. 945.⁶ In later times the epigraphic instances become more frequent, and the ancient palm-leaf MSS. of the Jainas,⁷ as well as the later paper MSS., offer a good many. The notations of this kind have been caused sometimes by the vanity of the clerks and copyists, who wished to prove their acquaintance with the methods of the astronomers, and perhaps still more frequently by metrical reasons in the case of dates given in verse.

c9.s3.t1.56

² A. BARTH, Inscrs. Sansk. du Cambodge, No. 5 ff.; BERGAIGNE-BARTH, Inscrs. Sansk. de Campā et du Cambodge, No. 22 ff.

c9.s3.t1.57

³ IA. 21, 48, No. 2.

c9.s3.t1.58

⁴ IA. 12, 11; declared to be suspicious by FLEET, Kanarese Dynasties, Bombay Gazetteer, i, ii, 399, note 7.

c9.s3.t1.59

⁵ ZDMG. 40, 42, verse 23; pointed out by KIELHORN.

c9.s3.t1.60

⁶ IA. 7, 18.

c9.s3.t1.61

⁷ KIELHORN, Report, 1880-81, No. 58; PETERSON, Third Rep., App. I, Nos. 1876, 251, 253, 256, 270, &c.

B. — Numeral notation by letters

c9.s3.t2.1

Two systems of numeral notation, according to BURNELL originally South-Indian, which both employ the phonetically arranged characters of the alphabet, have still to be described, as they are not without interest for paleography. In the first system,⁸ only the vowelless consonants have any importance, and their numeral values are : —

c9.s3.t2.2

⁸ Compare B.ESIP. 79; W.IS. 8, 160; IA. 4, 207.

c9.s3.t2.3

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| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| *k* | *kh* | *g* | *gh* | *ṅ* | *c* | *ch* | *j* | *jh* | *ñ* | = | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
| *ṭ* | *ṭh* | *ḍ* | *ḍh* | *ṇ* | *t* | *th* | *d* | *dh* | *n* | = | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
| *p* | *ph* | *b* | *bh* | *m* | ... | ... | ... | ... | ... | = | 1 | 2 | 3 | 4 | 5 | | | | | |
| *y* | *r* | *l* | *v* | *ś* | *ṣ* | *s* | *h* | *ḷ* | ... | = | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

c9.s3.t2.4

The consonants are, however, not used by themselves, but for the formation of chronograms, containing any vowels and also compound consonants, of which the last element alone has numerical value. In the figures, resulting from those chronograms, the units invariably stand on the left, and the whole sum has to be turned round. An interesting instance of this notation, probably the most ancient hitherto discovered, occurs at the end of Ṣaḍguruśiṣya’s commentary on the Sarvānukramaṇī (MACDONELL, page 168), where the chronogram, according to KIELHORN’s undoubtedly correct emendation, is :¹ — $2 & 3 & 1 & 5 & 6 & 5 & 1$ $khago=ntyān=meṣam=apa.$

c9.s3.t2.5

¹ IA. 21, 49 f., No. 4.

c9.s3.t2.6

As the author himself adds, this has the value of 1,565,132. And this figure corresponds, as the author likewise says, to the number of the days elapsed since the beginning of the Kaliyuga, and yields the vernal equinox, 24th March, A. D. 1184, as the date of the completion of the work. The equinox is indicated also by the verbal meaning of the chronogram: — “(Coming) from the last (sign of the Zodiac), the sun reached Aries.”

c9.s3.t2.7

The second system to be considered,² which is still used in Ceylon, Siam and Burma for the pagination of MSS., and according to BURNELL formerly also [83] occurred in Southern India, utilises the Brahmanical *Bārākhaḍī* (see page 2 above). According to BURNELL, the Akṣaras *ka* to *ḷa* are equivalent to 1 to 34; *kā* to *ḷā* = 35 to 68; *ki* to *ḷi* = 69 to 102; and so on. But in the Pali MSS. of the Viennese Court Library from Burma, I find *ka* to *kaḥ* = 1 to 12; *kha* to *khaḥ* = 13 to 24; and so on: and in those from Ceylon, where the *Bārākhaḍī* includes the vowels *ṛ*, *ṝ*, *ḷ*, and *ḹ*, *ka* to *kaḥ* = 1 to 16, and *kha* to *khaḥ* = 17 to 32, whereby a somewhat different employment of the Akṣaras results.³ FAUSBÖLL has kindly informed me that the last two methods alone (not that mentioned by BURNELL) are used in the Pali MSS. known to him. And he adds that, after the exhaustion of the whole *Bārākhaḍī*, the Ceylonese MSS. begin again with 2 *ka*, 2 *kā*, and so on, and further that the pagination of Siamese MSS. agrees exactly with those from Burma.

c9.s3.t2.8

² B.ESIP. 80.

c9.s3.t2.9

³ Compare Guru pūjākaumu li, 110.

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