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Indian Palaeography from about B.C. 350 to about A.D. 1300 c9.s3: § 35. — Numeral notation by words and letters

Indian Palaeography from about B.C. 350 to about A.D. 1300 c9.s3

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§ 35. — Numeral notation by words and letters

A. — The word-numerals

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[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.

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⁴ W.IS, 8, 166 f.

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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—

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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."

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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.).

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

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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."

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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."

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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."

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

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⁴ See BRW. *sub hac voce*.

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⁵ Yudhishṭhira, Bhīma and Arjuna (CARTELLIERI).

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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."

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

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⁷ Rāma, Lakṣmaṇa, &c.

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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."

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

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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" (?).

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⁹ Compare EI. 1, 324, line 48,

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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.), (?).

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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."

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¹ Compare *aṣṭamaṅgala*.

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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.), (?).

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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

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

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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.), (?).

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

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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."

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

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⁴ SB. WA. 126, 5, 58.

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

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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)."

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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."

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

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

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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)."

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

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

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

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

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

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

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

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

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

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

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

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

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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."

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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:—

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

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

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

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

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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.

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

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³ IA. 21, 48, No. 2.

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

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

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⁶ IA. 7, 18.

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

B. — Numeral notation by letters

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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 : —

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

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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 | |

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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 — $2 & 3 & 1 & 5 & 6 & 5 & 1$ $khago=ntyān=meṣam=apa.$

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¹ IA. 21, 49 f., No. 4.

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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.”

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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.

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² B.ESIP. 80.

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³ Compare Guru pūjākaumu li, 110.

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