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THE ASIATIC SOCIETY:

No. 25.-January, 1834.

I.-Professor Schlegel's Enigma.-Mode of expressing numerals in the Sanskrit and Tibetan languages.

Ar the end of the pamphlet lately addressed by Professor SCHLEGEL to Sir JAMES MACKINTOSH, on the subject of the Oriental Translation Committee of the Royal Asiatic Society*, we find a morceau of enlightenment for the continental orientalists, on the Hindú method of expressing numerals by symbolical words, which the learned author states himself to be the first to expound to European scholars.

It is certainly a curious circumstance that neither COLEBROOKE, Davis, nor BENTLEY, when quoting, translating, and commenting on the text of Sanskrit astronomical works, should have taken occasion to explain the system invariably used by their authors in expressing verbally the numbers occurring in their computations and formulæ; it must doubtless be attributed to their considering the subject too trite and obvious to need any remark, or otherwise the very passage quoted by Professor SCHLEGEL Would surely have elicited some observation by the translator. It is true however that many of the terms thus technically adopted by the Sanskrit arithmeticians and astronomers, as the only mode perhaps of screwing the uncouth elements they had to deal with into the

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* This pamphlet contains also an attack upon Dr. H. H. WILSON, which that gentleman will doubtless answer for himself, and some severe criticism on the careless manner in which oriental works are issued from the press by Calcutta Editors generally. We trust our Orientalists will be able to shew that such censure is not deserved, or at any rate that it applies but partially; and we should like to have the opportunity of pointing out those works (such as the Sháh nâma) to the accuracy of which real editorial care was devoted, and on which the confidence of the reader may be implicitly placed.-ED.

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tean bed of poetical metre, are not to be found in the best dictionaries; for instance, veda, for 4;nanta for 0; Rudra for 7; while on the other hand many, such as a forzero; vasu, for 8, &c. will be found in WILSON'S last edition.

I extract the. Professor's remarks at length, since equal credit is due to his ingenuity in unravelling the mystery, in the absence of native pundits, who would have cleared it up in a moment, as if it had altogether been a sealed book of hieroglyphics to the more fortunate student on this side the water, as to the rising schools of Sanskrit 'philosophy in Germany and France.

Explication d'une Enigme.

"Dans les Recherches Asiatiques, vol. xii. p. 231, M. COLEBROOKE cite un auteur qui dit que le nombre des jours sidéraux compris dans la grande époque, appelée Calpa, est: 1,582,236,450,000. Il donne le texte même, dont les mots qui répondent à ce nombre, signifient litteralement]: quatre espaces vides (ou zero), cinq, véda, goût, feu, jumeaux, aile, huit, flêche, lune. Tout ces mots sont réunis en un seul composé agrégatif,

Qu'on se figure maintenant l'embarras des écoliers interpellés pour expliquer comment cette bigarrure fait precisément un trillion cinq cents quatre-vingt-deux billions, deux cents trente six millions, et quatre cents cinquante mille. La chose est pourtant bien sure: il ne peut y avoir erreur. Voici le mot de l'enigme. Les mathématiciens Indiens ont une méthode d'exprimer les chiffres par des noms restreints à un certain nombre d'objets. Ils commencent à la droite par les unités, et remontent vers les chiffres d'un ordre supérieur. Cela a l'air d'une puérilité, il y a pourtant là-dessous un but raisonnable. Ou a voulu se prémunir contre l'altération des chiffres qui se glisse si facilement dans les livres copiés à la main. Quand le traité etait rédigé en vers, comme c'est un ancien usage dans l'Inde d'employer la versification même dans les livres scientifiques, la garantie en devenait d'autant plus forte.

Voici l'explication. Les deux premiers termes, étant des chiffres sans déguisement, n'en ont besoin. Véda; ces livres sacrés sout au nombre de quatre. Gout: on en compte six espéces principales: le doux, l'amer, le salé, l'aigre, le poignant et l'astringent. Feu signifie trois; par rapport aux trois feux sacrés que les brahmanes entretiennent. Jumeaux, aile, signifient naturellement deux; le dernier mot est employé aussi pour les deux moitiés d'une lunaison. Flêche signifie cinq ce sont les cinq flêches du dieu de l'amour, dont les pointes sont armées de fleurs. Ces flêches sont un emblème des cinq sens par lesquels l'amour pénètre dans l'ame. Lune est un, parcequ'il n'y à qu'une seule lune.

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On voit cependant qu'il y a là dedans quelque chose de conventionnel. Par exemple, le mot de goût, chez les Indiens comme chez nous, est employé aussi métaphoriquement, pour les différentes impressions que produit la poésie. Alors l'énumération varie de huit à dix. Il faut dont savoir que, lorsque ce mot est substitué à un chiffre, l'on doit entendre le goût matériel.

Un autre auteur cité par M. COLEBROKE, exprime le même nombre de la maniere suivante, &c."

The only difference in the second enumeration quoted by the Professor consists in the substitution of ocean, quality, vasu, and lunar day, for 4, 3, 8 and 15, respectively: of which vasu alone requires explanation, being the name of a species of inferior divinities, eight in number.

The astronomical pundit of the Sanskrit College has enabled me to publish a catalogue of the principal terms thus numerically employed in the Surya-siddhánta, the Arya-siddhánta, the Bhásvatís, and the other numerous astronomical works of the Hindús. It does not seem necessary to offer any explanation, beyond a simple translation of the terms, since in most cases their origin is obvious to such as are acquainted with the metaphysical or mythological systems of the Hindús. The only equivocal expression in the list appears to be , occean, which may समुद्र, either represent four or seven: but it is invariably employed in the former sense in the Surya-Siddhanta and other best authorities.

The mode of expressing any number greater than nine is, by placing consecutively, the term for each figure, beginning with the lowest or right-hand figure, as will readily be understood from the example quoted by Professor SCHLEGEL; and as there are numerous synonymes of most of the simple terms, which may be selected as they may be the best adapted to the metre of the intended aslok, an infinity of compounds may be thus formed which must be perplexing enough to a student, in addition to all the other difficulties of a science of calculations. For a few compounds, however, as 11, 12, 15, 32, &c. single expressions have been created, founded on the names of Siva, the signs of the zodiac, the days in a half-lunation, the number of human teeth, and other similar analogies, that are easily retained in the memory.

The following is the list alluded to, omitting most of the synonymes of each word, which would have swelled it to an inconvenient length. kha; vacuity,, * &c. space, heaven, zero, cypher. prithví; the earth, (and its synonymes f#, H,

o or 0.

or 1.

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चन्द्र chandra ; the moon, (चन्द्रमा, इन्दु, हिमांश, &c.)

Tч rúp; form, colour, &c.

or 2. paksh; a wing, the half of a lunar mouth,

नेत्र nétra ; the eye, (नयन, चक्षु, अक्षि, &c.)

bhuja; an arm, (3, 1, &c.)

yam; twin, also the deity of Naraha or hell. fashwina; the twin sons of Surya.

■ chhada; jaw, (the two jaws.)

or 3. af banhi; fire, (f, and its synonymes.)

&c.)

Ráma, the deity Ráma; (the three are Ráma, Balaráma, and Parasurama.)

fa Pinákanayana ; a name of Siva, (trilochan, 3-eyed.) guna; the three qualities, good, middling, and bad.

2 or 4. a Veda; the four Védas, (and their synonymes.)

fabdhi; an ocean, (, &c.) N. E. s. and W. seas. कृत Krita ; the first of the four ages of the world.

ч Yuga, an age, as the preceding.

jala; water, aft, at, &c. (similar to ocean.) or 5. ván; an arrow, (and its synonymes.)

for 6.

prán; inspiration, the five modes of vital inspiration. anga; the members (head, arms, legs, and body.) Trasa; taste, the six savours.

rága; mode of music (the six Hindu musical modes.) lritu; the six seasons according to the Hindu division. tark; Shastra: the six Shastras.

fari; the enemy, the six dangers, or temptations.

or 7. fa Muni, a saint, sage, (and its synonymes, &c.)
Eswara; vowel, the six vowels.

naga; a mountain,, and other synonymes.
ashwa; a horse, (the 7-faced horse of SURYA.)

samudra; an ocean, the seven encircling seas*.

or 8. Vasu; the eight demigods so called.

gaj; an elephant (and its synonymes.) Eight elephants support the eight Dishás, or cardinal points.

nága; a serpent; the eight species of snakes.

mangala, happiness, good fortune.

or 9. anka; a numeral : the nine units from 1 to 9.

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chhidra; an inlet, (the nine orifices of the body.)

graha; a planet, (the 7 planets and two lunar nodes.)

3 or 10. f dishá; a side, quarter, (and its synonymes,) the eight cardinal points, with the zenith and nadir. For this and all numbers composed of two or more figures other compound expressions may be formed, as .cypher-earth cypher-moon, meaning zero, one, or 10, as explained in the foregoing remarks: the following numbers however have simple expressions likewise.

or 11. or 12.

Isha ; a name of Rudra or Siva, (and his other 11 names.) Súrya; the sun, (from his 12 monthly appellations.) chakra; a wheel, the zodiac.

or 13. fa Vishva; the universe, (the 14 bhuwanas, deducting baikunt on Vishnu's heaven): see the next number.

Káma; Cupid; the Swámíor lord of the 13th títhíor lunar day. * Only used in the Granthas of South India.

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bhuwana; the world, or universe: the seven upper
seven lower heavens.

and

Indra, a name of the god Indra, (renewed at fourteen epochs.)
Manu; the fourteen munoos, or saints.

34 or 15. fafa tithi; a lunar day, (fifteen in a semilunation.)
aha; a day, (from the same analogy.)

or 16. kalá; a digit, one-sixteenth of the moon's diameter. afe akhri; a metre, consisting of four lines, having sixteen syllables in each.

nripa; a king, (and its synonymes, from the tale of the 16 rajás in the Mahabharat.)

30 or 17. fe atyakhri ; a stanza of four lines, with seventeen syllables to the line.

or 18.

fa dhriti; ditto having eighteen syllables in a line.

2 or 19. afaefa atidhriti, ditto with nineteen syllables in each line. nakh ; a finger nail.

or 20.

* or 21.

RR or 22.

8 or 24. f

Ry or 25. A 3 or 26.

RO or 27.

or 32. 3 or 33.

f Swerga; heaven. The twenty one heavens.
ifa Játi, kind, sort; race, family, cast.

Jina; the 24 Jinas of the Buddh religion.
tatwa; the 25 essences: the five quintuple elements.
aafa utkriti; in prosody, a stanza of four lines of twenty-
six syllables each.

Hornakshatra; a star, the 27 lunar mansions.
danta; a tooth, the number of human teeth.

8 or 49. A

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Deva, a god, for the 33 crores of Hindu gods; or by other accounts, 11 Rudras, 12 Suryas, 8 Vasus, and 2 Viswadevas. tána; tune; the seven octaves (of seven notes each.) váyu, the air, the 7 vayus and their 7 subspecies.

On looking over Mr. A. CSOMA's manuscript translations and extracts from the Tibetan works in the Society's library, my attention was attracted to the passage in his life of SHAKYA, where the Tibetan author quotes the epoch of BUDDHA from a variety of different authorities : here the same numerical system is seen to prevail ;—the printed Tibetan text has the dates in figures above, and written at length in the body of the text, in the same kind of symbolical words, as if to secure them from the danger of alteration; this system in fact gives the same safeguard against the incertitude of figures as the mode of writing values and To elucisums at length in European documents is intended to secure. date the subject at the time, a separate note was drawn up by Mr. CSOMA, shewing that the symbolical terms employed by the Tibetan writers were chiefly if not entirely derived, like their literature in general, from Sans

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