Sanskrit Grammar/Chapter VI
475. The simple cardinal numerals for the first ten numbers (which are the foundation of the whole class), with their derivatives, the tens, and with some of the higher members of the decimal series, are as follows:
a. The accent saptá and aṣṭá is that belonging to these words in all accentuated texts; according to the grammarians, they are sápta and áṣṭa in the later language. See below, 483.
b. The series of decimal numbers may be carried still further; but there are great differences among the different authorities with regard to their names; and there is more or less of discordance even from ayúta on.
c. Thus, in the TS. and MS. we find ayúta, niyúta, prayúta, árbuda, nyàrbuda, samudrá, mádhya, ánta, parārdhá; K. reverses the order of niyúta and prayúta, and inserts badva after nyarbuda (reading nyarbudha): these are probably the oldest recorded series.
d. In modern time, the only numbers in practical use above thousand are lakṣa (lac or lakh) and koṭi (crore); and an Indian sum is wont to be pointed thus: 123,45,67,890, to signify 123 crores, 45 lakhs, 67 thousand, eight hundred and ninety.
e. As to the alleged stem-forms pañcan etc., see below, 484. As to the form ṣakṣ instead of ṣaṣ, see above, 146b. The stem dva appears in composition and derivation also as dvā and dvi; catúr in composition is accented cátur. The older form of aṣṭa is aṣṭā: see below, 483. Forms in -çat and -çati for the tens are occasionally interchanged: e. g. viṅçat (MBh. R.), triṅçati (AB.), pañcāçati (RT.).
f. The other numbers are expressed by the various composition and syntactical combination of those given above. Thus :
476. The odd numbers between the even tens are made by prefixing the (accented) unit to the ten to which its value is to be added: but with various irregularities. Thus:
a. eka in 11 becomes ekā, but is elsewhere unchanged;
b. dva becomes everywhere dvā; but in 42–72 and in 92 it is interchangeable with dvi, and in 82 dvi alone is used;
c. for tri is substituted its nom. pl. masc. tráyas; but tri itself is also allowed in 43–73 and in 93, and in 83 tri alone is used;
d. ṣaṣ becomes ṣo in 16, and makes the initial d of daça lingual (199d); elsewhere its final undergoes the regular conversion (226 b, 198 b) to ṭ or ḍ or ṇ; and in 96 the n of navati is assimilated to it (199c);
e. aṣṭa becomes aṣṭā (483) in 18–38, and has either form in the succeeding combinations.
g. The numbers 21–29 are made like those for 31–39; the numbers 41–49, 51–59, 71–79, and 91–99 are made like those for 61–69.
h. The forms made with dvā and trayas are more usual than those with dvi and tri, which are hardly to be quoted from the older literature (V. and Br.). The forms made with aṣṭā (instead of aṣṭa) are alone found in the older literature (483), and are usual in the later.
477. The above are the normal expressions for the odd numbers. But equivalent substitutes for them are also variously made. Thus:
a. By use of the adjectives ūna deficient and adhika redundant, in composition with lesser numbers which are to be subtracted or added, and either independently qualifying or (more usually) in composition with larger numbers which are to be increased or diminished by the others: thus, tryūnaṣaṣṭiḥ sixty deficient by three (i. e. 57); aṣṭādhikanavatiḥ ninety increased by eight (i. e. 98); ekādhikaṁ çatam a hundred increased by one (i. e. 101); pañconaṁ çatam 100 less 5 (i. e. 95). For the nines, especially, such substitutes as ekonaviṅçatiḥ 20 less 1, or 19, are not uncommon; and later the eka 1 is left off, and ūnaviṅçati etc. have the same value.
b. A case-form of a smaller number, generally éka one is connected by ná not with a larger number from which it is to be deducted: thus, ékayā ná triṅçát (ÇB. PB. KB.) not thirty by one (29); dvābhyāṁ ná ’çītím (ÇB.) not eighty by two (78); pañcábhir ná catvā́ri çatā́ni (ÇB.) not four hundred by five (395); ékasmān ná pañcāçát (in ordinal) 49 (TS.); ékasyāi (abl. fem. : 307 h) ná pañcāçát 49 (TS.); most often, ékān (i. e. ékāt, irregular abl. for ékasmāt) ná viṅçatíḥ 19; ékān ná çatám 99. This last form is admitted also in the later language; the others are found in the Brāhmaṇas.
c. Instances of multiplication by a prefixed number are occasionally met with: thus, triṣaptá thrice seven; triṇavá thrice nine; tridaçá thrice ten.
d. Of course, the numbers to be added together may be expressed by independent words, with connecting and: thus, náva ca navatíç ca, or náva navatíç ca ninety and nine; dvāú ca viṅçatíç ca two and twenty. But the connective is also (at least, in the older language) not seldom omitted: thus, navatír náva 99; triṅçátaṁ trī́n 33; açītír aṣṭāú 88.
478. The same methods are also variously used for forming the odd numbers above 100. Thus:a. The added number is prefixed to the other, and takes the accent: for example, ékaçatam 101; aṣṭāçatam 108; triṅçácchatam 130; aṣṭāviṅçatiçatam 128; cátuḥsahasram (RV.: unless the accent is wrong) 1004; açītisahasram 1080.
b. Or, the number to be added is compounded with adhika redundant, and the compound is either made to qualify the other number or is further compounded with it: thus, pañcādhikaṁ çatam or pañcādhikaçatam 105. Of course, ūna deficient (as also other words equivalent to ūna or adhika) may be used in the same way: thus, pañconaṁ çatam 95, ṣaṣṭiḥ pañcavarjitā 55; çatam abhyadhikaṁ ṣaṣṭitaḥ 160.
c. Syntactical combinations are made at convenience: for example, dáça çatáṁ ca 110; çatám ékaṁ ca 101.
479. Another usual method (beginning in the Brāhmaṇas) of forming the odd numbers above 100 is to qualify the larger number by an adjective derived from the smaller, and identical with the briefer ordinal (below, 487): thus, dvādaçáṁ çatám, 112 (lit'ly a hundred of a 12-sort, or characterised by 12); catuçcatvāriṅçáṁ çatám 144; ṣaṭṣaṣṭáṁ çatám 166.
480. To multiply one number by another, among the higher or the lower denominations, the simplest and least ambiguous method is to make of the multiplied number a dual or plural, qualified by the other as any ordinary noun would be; and this method is a common one in all ages of the language. For example: páñca pañcāçátas five fifties (250); náva navatáyas nine nineties (810); açītíbhis tisṛ́bhis with three eighties (240); páñca çatā́ni five hundreds; trī́ṇi sahásrāṇi three thousands; ṣaṣṭíṁ sahásrāṇi 60,000; daça ca sahasrāṇy aṣṭāu ca çatāni 10,800: and, combined with addition, trī́ṇi çatā́ni tráyastriṅçataṁ ca 333; sahasre dve pañconaṁ çatam eva ca 2095.
a. In an exceptional case or two, the ordinal form appears to take the place of the cardinal as multiplicand in a like combination: thus, ṣaṭtriṅçā́ṅç ca catúraḥ (RV.) 36x4 (lit. four of the thirty-six kind); trī́ṅr ekādaçā́n (RV.) or traya ekādaçāsaḥ (ÇÇS. viii. 21. 1) 11x3.
b. By a peculiar and wholly illogical construction, such a combination as trīṇi ṣaṣṭiçatāni, which ought to signify 480 (3x100+60), is repeatedly used in the Brāhmaṇas to mean 360 (3x100+60); so also dvé catustriṅçé çaté 234 (not 268); dvāṣaṣṭāni trīṇi çatāni 362; and other like cases. And even R. has trayaḥ çataçatārdhāḥ 350.
481. But the two factors, multiplier and multiplied, are also, and in later usage more generally, combined into a compound (accented on the final); and this is then treated as an adjective, qualifying the numbered noun; or else its neuter or feminine (in ī) singular is used substantively: thus, daçaçatā́s 1000; ṣaṭçatāiḥ padātibhiḥ (MBh.) with 600 foot-soldiers; tráyastriṅçat triçatā́ḥ ṣaṭsahasrāḥ (AV.) 6333; dviçatám or dviçatī́ 200; aṣṭādaçaçatī 1800.a. In the usual absence of accentuation, there arises sometimes a question as to how a compound number shall be understood: whether aṣṭaçatam, for example, is aṣṭáçatam 108 or aṣṭaçatám 800, and the like.
482. Inflection. The inflection of the cardinal numerals is in many respects irregular. Gender is distinguished only by the first four.
a. Eka one is declined after the manner of a pronominal adjective (like sárva, below, 524); its plural is used in the sense of some, certain ones. Its dual does not occur.
b. Occasional forms of the ordinary declension are met with: thus, éke (loc. sing.), ékāt (477 b).
c. In the late literature, eka is used in the sense of a certain, or even sometimes almost of a, as an indefinite article. Thus, eko vyāghraḥ (H.) a certain tiger; ekasmin dine on a certain day; haste daṇḍam ekam ādāya (H.) taking a stick in his hand.
d. Dva two is dual only, and is entirely regular: thus, N. A. V. dvāú (dvā́, Veda) m., dvé f. n.; I. D. Ab. dvā́bhyām; G. L. dváyos.
e. Tri three is in masc. and neut. nearly regular, like an ordinary stem in i; but the genitive is as if from trayá (only in the later language: the regular trīṇā́m occurs once in RV.). For the feminine it has the peculiar stem tisṛ́, which is inflected in general like an ṛ-stem; but the nom. and accus. are alike, and show no strengthening of the ṛ; and the ṛ is not prolonged in the gen. (excepting in the Veda). Thus:
f. The Veda has the abbreviated neut. nom. and accus. trī́. The accentuation tisṛbhís, tisṛbhyás, tisṛ́ṇām, and tisṛṣú is said to be also allowed in the later language. The stem tisṛ occurs in composition in tisṛdhanvá (B.) a bow with three arrows.
g. Catúr four has catvā́r (the more original form) in the strong cases; in the fem. it substitutes the stem cátasṛ, apparently akin with tisṛ́, and inflected like it (but with anomalous change of accent, like that in the higher numbers: see below, 483). Thus:
h. The use of n before ām of the gen. masc. and neut. after a final consonant of the stem is (as in ṣaṣ: below, 483) a striking irregularity. The more regular gen. fem. catasṝṇām also sometimes occurs. In the later language, the accentuation of the final syllable instead of the penult is said to be allowed in inst., dat.-abl., and loc.
483. The numbers from 5 to 19 have no distinction of gender, nor any generic character. They are inflected, somewhat irregularly, as plurals, save in the nom.-acc., where they have no proper plural form, but show the bare stem instead. Of ṣáṣ (as of catúr), nām is the gen. ending, with mutual assimilation (198 b) of stem-final and initial of the termination. Aṣṭá (as accented in the older language) has an alternative fuller form, aṣṭā́, which is almost exclusively used in the older literature (V. and B), both in inflection and in composition (but some compounds with aṣṭa are found as early as the AV.); its nom.-acc. is aṣṭá (usual later: found in RV. once, and in AV.), or aṣṭā́ (RV.), or aṣṭāú (most usual in RV.; also in AV., B., and later).
a. The accent is in many respects peculiar. In all the accented texts, the stress of voice lies on the penult before the endings bhis, bhyas, and su, from the stems in a, whatever be the accent of the stem: thus, pañcábhis from páñca, navábhyas from náva, daçásu from dáça, navadaçábhis from návadaça, ekādaçábhyas from ékādaça, dvādaçásu from dvā́daça (according to the grammarians, either the penult or the final is accented in these forms in the later language). In the gen. pl., the accent is on the ending (as in that of i-, u-, and ṛ-sterns): thus, pañcadaçānā́m, saptadaçānā́m. The cases of ṣaṣ, and those made from the stem-form aṣṭā, have the accent throughout upon the ending.
b. Examples of the inflection of these words are as follows:
c. Saptá (in the later language sápta, as áṣṭa for aṣṭá) and náva and dáça, with the compounds of dáça (11–19), are declined like páñca, and with the same shift of accent (or with alternative shift to the endings, as pointed out above).
484. The Hindu grammarians give to the stems for 5 and 7–19 a final n: thus, pañcan, saptan, aṣṭan, navan, daçan, and ekādaçan etc. This, however, has nothing to do with the demonstrably original final nasal of 7, 9, and 10 (compare septem, novem, decem; seven, nine, ten); it is only owing to the fact that, starting from such a stem-form, their inflection is made to assume a more regular aspect, the nom.-acc. having the form of a neut. sing. in an, and the instr., dat.-abl., and loc. that of a neut. or masc. pl. in an: compare nā́ma, nā́mabhis, nā́mabhyas, nā́masu — the gen. alone being, rather, like that of an a-stem: compare daçānā́m with índrāṇām and nā́mnām or ātmánām. No trace whatever of a final n is found anywhere in the language, in inflection or derivation or composition, from any of these words (though ÇB. has twice daçaṁdaçín, for the usual daçadaçín).
485. a. The tens, viṅçatí and triṅçát etc., with their compounds, are declined regularly, as feminine stems of the same endings, and in all numbers.
b. Çatá and sahásra are declined regularly, as neuter (or, rarely, in the later language, as masculine) stems of the same final, in all numbers.
c. The like is true of the higher numbers — which have, indeed, no proper numeral character, but are ordinary nouns.
486. Construction. As regards their construction with the nouns enumerated by them —
a. The words for 1 to 19 are in the main used adjectively, agreeing in case, and, if they distinguish gender, in gender also, with the nouns: thus, daçábhir vīrāíḥ with ten heroes; yé devā́ divy ékādaça sthá (AV.) what eleven gods of you are in heaven; pañcásu jáneṣu among the five tribes; catasṛbhir gīrbhíḥ with four songs. Rarely occur such combinations as dáça kaláçānām (RV.) ten pitchers, ṛtūnāṁ ṣaṭ (R.) six seasons.
b. The numerals above 19 are construed usually as nouns, either taking the numbered noun as a dependent genitive, or standing in the singular in apposition with it: thus, çataṁ dāsīḥ or çataṁ dāsīnām a hundred slaves or a hundred of slaves; viṅçatyā́ háribhiḥ with twenty bays; ṣaṣṭyā́ṁ çarátṣu in 60 autumns; çaténa pā́çāiḥ with a hundred fetters; çatáṁ sahásram ayútaṁ nyàrbudaṁ jaghā́na çakró dásyūnām (AV.) the mighty [Indra] slew a hundred, a thousand, a myriad, a hundred million, of demons. Occasionally they are put in the plural, as if used more adjectively: thus, pañcāçadbhir bāṇāiḥ with fifty arrows.
c. In the older language, the numerals for 5 and upward are sometimes used in the nom.-acc. form (or as if indeclinably) with other cases also: thus, páñca kṛṣṭíṣu among the five races; saptá rṣīṇām of seven bards; sahásram ṛ́ṣibhiḥ with a thousand bards; çatám pūrbhíḥ with a hundred strongholds. Sporadic instances of a like kind are also met with later.487. Ordinals. Of the classes of derivative words coming from the original or cardinal numerals, the ordinals are by far the most important; and the mode of their formation may best be explained here.
Some of the first ordinals are irregularly made: thus,
a. éka 1 forms no ordinal; instead is used prathamá (i. e. pratama foremost); ādya (from ādi beginning) appears first in the Sūtras, and ādima much later;
b. from dvá 2, and trí 3, come dvitī́ya and tṛtī́ya (secondarily, through dvita and abbreviated trita);
c. catúr 4, ṣáṣ 6, and saptá 7, take the ending tha: thus, caturthá, ṣaṣṭhá, saptátha; but for fourth are used also turī́ya and túrya, and saptátha belongs to the older language only; pañcatha, for fifth, is excessively rare;
d. the numerals for 5 and 7 usually, and for 8, 9, 10, add ma, forming pañcamá, saptamá, aṣṭamá, navamá, daçamá;
e. for 11th to 19th, the forms are ekādaçá, dvādaçá, and so on (the same with the cardinals, except change of accent); but ekādaçama etc. occasionally occur also;
f. for the tens and intervening odd numbers from 20 onward, the ordinal has a double form — one made by adding the full (superlative) ending tamá to the cardinal: thus, viṅçatitamá, triṅçattamá, açītitamá, etc.; the other, shorter, in a, with abbreviation of the cardinal: thus, viṅçá 20th; triṅçá 30th; catvāriṅçá 40th; pañcāçá 50th; ṣaṣṭá 60th; saptatá 70th; açītá 80th; navatá 90th; and so likewise ekaviṅçá 21st, catustriṅçá 34th; aṣṭācatvāriṅçá 48th; dvāpañcāçá 52d; ekaṣaṣṭá 61st; and ekānnaviṅçá and ūnaviṅçá and ekonaviṅçá 19th; — and so on. Of these two forms, the latter and briefer is by far the more common, the other being not quotable from the Veda, and extremely rarely from the Brāhmaṇas. From 50th on, the briefer form is allowed by the grammarians only to the odd numbers, made up of tens and units; but it is sometimes met with, even in the later language, from the simple ten.
g. Of the higher numbers, çatá and sahásra form çatatamá and sahasratamá; but their compounds have also the simpler form: thus, ekaçatá or ekaçatatama 101st.
h. Of the ordinals, prathamá (and ādya), dvitī́ya, tṛtī́ya, and turī́ya (with túrya) form their feminine in ā; all the rest make it in ī.
488. The ordinals, as in other languages, have other than ordinal offices to fill; and in Sanskrit especially they are general adjectives to the cardinals, with a considerable variety of meanings, as fractionals, as signifying composed of so many parts or so-many-fold, or containing so many, or (as was seen above, 479) having so many added.
a. In a fractional sense, the grammarians direct that their accent be shifted to the first syllable: thus, dvítīya half; tṛ́tīya third part; cáturtha quarter; and so on. But in accented texts only tṛ́tīya third, and cáturtha (ÇB.) and túrīya quarter, are found so treated; for half occurs only ardhá; and caturthá (MS. etc.), pañcamá, and so on, are accented as in their ordinal use.
489. There are other numeral derivatives: thus —
a. multiplicative adverbs, as dvís twice, trís thrice, catús four times;
b. adverbs with the suffixes dhā (1104) and ças (1106): for example, ekadhā́ in one way, çatadhā́ in a hundred ways; ekaças one by one, çataçás by hundreds;
c. collectives, as dvítaya or dvayá a pair, dáçjataya or daçát a decade;
d. adjectives like dvika composed of two, pañcaka consisting of five or fives;
and so on; but their treatment belongs rather to the dictionary, or to the chapter on derivation.