CHAPTER VI.

CHAPTER VI.    

NUMERALS.

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:

1

एक
 éka

10

दश
 dáça

100

शत
 çatá

2

द्व
 dvá

20

विंशति
 viṅçatí

1000

सहस्र
 sahásra

3

त्रि
 trí

30

त्रिंशत्
 triṅçát

10,000

अयुत
 ayúta

4

चतुर्
 catúr

40

चत्वारिंशत्
 catvāriṅçát

100,000

लक्ष
 lakṣá

5

पञ्च
 páñca

50

पञ्चाशत्
 pañcāçát

1,000,000

प्रयुत
 prayúta

6

षष्
 ṣáṣ

60

षष्टि
 ṣaṣṭí

10,000,000

कोटि
 kóṭi

7

सप्त
 saptá

70

सप्तति
 saptatí

108

अर्बुद
 arbudá

8

अष्ट
 aṣṭá

80

अशीति
 açītí

109

महार्बुद
 mahārbuda

9

नव
 náva

90

नवति
 navatí

1010

खर्व
 kharvá

10

दश
 dáça

100

शत
 çatá

1011

निखर्व
 nikharva

a. The accent saptá and aṣṭá is that belonging to these words in all accentuated texts; according to the grammarians, they are sápta andáṣṭa 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 withregard to their names; and there is more or less of discordance even from ayúta on.

c. Thus, in the TS. and MS. we find ayútaniyútaprayútaárbudanyàrbudasamudrámádhyaántaparārdhá; K. reverses the order ofniyúta 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 dvicatúr 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  or  or ; 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.

f. Thus:

11

ékādaça

31

ékatriṅçat

61

ékaṣaṣṭi

81

ékāçīti

12

dvā́daça

32

dvā́triṅçat

62

dvā́ṣaṣṭi

82

dvyàçīti

dvíṣaṣṭi

13

tráyodaça

33

tráyastriṅçat

63

tráyaḥṣaṣṭi

83

tryàçīti

tríṣaṣṭi

14

cáturdaça

34

cátustriṅçat

64

cátuḥṣaṣṭi

84

cáturaçīti

15

páñcadaça

35

páñcatriṅçat

65

páñcaṣaṣṭi

85

páñcāçīti

16

ṣóḍaça

36

ṣáṭtriṅçat

66

ṣáṭṣaṣṭi

86

ṣáḍaçīti

17

saptádaça

37

saptátriṅçat

67

saptáṣaṣṭi

87

saptā́çīti

18

aṣṭā́daça

38

aṣṭā́triṅçat

68

aṣṭáṣaṣṭi

88

aṣṭā́çīti

aṣṭā́ṣaṣṭi

19

návadaça

39

návatriṅçat

69

návaṣaṣṭi

89

návāçīti

g. The numbers 21–29 are made like those for 31–39; the numbers 41–4951–5971–79, 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 çatama hundred increased by one (i. e. 101); pañconaṁ çatam 100 less 5 (i. e. 95). For the nines, especially, such substitutes asekonaviṅçatiḥ 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  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 ékasmātná viṅçatíḥ 19ékān 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 seventriṇavá thrice ninetridaçáthrice ten.

d. Of course, the numbers to be added together may be expressed by independent words, with connecting and: thus, náva ca navatíç ca, ornáva navatíç ca ninety and ninedvāú ca viṅçatíç ca two and twenty. But the connective is also (at least, in the older language) not seldom omitted: thus, navatír náva 99triṅçátaṁ trī́n 33açītír 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 toūna or adhika) may be used in the same way: thus, pañconaṁ çatam 95, ṣaṣṭiḥ pañcavarjitā 55çatam abhyadhikaṁ ṣaṣṭitaḥ 160.

c. Syntactical combinations are made at convenience: for example, dáça çatáṁ ca 110çatám 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 çatám112 (lit'ly a hundred of a 12-sort, or characterised by 12); catuçcatvāriṅçáṁ çatám 144ṣaṭṣaṣṭáṁ 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 hundredstrī́ṇi sahásrāṇi three thousandsṣaṣṭíṁ sahásrāṇi 60,000daça ca sahasrāṇy aṣṭāu ca çatāni 10,800: and, combined with addition, trī́ṇi çatā́ni tráyastriṅçataṁ ca 333sahasre 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 1000ṣaṭçatāiḥ padātibhiḥ (MBh.) with 600 foot-soldierstráyastriṅçat triçatā́ḥ ṣaṭsahasrāḥ(AV.) 6333dviçatám or dviçatī́ 200aṣṭādaçaçatī 1800.

a. In the usual absence of accentuation, there arises sometimes a question as to how a compound number shall be understood: whetheraṣṭaçatam, 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 tigerekasmin dine on a certain dayhaste 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-stem; but the nom. and accus. are alike, and show no strengthening of the ; and the  is not prolonged in the gen. (excepting in the Veda). Thus:

m.

n.

f.

N.

tráyas

trī́ṇi

tisrás

A.

trī́n

trī́ṇi

tisrás

I.

tribhís

tisṛ́bhis

D. Ab.

tribhyás

tisṛ́bhya

G.

trayāṇā́m

tisṛṇā́m

L.

triṣú

tisṛ́ṣu

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 withtisṛ́, and inflected like it (but with anomalous change of accent, like that in the higher numbers: see below, 483). Thus:

m.

n.

f.

N.

catvā́ras

catvā́ri

cátasras

A.

catúras

catvā́ri

cátasras

I.

catúrbhis

catasṛ́bhis

D. Ab.

catúrbhyas

catasṛ́bhyas

G.

caturṇā́m

catasṛṇā́m

L.

catúrṣu

catasṛ́ṣu.

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 fromdáça, 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 -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:

N.A.

páñca

ṣáṭ

aṣṭāú

aṣṭá

I.

pañcábhis

ṣaḍbhís

aṣṭābhís

aṣṭábhis

D. Ab.

pañcábhyas

ṣaḍbhyás

aṣṭābhyás

aṣṭábhyas

G.

pañcānā́m

ṣaṇṇā́m

aṣṭānā́m

L.

pañcásu

ṣaṭsú

aṣṭāsú

aṣṭásu.

c. Saptá (in the later language sápta, as áṣṭa for aṣṭá) and náva and dáça, with the compounds of dáça (11–19), are declined likepáñca, 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 79, 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, nā́mabhyasnā́masu — the gen. alone being, rather, like that of an a-stem: compare daçānā́m with índrāṇām and nā́mnām orātmánām. 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 heroesyé devā́ divy ékādaça sthá (AV.) what eleven gods of you are in heavenpañcásu jáneṣuamong the five tribescatasṛbhir gīrbhíḥ with four songs. Rarely occur such combinations as dáça kaláçānām (RV.) ten pitchersṛtūnāṁ 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 slavesviṅçatyā́ háribhiḥ with twenty baysṣaṣṭyā́ṁ çarátṣu in 60 autumnsçaténa pā́çāiḥ with a hundred fettersçatáṁ 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 racessaptá rṣīṇām of seven bardssahásram ṛ́ṣibhiḥ with a thousand bardsçatám 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, andādima much later;

b. from dvá 2, and trí 3, come dvitī́ya and tṛtī́ya (secondarily, through dvita and abbreviated trita);

c. catúr 4ṣáṣ 6, and saptá 7, take the ending tha: thus, caturtháṣaṣṭhásaptátha; 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 8910, add ma, forming pañcamásaptamáaṣṭamánavamádaçamá;

e. for 11th to 19th, the forms are ekādaçádvādaçá, and so on (the same with the cardinals, except change of accent); but ekādaçamaetc. 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, viṅçatitamátriṅçattamáaçītitamá, etc.; the other, shorter, in a, with abbreviation of the cardinal: thus, viṅçá 20thtriṅçá 30thcatvāriṅçá 40thpañcāçá 50thṣaṣṭá 60thsaptatá 70thaçītá 80thnavatá 90th; and so likewise ekaviṅçá 21stcatustriṅçá 34thaṣṭācatvāriṅçá 48thdvāpañcāçá 52dekaṣaṣṭá 61st; and ekānnaviṅçá and ūnaviṅçá andekonaviṅçá 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, ekaçatáor ekaçatatama 101st.

h. Of the ordinals, prathamá (and ādya), dvitī́yatṛtī́ya, 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 halftṛ́tīya third partcáturtha 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 twicetrís thricecatús four times;

b. adverbs with the suffixes dhā (1104) and ças (1106): for example, ekadhā́ in one wayçatadhā́ in a hundred waysekaças one by one, çataçás by hundreds;

c. collectives, as dvítaya or dvayá a pairdáçjataya or daçát a decade;

d. adjectives like dvika composed of twopañcaka consisting of five or fives;

and so on; but their treatment belongs rather to the dictionary, or to the chapter on derivation.