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 asta) 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, tryūnasasti, 'sixty deficient by three' (i. e. '57'); aṣṭādhikanavati, ninety increased by eight' (i. e. '98'); ekādhikam çatam, 'a hundred increased by one' (i. e. '101'); pañconaṁ çatam, '100 less 5' (i. e. '95'). For the nines, especially, such substitutes as ekonavinçati, 20 less 1', or '19', are not uncommon; and later the eka, '1', is left off, and unavinçati etc. have the same value. b. A case-form of éka, 'one', is connected by ná, 'not', with a larger number from which one is to be deducted: thus, ékayā ná trinçát (ÇB. PB. KB.), 'not thirty by one' (i. e. '29'); ékasmān ná pañcāçát (in ordinal), '49' (TS.); ékasyāi (abl. fem.: 366.3) ná pañcāçát, '49' (TS.); most often, ékān (i. e. ékāt, irregular abl, for ékasmāt) ná viñçatí, '19'; ékān nû 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'; triņavá, 'thrice nine'; tridaçá, 'thrice ten'. d. Of course, the numbers to be added together may be expressed by independent words, with connecting 'and': thus, núva ca navatíç ca, or náva navatím ca, ninety and nine'; dvāú ca viñçatíç ca, 'two and twenty'. But the connective is also (at least, in the older language) not seldom omitted: thus, navatír náva, ‘99'; trinçátaṁ trin, ‘33'; açitír 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'; aṣṭáçatam, '108'; trinçáchatam, ‘130'; aṣṭāvinçatiçatam, '148'; cátuḥsahasram (RV.: unless the accent is wrong), '1004'.

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, una, 'deficient' (as also other words equivalent to ūna or adhika), may be used in the same way: thus, pañconaṁ çatam, '95'.

c. Syntactical combinations are made at convenience: for example, dáça çatám 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, dvadaçám çatám, '112' (lit'ly, 'a hundred of a 12-sort, or characterised by 12'); catuçcatvārinçáṁ çatám, ‘124'; 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'); açitibhis tisŕbhis, 'with three eighties' ('240'); páñca çatani, 'five hundreds'; trini sahásrāni, 'three thousands'; ṣaṣṭiṁ sahásrāni, '60,000'; daça ca sahasrany aṣṭāu ca çatāni, 10,800': and, combined with addition, trini çatáni tráyastrincatam ca, '333'; sahasre dve pañconaṁ çatam eva ca, '2095'.

By a peculiar and wholly illogical construction, such a combination as trīņi saṣṭiçatāni, which ought to signify '480' (3×100+60), is frequently used in the Brāhmaṇas to mean '360' (3×100+60); so also dvé catustrincé çaté, '234' (not "268'); and other like cases.

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) singular is used substantively: thus, daçaçatás, '1000'; satcataiḥ padātibhiḥ (MBh.), 'with 600 foot-soldiers'; tráyastrinçat triçatáḥ satsahasráḥ (AV.), '6333'; dviçatám or dviçati, '200'; asṭādaçaçatı, '1800'.

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 astáçatam, '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. Ekā, '1', 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. Occasional forms of the ordinary declension are met with : thus, éke (loc. sing.), ékāt.

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 vyaghraḥ (H.), 'a certain tiger'; ekasmin dine, 'on a certain day'; haste dandam ekam ādāya (H.), 'taking a stick in his hand'.

b. Dva, '2', is dual only, and is entirely regular thus, N. A. V. dvaú (V. dvá), m., dvé, f. n.; I.D. Ab. drábhyām; G. L. dváyos.

c. Tri, '3', is in masc. and neut. nearly regular, like an ordinary stem in i; but their genitive is as if from trayá (only in the later language: the regular trinám occurs once in RV.). For the feminine it has the peculiar stem tis?, which is inflected in general like an r-stem; but the nom. and accus. are alike, and show no strengthening of the r; and the r is not prolonged in the gen. (excepting in the Veda). Thus

The Veda has the abbreviated neut. nom. and accus. trí. The accentuation tisṛbhis, tisṛbhyas, tisṛṇām, and tisṛsú is said to be also allowed in the later language.

The stem tis occurs in composition in tisṛdhanvá (Br.), 'a bow along with three arrows'.

d. Catúr, '4', has catvár (the more original form) in the strong cases; in the fem. it substitutes the stem cátasṛ, apparently akin with tis?, and inflected like it (but with anomalous change of accent, like that in the higher numbers: see below, 483).

The use of n before am of the gen. masc. and neut. after a final consonant of the stem is (as in sas: below, 483) a striking irregularity. The more regular gen. fem. catasṛṇām also sometimes occurs. In the later language, the accentuation of the final syllable instead of the penult is 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 sás (as of catúr), nām is the gen. ending, with mutual assimilation (198 b) of stem-final and initial of the termination. Astá (as

accented in the older language) has an alternative fuller form, astá, which is almost exclusively used in the older literature (V. and Br.), both in inflection and in composition (but some compounds with asta are found as early as the AV.); its nom.acc. is astá (usual later: found in RV. once, and in AV.), or astá (RV.), or astāú (most usual in RV.; also in AV., Br., and later).

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 dvádaça; 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 r-stems). The cases of sas, and those made from the stemform aṣṭā, have the accent throughout upon the ending.

Examples of the inflection of these words are as follows:

Saptá (in the later language súpta, as áṣṭa for aṣṭá) and náva and dáça, with the compounds of dúça ('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 náma, námabhis, námabhyas, námasu the gen. alone being like that, rather, of a a-stem: compare daçānām with îndrāṇām and námnām or ātmānām. No trace whatever of a final n is found anywhere in the language, in inflection or derivation or composition, from any of these words.

485. The tens, vinçati and trinçát etc., with their compounds, are declined regularly, as feminine stems of the same endings, and in all numbers.

Çatá and sahásra are declined regularly, as neuter (or, rarely, in the later language, as masculine) stems of the same final, in all numbers.

The like is true of the higher numbers

which have, in

deed, 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 used adjectively, agreeing in case, and, if they distinguish gender, in gender also, with the nouns thus, daçábhir vīrāiḥ, 'with ten heroes'; yé devá divy ékādaça sthá (AV.), 'what eleven gods of you are in heaven'; pañcásu jáneṣu, among the five tribes'; catasṛbhir girbhiḥ, 'with four songs'.

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, çatam dāsīḥ or çataṁ dāsīnām, ‘a hundred slaves' or 'a hundred of slaves'; vinçatya háribhis, 'with twenty bays'; ṣaṣtyám çarátsu, ‘in 60 autumns'; çaténa páçaiḥ, with a hundred fetters'; çatám sahásram ayútam nyarbudam jaghána 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 vāṇāiḥ, '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 kṛṣṭiṣu, among the five races'; saptá rṣīņām, 'of seven bards'; sahásram ṛṣibhiḥ, 'with a thousand bards'; çatám purbhiḥ, 'with a hundred strongholds'.

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,

éka, '1', forms no ordinal; instead is used prathamá (i. e. pra-tama, 'foremost'); ādi is rare in the Brāhmaṇas, and adya even in the Sūtras;

from drá, '2', and tri, '3', come dritiya and tṛtiya (secondarily, through drita and abbreviated trita);

catúr, 4, sás, '6', and saptá, '7', take the ending tha: thus, caturtha, ṣasthá, saptátha; but for 'fourth' are used also turiya and túrya, and saptátha belongs to the older language only pañcatha, for fifth, is excessively rare;

the numerals for 5 and 7 usually, and for 'S', '9', '10', add me, forming pañcamá, saptamá, aṣṭamá, navamá, daçamá;