#### NUMERALS

132. The Latin Numerals may be classified as follows:—

1. Cardinal Numbers, answering the question how many? as, ūnus, one; duo, two, etc.
2. Ordinal Numbers,1 adjectives derived (in most cases) from the Cardinals, and answering the question which in order? as, prīmus, first; secundus, second, etc.
3. Distributive Numerals, answering the question how many at a time? as, singulī, one at a time; bīnī, two by two, etc.
II. NUMERAL ADVERBS, answering the question how often? as, semel, once; bis, twice, etc.

#### Cardinals and Ordinals

133. These two series are as follows:—

 CARDINAL ORDINAL ROMAN NUMERALS 1. ūnus, ūna, ūnum, one prīmus, -a, -um, first I 2. duo, duae, duo, two secundus (alter), second II 3. trēs, tria, three tertius, third III 4. quattuor quārtus IIII or IV 5. quīnque quīntus V 6. sex sextus VI 7. septem septimus VII 8. octō octāvus VIII 9. novem nōnus VIIII or IX 10. decem decimus X 11. ūndecim ūndecimus XI 12. duodecim duodecimus XII 13. tredecim (decem (et) trēs） (decimus (et） tertius） XIII 14. quattuordecim XIIII or XIV 15. quīndecim XV 16. sēdecim XVI 17. septendecim XVII 18. duodēvīgintī (octōdecim) duodēvīcēnsimus (） XVIII

Note 1.--The forms in are often written without the n: as, , etc.

Note 2.--The forms octōdecim, novendecim are rare, duodēvīgintī (two from twenty), ūndēvīgintī (one from twenty), being used instead. So 28, 29; 38, 39; etc. may be expressed either by the subtraction of two and one or by the addition of eight and nine respectively.

 CARDINAL ORDINAL ROMAN NUMERALS 19. ūndēvīgintī (novendecim) ūndēvīcēnsimus(nōnus decimus） XVIIII or XIX 20. vīgintī vīcēnsimus (vīgēnsimus) XX 21. (or , etc.） vīcēnsimus prīmus (, etc.） XXI 30. trīgintā trīcēnsimus XXX 40. quadrāgintā quadrāgēnsimus XXXX or XL 50. quīnquāgintā quīnquāgēnsimus ↓ or L 60. sexāgintā sexāgēnsimus LX 70. septuāgintā septuāgēnsimus LXX 80. octōgintā octōgēnsimus LXXX 90. nōnāgintā nōnāgēnsimus LXXXX or XC 100. centum centēnsimus C 101. centum (et) ūnus, etc. centēnsimus prīmus, etc. CI 200. ducentī, -ae, -a ducentēnsimus CC 300. trecentī trecentēnsimus CCC 400. quadringentī quadringentēnsimus CCCC 500. quīngentī quīngentēnsimus D 600. sescentī sescentēnsimus DC 700. septingentī septingentēnsimus DCC 800. octingentī octingentēnsimus DCCC 900. nōngentī nōngentēnsimus DCCCC 1000. mīlle mīllēnsimus [oolig ] (CIↃ) or M 5000. (mīllia) quīnquiēns mīllēnsimus IↃↃ 10,000. (mīllia) deciēns mīllēnsimus CCIↃↃ 100,000. centum mīlia (mīllia) centiēns mīllēnsimus CCCIↃↃↃ

#### Declension of Cardinals and Ordinals

134. Of the Cardinals only , , , the hundreds above one hundred, and when used as a noun, are declinable.

a. For the declension of , see § 113. It often has the meaning of same or only. The plural is used in this sense; but also, as a simple numeral, to agree with a plural noun of a singular meaning: as, , one camp (cf. § 137. b). The plural occurs also in the phrase , one party and the other (the ones and the others).

b. Duo,2 two, and trēs, three, are thus declined:—

Note.-- Ambō, both, is declined like .

 M. F. N. M., F. N. NOM. GEN. DAT. ACC. (du） (tr） ABL.

c. The hundreds, up to 1000, are adjectives of the First and Second Declensions, and are regularly declined like the plural of bonus.

d. Mīlle, a thousand, is in the singular an indeclinable adjective:—

1. , in a thousand ways.
2. , with a thousand men.
3. (Aen. 4.701) , drawing out a thousand various colors.

In the plural it is used as a neuter noun, and is declined like the plural of (§ 69): , , , etc.

Note.--The singular is sometimes found as a noun in the nominative and accusative: as, , he sent a thousand (of) men; in the other cases rarely, except in connection with the same case of : as, , , with eight thousand foot and a thousand horse.

e. The ordinals are adjectives of the First and Second Declensions, and are regularly declined like bonus.

135. Cardinals and Ordinals have the following uses:—

a. In numbers below 100, if units precede tens, is generally inserted: duo et vīgintī; otherwise is omitted: .

b. In numbers above 100 the highest denomination generally stands first, the next second, etc., as in English. Et is either omitted entirely, or stands between the two highest denominations: () septingentī sexāgintā quattuor , 1764.

Note.--Observe the following combinations of numerals with substantives:—

1. ūnus et vīgintī mīlitēs , or vīgintī mīlitēs () ūnus, 21 soldiers.
2. duo mīlia quīngentī mīlitēs , or , 2500 soldiers.
3. , 1231 soldiers.

c. After the name of the objects enumerated is in the genitive:

1. , two thousand men. 3
2. , with three thousand soldiers.
3. , three thousand paces (three miles).

d. For million, billion, trillion, etc., the Romans had no special words, out these numbers were expressed by multiplication (cf. § 138. a).

e. Fractions are expressed, as in English, by cardinals in the numerator and ordinals in the denominator. The feminine gender is used to agree with expressed or understood:—two-sevenths, (sc. ); three-eighths, (sc. ).

One-half is or .

Note 1.--When the numerator is one, it is omitted and is expressed: onethird, one-fourth, .

Note 2.--When the denominator is but one greater than the numerator, the numerator only is given: two-thirds, three-fourths, , etc.

Note 3.--Fractions are also expressed by special words derived from as, a pound: as, triēns, a third; bēs, two-thirds. See § 637.

#### Distributives

136. Distributive Numerals are declined like the plural of bonus.

Note.--These answer to the interrogative quotēnī, how many of each? or how many at a time?

 1. singulī, one by one 18. octōnī dēnī or duodēvīcēnī 100. centēnī 2. bīnī, two by two 200. ducēnī 3. ternī, trīnī 19. novēnī dēnī or ūndēvīcēnī 300. trecēnī 4. quaternī 400. quadringēnī 5. quīnī 20. vīcēnī 500. quīngēnī 6. sēnī 21. vīcēnī singulī, etc. 600. sescēnī 7. septēnī 30. trīcēnī 700. septingēnī 8. octōnī 40. quadrāgēnī 800. octingēnī 9. novēnī 50. quīnquāgēnī 900. nōngēnī 10. dēnī 60. sexāgēnī 1000. mīllēnī 11. ūndēnī 70. septuāgēnī 2000. 12. duodēnī 80. octōgēnī 10,000. 13. , etc. 90. nōnāgēnī 100,000.

137. Distributives are used as follows:—

a. In the sense of so many apiece or on each side: as, , one apiece (one each to each one); agrī septēna iūgera plēbī dīvīsa sunt , i.e. seven jugera to each citizen (seven jugera each), etc.

b. Instead of cardinals, to express simple number, when a noun plural in form but usually singular in meaning is used in a plural sense: as, , two camps ( would mean two forts). With such nouns , not , is used for three: as, (not ) castra, three camps; means camps in threes.

c. In multiplication: as, , twice two; , in thrice seven days.

d. By the poets instead of cardinal numbers, particularly where pairs or sets are spoken of: as, , two shafts (two in a set).

138. The Numeral Adverbs answer the question quotiēns (), how many times? how often?

 1 semel, once 2 bis, twice 3 ter, thrice 4 quater 5 quīnquiēns (-ēs)4 6 sexiēns 7 septiēns 8 octiēns 9 noviēns 10 deciēns 11 ūndeciēns 12 duodeciēns 13 terdeciēns 14 quaterdeciēns 15 quīndeciēns 16 sēdeciēns 17 septiēsdeciēns 18 duodēvīciēns 19 ūndēvīciēns 20 vīciēns 21 ,5 etc. 30 trīciēns 40 quadrāgiēns 50 quīnquāgiēns 60 sexāgiēns 70 septuāgiēns 80 octōgiēns 90 nōnāgiēns 100 centiēns 200 ducentiēns 300 trecentiēns 1000 mīliēns 10,000

a. Numeral Adverbs are used with to express the higher numbers:

1. () sēstertium, 3,300,000 sesterces (three and thirty times a hundred thousand sesterces).
2. vīciēs ac septiēs mīliēs () sēstertium, 2,700,000,000 sesterces (twenty-seven thousand times a hundred thousand).

Note.--These large numbers are used almost exclusively in reckoning money, and is regularly omitted (see § 634).

#### Other Numerals

139. The following adjectives are called Multiplicatives:—
1. simplex, single; duplex, double, twofold; triplex, triple, threefold; , quīnquiplex, septemplex, decemplex, centuplex, sēsquiplex (1 1/2), multiplex (manifold).

a. Proportionals are: , , , , etc., twice as great, thrice as great, etc.

b. Temporals: , trīmus, of two or three years' age; , triennis, lasting two or three years; , trimēstris, of two or three months; bīduum, a period of two days; biennium, a period of two years.

c. Partitives: , ternārius, of two or three parts.

d. Other derivatives are: ūniō, unity; bīniō, the two (of dice); of the first legion; prīmārius, of the first rank; of 10 asses bīnus (distributive), double, etc.

1 The Ordinals (except ) are formed by means of suffixes related to those used in the superlative and in part identical with them. Thus, (compare the form ) may be regarded as the last of a series of ten;prīmus is a superlative of a stem akin to prō; the forms in -tus (） may be compared with the corresponding Greek forms in -τος, and with superlatives in -ισ-το-ς, while the others have the superlative ending (changed to ). Of the exceptions, is a participle of is a comparative form (compare -τερος in Greek), andnōnus is contracted from †novenos. The cardinal multiples of ten are compounds of -gint- ‘ten’ (a fragment of a derivative from ).

2 The form in -o is a remnant of the dual number, which was lost in Latin, but is found in cognate languages. So in ambō, both, which preserves -ō (cf. δύω and § 629. b).

3 Or, in poetry, , twice a thousand men.

4 Forms in -ns are often written without the n.

5 Also written or , etc.

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