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NUMERALS

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

I. NUMERAL ADJECTIVES:

  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） tertius decimus (decimus (et） tertius） XIII
14. quattuordecim quārtus decimus XIIII or XIV
15. quīndecim quīntus decimus XV
16. sēdecim sextus decimus XVI
17. septendecim septimus decimus XVII
18. duodēvīgintī (octōdecim) duodēvīcēnsimus (octāvus decimus） XVIII

Note 1.--The forms in -ēnsimus are often written without the n: as, vīcēsimus , 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. vīgintī ūnus (or ūnus et vīgintī, etc.） vīcēnsimus prīmus (ūnus et vīcēnsimus, 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. quīnque mīlia (mīllia) quīnquiēns mīllēnsimus IↃↃ
10,000. decem mīlia (mīllia) deciēns mīllēnsimus CCIↃↃ
100,000. centum mīlia (mīllia) centiēns mīllēnsimus CCCIↃↃↃ

Declension of Cardinals and Ordinals

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

a. For the declension of ūnus , 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, ūna castra, one camp (cf. § 137. b). The plural occurs also in the phrase ūnī et alterī, 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 duo .

M. F. N. M., F. N.
NOM. duo duae duo trēs tria
GEN. duōrum duārum duōrum trium trium
DAT. duōbus duābus duōbus tribus tribus
ACC. duōs (du o ） duās duo trēs (tr īs ） tria
ABL. duōbus duābus duōbus tribus tribus

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. mīlle modīs, in a thousand ways.
  2. cum mīlle hominibus, with a thousand men.
  3. “ mīlle trahēns variōs colōrēs ” (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 sedīle (§ 69): mīlia , mīlium , mīlibus , etc.

Note.--The singular mīlle is sometimes found as a noun in the nominative and accusative: as, mīlle hominum mīsit, he sent a thousand (of) men; in the other cases rarely, except in connection with the same case of mīlia : as, cum octō mīlibus peditum , mīlle equitum, 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, et is generally inserted: duo et vīgintī; otherwise et is omitted: vīgintī duo .

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: mīlle ( et ) septingentī sexāgintā quattuor , 1764.

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

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

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

  1. duo mīlia hominum, two thousand men. 3
  2. cum tribus mīlibus mīlitum, with three thousand soldiers.
  3. mīlia passuum tria, 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 pars expressed or understood:—two-sevenths, duae septimae (sc. partēs ); three-eighths, trēs octāvae (sc. partēs ).

One-half is dīmidia pars or dīmidium .

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

Note 2.--When the denominator is but one greater than the numerator, the numerator only is given: two-thirds, duae partēs; three-fourths, trēs partēs , 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. bīna mīlia
12. duodēnī 80. octōgēnī 10,000. dēna mīlia
13. ternī dēnī, etc. 90. nōnāgēnī 100,000. centēna mīlia

137. Distributives are used as follows:—

a. In the sense of so many apiece or on each side: as, singula singulīs, 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, bīna castra, two camps ( duo castra would mean two forts). With such nouns trīnī , not ternī , is used for three: as, trīna (not terna ) castra, three camps; terna castra means camps in threes.

c. In multiplication: as, bis bīna, twice two; ter septēnīs diēbus, in thrice seven days.

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

Numeral Adverbs

138. The Numeral Adverbs answer the question quotiēns ( quotiēs ), 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 semel vīciēns,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 deciēns mīliēns

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

  1. ter et trīciēns ( centēna mīlia ) sēstertium, 3,300,000 sesterces (three and thirty times a hundred thousand sesterces).
  2. vīciēs ac septiēs mīliēs ( centēna mīlia ) 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 centēna mīlia is regularly omitted (see § 634).

Other Numerals

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

a. Proportionals are: duplus , triplus , quadruplus , octuplus , etc., twice as great, thrice as great, etc.

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

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

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

1 The Ordinals (except secundus, tertius,octāvus, nōnus) are formed by means of suffixes related to those used in the superlative and in part identical with them. Thus, decimus (compare the form īnfimus ) 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 (quārtus, quīntus, sextus） may be compared with the corresponding Greek forms in -τος, and with superlatives in -ισ-το-ς, while the others have the superlative ending -timus (changed to -simus). Of the exceptions, secundus is a participle of sequor; alter 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 decem ).

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, bis mīlle hominēs, twice a thousand men.

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

5 Also written vīciēns et semel or vīciēns semel , etc.

Ginn and Company, 1903.

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