NUMERALS

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, 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.

These two series are as follows:—

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

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).

Duo,

two, and trēs, three, are thus declined:—

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

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.

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

Cardinals and Ordinals have the following uses:—

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

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.

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.

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

1. duo mīlia hominum, two thousand men.
2. cum tribus mīlibus mīlitum, with three thousand soldiers.
3. mīlia passuum tria, three thousand paces (three miles).

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

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.

Distributive Numerals are declined like the plural of bonus.

Distributives are used as follows:—

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.

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.

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

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

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).

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

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.

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

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.