NUMERALS

CLASSES OF NUMERALS

132. The Latin Numerals may be classified as follows.

I. NUMERAL ADJECTIVES:

  1. Cardinal Numbers, answering the question how many?

    ūnus one
    duo two, etc.

  2. Ordinal Numbers,1 adjectives derived (in most cases) from the Cardinals, and answering the question which in order?

    prīmus first
    secundus second, etc.

  3. Distributive Numerals, answering the question how many at a time?

    singulī one at a time
    bīnī two by two, etc.

II. NUMERAL ADVERBS, answering the question how often?

semel once
bis twice, etc.

Footnotes

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), and nōnus is contracted from †novenos. The cardinal multiples of ten are compounds of -gint-, ten (a fragment of a derivative from decem).

 

CARDINAL AND ORDINAL NUMBERS

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

19. ūndēvīgintī
     (novendecim)

ūndēvīcēnsimus 
(nōnus decimus)

 XVIIII or XIX
20. vīgintī

vīcēnsimus
(vīgēnsimus)

 XX

21. vīgintī ūnus 
     [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 ∞ (CIϽ) or M
5000. quīnque mīlia (mīllia) quīnquiēns mīllēnsimus IϽϽ
10,000. decem mīlia (mīllia) deciēns mīllēnsimus CCIϽϽ
100,000. centum mīlia (mīllia) centiēns mīllēnsimus CCCIϽϽϽ

Note 1— The forms in -ēnsimus are often written without the n:

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.

 

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.

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. Duo1 (two) and trēs (three) are thus declined.

Declension of the numbers Duo (two) and trēs (three)

Note— Ambō (both) is declined like duo.

c. The hundreds, up to 1000, are adjectives of the 1st and 2nd Declensions, and are regularly declined like the plural of bonus.

d. Mīlle (a thousand) is an indeclinable adjective in the singular.

mīlle modīs in a thousand ways
cum mīlle hominibus with a thousand men


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:

Mīlle hominum mīsit.  He sent a thousand (of) men.

in the other cases rarely, except in connection with the same case of mīlia.

cum octō mīlibus peditum, mīlle equitum
with eight thousand foot and a thousand horse

e. The ordinals are adjectives of the 1st and 2nd Declensions, and are regularly declined like bonus.

Footnotes

1. 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).

 

USES OF CARDINALS AND ORDINALS

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:

ūnus et vīgintī mīlitēs or vīgintī mīlitēs (et) ūnus 21 soldiers
duo mīlia quīngentī mīlitēs 2500 soldiers or
duo mīlia mīlitum et quīngentī 2500 soldiers
mīlitēs mīlle ducentī trīgintā ūnus 1231 soldiers

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

duo mīlia hominum two thousand men1
cum tribus mīlibus mīlitum with three thousand soldiers
mīlia passuum tria three thousand paces (three miles)

d. For million, billion, trillion, etc., the Romans had no special words, but 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.

duae septimae (sc. partēs) two-sevenths
trēs octāvae (sc. partēs) three-eighths

One-half is rendered dīmidia pars or dīmidium.

Note 1— When the numerator is one, it is omitted and pars is expressed.

tertia pars one-third
quārta pars one-fourth

Note 2— When the denominator is one greater than the numerator, only the numerator is given.

duae partēs two-thirds
trēs partēs three-fourths, etc.

Note 3— Fractions are also expressed by special words derived from as (a pound).

triēns a third
bēs two-thirds

See § 637.

Footnotes

1. Or, in poetry, bis mīlle hominēs (twice a thousand men).

 

DISTRIBUTIVES

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

Note— These answer the interrogative quotēnī (how many of each? or how many at a time?).

1. singulī  one by one 18. octōnī dēnī or
      duodēvīcēnī		 300. trecēnī
2. bīnī  two by two 19. novēnī dēnī or
      ūndēvīcēnī		 400. quadringēnī
3. ternī, trīnī 20. vīcēnī 500. quīngēnī
4. quaternī 21. vīcēnī singulī, etc. 600. sescēnī
5. quīnī 30. trīcēnī 700. septingēnī
6. sēnī 40. quadrāgēnī 800. octingēnī
7. septēnī 50. quīnquāgēnī 900. nōngēnī
8. octōnī

60. sexāgēnī 1000. mīllēnī
9. novēnī 70. septuāgēnī 2000. bīna mīlia
10. dēnī 80. octōgēnī 10,000. dēna mīlia
11. ūndēnī 90. nōnāgēnī 100,000. centēna mīlia
12. duodēnī 100. centēnī etc.
13. ternī dēnī, etc. 200. ducēnī

137. Distributives are used as follows:

a. In the sense of so many apiece or on each side.

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.

bīna castra two camps1

With such nouns trīnī, not ternī, is used for three.

trīna castra2 three camps

c. In multiplication.

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.

bīna hastīlia two shafts (two in a set)

Footnotes

1. Duo castra would mean two forts.

2. Terna castra means camps in threes.

 

NUMERAL ADVERBS

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

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

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

ter et trīciēns (centēna mīlia) sēstertium
3,300,000 sesterces (three and thirty times a hundred thousand sesterces)

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).

Footnotes

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

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

 

OTHER NUMERALS

139. The following adjectives are called Multiplicatives.

simplex single
duplex double, twofold
triplex triple, threefold
quadruplex, quīnquiplex, septemplex
decemplex, centuplex
sēsquiplex 1 1/2
multiplex manifold

a. The following are Proportionals.

duplus, triplus, quadruplus, octuplus, etc.
twice as great, thrice as great, etc.

b. Temporals.

bīmus of two years' age, trīmus three years' age
biennis lasting two years, triennis lasting three years
bimēstris of two months, trimēstris of three months
bīduum a period of two days
biennium a period of two years

c. Partitives.

bīnārius of two parts
ternārius three parts

d. Other derivatives are as follows.

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.