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Numerals

A&G §132–139|8 rules|5 practice questions

Latin numbers come in four flavors. Cardinals (ūnus, duo, trēs, quattuor) count how many; ordinals (prīmus, secundus, tertius) rank what position; distributives (singulī, bīnī, ternī) say how many each; numeral adverbs (semel, bis, ter) say how many times.

The good news: most cardinals from quattuor through centum don't decline at all — you just memorize the word.

The trap is the few that DO decline: ūnus, duo, trēs, the hundreds (ducentī, trecentī…), and mīlle — and mīlle itself flips between an indeclinable adjective in the singular and a noun (mīlia) in the plural that demands a partitive genitive.

Roman numerals work the same way English does, with one quirk: 18 and 19 are usually duodēvīgintī and ūndēvīgintī — "two from twenty," "one from twenty."

Pattern
cardinal · ordinal · distributive · adverb
ūnus · prīmus · singulī · semel
duo · secundus · bīnī · bis
trēs · tertius · ternī · ter
The Four Series of Numerals

How many · which in order · how many each · how many times — every Latin number lives in one of these four columns.

Of the cardinals, only ūnus, duo, trēs, the hundreds, and mīlle decline. quattuor through centum are frozen forms — no endings to learn.

ūnus, ūna, ūnum — one
CaseM.F.N.Use
Nom.ūn-usūn-aūn-umsubject
Gen.ūn-īusūn-īusūn-īuspronominal -īus across all genders
Dat.ūn-īūn-īūn-īpronominal -ī across all genders
Acc.ūn-umūn-amūn-umdirect object
Abl.ūn-ōūn-āūn-ōby/with/from
duo, duae, duo — two
CaseM.F.N.Use
Nom.duoduaeduosubject — note dual-number remnant -o
Gen.duōrumduārumduōrumof the two
Dat.duōbusduābusduōbusto/for the two
Acc.duōs (duo)duāsduoambō, 'both,' declines the same way
Abl.duōbusduābusduōbusby/with/from the two
trēs, tria — three
CaseM./F.N.Use
Nom.trēstriasubject — i-stem 3rd-decl. pattern
Gen.triumtriumof three
Dat.tribustribusto/for three
Acc.trēs (trīs)triadirect object
Abl.tribustribusby/with/from three
Numerals you'll meet (cardinals · ordinals · distributives · adverbs)
1
1 — ūnus, -a, -um
prīmus · singulī · semel
critical
2
2 — duo, duae, duo
secundus (or alter) · bīnī · bis
critical
3
3 — trēs, tria
tertius · ternī (trīnī with pluralia tantum) · ter
critical
4
4 — quattuor (indeclinable)
quārtus · quaternī · quater
critical
5
5 — quīnque
quīntus · quīnī · quīnquiēns
critical
6
10 — decem
decimus · dēnī · deciēns
important
7
11–17 — ūndecim, duodecim, … septendecim
ūndecimus, duodecimus, …
important
8
18, 19 — subtractive duodēvīgintī, ūndēvīgintī
"two from twenty," "one from twenty"
critical
9
20 — vīgintī (indeclinable)
vīcē(n)simus · vīcēnī · vīciēns
important
10
21+ — vīgintī ūnus OR ūnus et vīgintī
et inserted when units come first
common
11
100 — centum (indeclinable)
centē(n)simus · centēnī · centiēns
important
12
200–900 — ducentī, trecentī, … (decline like bonī)
ducentī mīlitēs — gen. ducentōrum
common
13
1000 — mīlle (sg. adj.) / mīlia (pl. noun + gen.)
mīlle hominēs / duo mīlia hominum
critical
14
Distance — mīlia passuum N
mīlia passuum tria = three Roman miles
critical
15
Distributives with castra, litterae
bīna castra = two camps (not duo castra)
common
16
Big money — adverb × centēna mīlia
vīciēs sēstertium = 2,000,000 sesterces
rare

See It In Action

Gallia est omnis divisa in partes tres, quarum unam incolunt Belgae, aliam Aquitani, tertiam qui ipsorum lingua Celtae, nostra Galli appellantur.
All Gaul is divided into three parts, of which one is inhabited by the Belgae, another by the Aquitani, and the third by those called Celts in their own language and Gauls in ours.

— B. G. i.1.1

The opening line of the Gallic War packs three numeral types into one sentence: cardinal trēs (acc. f. pl.), the pronominal ūnam, and the ordinal tertiam. Notice tertiam declines like a normal 1st/2nd adjective.

Eo die quo consuerat intervallo hostes sequitur et milia passuum tria ab eorum castris castra ponit.
On that day he follows the enemy at the usual distance and pitches camp three miles from theirs.

— B. G. i.22.4

Roman miles literally counted paces: mīlia passuum tria = "three thousands of paces." mīlia is the noun (neuter pl.), passuum is the partitive genitive that comes with it.

ipse in Italiam magnis itineribus contendit duasque ibi legiones conscribit et tres, quae circum Aquileiam hiemabant, ex hibernis educit et … cum his quinque legionibus ire contendit.
He himself hurries into Italy by forced marches, enrolls two legions there, leads three more from winter quarters near Aquileia, and presses on with these five legions.

— B. G. i.10.3

Watch the contrast: duās and trēs both decline (here in the accusative), but quīnque sits frozen — the case sense rides entirely on legiōnibus. That's the rule for 4-100.

summa tranquillitate consecuta, secunda inita cum solvisset vigilia, prima luce terram attigit.
With great calm following, having set sail at the second watch, at first light he reached land.

— B. G. v.23.6

Two ordinals doing real work: secunda vigilia (the second night-watch — Romans split the night into four) and prīmā lūce ("at the first light" = dawn). Ordinals carry time of day and time of night in Caesar.

Translating numeral constructions
cardinal + noun

"N + noun" — straight count

quīnque legiōnibus = "with five legions"

ordinal as time-marker

"at the Nth + time-word" — prīmā lūce, secundā vigiliā

prīmā lūce = "at first light" (= at dawn)

mīlia + partitive gen.

"N thousand of X" — flip the counted noun to genitive

duo mīlia hominum = "two thousand men"

distributive with pluralia tantum

"N + plural-only noun" — read as a simple count, NOT "N each"

bīna castra = "two camps" (not "camps two each")

subtractive 18 / 19

"two/one from twenty" → translate as 18 / 19

ūndēvīgintī mīlitēs = "19 soldiers"

numeral adverb × number

"N times M" — multiplies the number that follows

bis bīna = "twice two" (= four)

mīlle (adjective) vs. mīlia (noun)

mīlle in the singular is an indeclinable adjective; mīlia in the plural is a noun that takes a genitive.

mīlle (sg., indeclinable adj.)

modifies a noun directly

mīlle mīlitēs

a thousand soldiers

mīlia (pl., neuter noun)

takes a partitive genitive

duo mīlia mīlitum

two thousand (of) soldiers

Tip: Ask: is the number 1000, or 2000+? At 1000 it's an adjective (nom. matches); at 2000+ it's a noun and the counted thing flips to genitive.

Quick Check

Caesar writes milia passuum tria ab eorum castris castra ponit (B. G. i.22.4). Why is passuum in the genitive?

Study Tips

  • •Drill 1-10 first as a chant, then tens to 100, then 200, 500, 1000. That's your full counting vocabulary in about 35 words.
  • •Practice the duo / trēs / mīlle paradigms until they're automatic — those are the only declensions you'll actually meet in Caesar.
  • •When you see mīlia in the wild, look for the genitive that follows: mīlia passuum (miles), mīlia hominum (men). That noun-with-genitive pattern is your tip-off.

Edited by Baris Yildirim·After Allen & Greenough §§132–139 (1903)

Last updated May 2, 2026·How antiq's grammar pages are made