Latin numerals

The Latin numerals are the words used to denote numbers within the Latin language. They are essentially based on their Proto-Indo-European ancestors, and the Latin cardinal numbers are largely sustained in the Romance languages. In Antiquity and during the Middle Ages they were usually represented by Roman numerals in writing.
Latin numeral roots are used frequently in modern English, particularly in the names of large numbers.

Overview

The Latin language had several sets of number words used for various purposes. Some of those sets are shown in the tables below.

Cardinal numerals

The cardinal numerals are the ordinary numbers used for counting ordinary nouns :
The conjunction between numerals can be omitted: vīgintī ūnus, centum ūnus. Et is not used when there are more than two words in a compound numeral: centum trīgintā quattuor. The word order in the numerals from 21 to 99 may be inverted: ūnus et vīgintī. Numbers ending in 8 or 9 are usually named in subtractive manner: duodētrīgintā, ūndēquadrāgintā. Numbers may either precede or follow their noun.
Most numbers are invariable and do not change their endings:

regnāvit Ancus annōs quattuor et vīgintī

However, the numbers 1, 2, 3, and 200, 300, etc. change their endings for gender and grammatical case. Ūnus 'one' declines like a pronoun and has genitive ūnīus and dative ūnī:
The first three numbers have masculine, feminine and neuter forms fully declined as follows :

Declension

1 m

2 m

3 mf

Nominative

ūnus

ūna

ūnum

duo

duae

duo

trēs

tria

Vocative

ūne

ūna

ūnum

duo

duae

duo

trēs

tria

Accusative

ūnum

ūnam

ūnum

duōs/duo

duās

duo

trēs/trīs

tria

Genitive

ūnīus/-ius

ūnīus

duōrum

duārum

duōrum

trium

Dative

ūnī

duōbus

duābus

duōbus

tribus

Ablative

ūnō

ūnā

ūnō

duōbus

duābus

duōbus

tribus

omnēs ūnius aestimēmus assis
duo ex tribus fīliīs
dīvidunt tōtam rem in duās partīs

Mīlle '1000' is indeclinable in the singular but variable in the plural:

dā mī bāsia mīlle, deinde centum
mīllia aliquantō plūra quam trecenta

When it is plural, the noun it refers to is put in the genitive case:

cum sex mīlibus equitum

Mīlle passūs '1000 paces' is the Latin for a mile:

quīcumque tē angariāverit mīlle passūs, vade cum illō et alia duo

When the number is plural, the genitive passuum is sometimes omitted:

non longius ab oppidō X mīlibus

Larger numbers such as 2000, 3000, etc. could be expressed using either cardinal numbers or distributive numbers :

Gracchus domō cum proficīscēbātur, numquam minus terna aut quaterna mīlia hominum sequēbantur

Ordinal numerals

Ordinal numerals all decline like normal first- and second-declension adjectives. When declining two-word ordinals, both words decline to match in gender, number and case.

'first'
'second'
'third'
/ 'twentieth'

Note: secundus only means 'second' in the sense of 'following'. The adjective meaning 'other ' was more frequently used in many instances where English would use 'second'.
Ordinal numbers, not cardinal numbers, are commonly used to represent dates, because they are in the format of 'in the tenth year of Caesar', etc. which also carried over into the anno Domini system and Christian dating, e.g. annō post Chrīstum nātum centēsimō for AD 100.

diē septimō pervēnit

Ordinal numerals + ''-ārius''

Based on the ordinary ordinals is another series of adjectives: prīmārius 'of the first rank', secundārius 'of the second class, of inferior quality', tertiārius 'containing a third part', quārtārius 'a quarter, fourth part', quīntārius 'containing five parts', 'five-sixths', sextārius 'a one-sixth part of a congius, 'pint', and so on.

domī suae vir prīmārius
secundāriī pānis quīnās sēlībrās
tertiārum
quārtāriōs vīnī
quīntārius numerus
oleī sextārius
octāvārium vectīgal

numerals

Certain nouns in Latin were plurālia tantum, i.e. nouns that were plural but which had a singular meaning, for example 'a letter', 'a camp', 'a set of chains', ' clothes', 'winter quarters', 'wedding', 'quadriga' etc. A special series of numeral adjectives was used for counting these, namely,,,,,, and so on. Thus Roman authors would write: 'one letter', 'three letters', 'five camps', etc.
Except for the numbers 1, 3, and 4 and their compounds, the plurale tantum numerals are identical with the distributive numerals.

non dīcimus bīga ūna, quadrīgae duae, nūptiae trēs, sed prō eō ūnae bīgae, bīnae quadrīgae, trīnae nūptiae
Tullia mea vēnit ad mē... litterāsque reddidit trīnās
Octāvius quīnīs castrīs oppidum circumdedit

Distributive numerals

Another set of numeral adjectives, similar to the above but differing in the adjectives for 1, 3, and 4, were the distributive numerals:,,,,,, and so on. The meaning of these is 'one each', 'two each' and so on, for example

ibī turrīs cum ternīs tabulātīs ērigēbat
bīnī senātōrēs singulīs cohortibus praepositī
lēgātī ternī in Āfricam... et in Numidiam missī
in singulōs equitēs... nummōs quīnōs vīcēnōs dedērunt

The word singulī is always plural in this sense in the classical period.
The distributive numerals are also used for multiplying:

ter terna, quae sunt novem

In numbers 13 to 19, the order may be inverted, e.g. dēnī ternī instead of ternī dēnī.

Distributive numerals + ''-ārius''

Based on the distributive numerals are derived a series of adjectives ending in -ārius: 'unique', 'extraordinary', 'of one part', 'singular', 'of two parts', 'of three parts', 'of four parts', and so on.
Often these adjectives specify the size or weight of something. The usual meaning is 'of so many units', the units being feet, inches, men, pounds, coins, or years, according to context:

scrobēs quaternāriī, hoc est quōquōversus pedum quattuor
quīnāria, dicta ā diametrō quīnque quadrantum
quīngēnāriae cohortēs
quīngēnārius thōrāx
quīngēnāria poena

They can also be used for specifying age:

exhērēdāta ab octōgēnāriō patre

Some of these words have a specialised meaning. The sēnārius was a kind of metre consisting of six iambic feet commonly used in spoken dialogue in Roman comedy. There were also metres called the septēnārius and octōnārius.
The dēnārius was a silver coin originally worth ten assēs ; but there was also a gold dēnārius, mentioned by Pliny the Elder and Petronius, worth 25 silver dēnāriī. The silver dēnārius is often mentioned in the New Testament, and was stated to be the day's pay in the parable of the Labourers in the Vineyard.

Adverbial numerals

Adverbial numerals are indeclinable adverbs, but because all of the other numeral constructions are adjectives, they are listed here with them. Adverbial numerals give how many times a thing happened. 'once', 'twice', 'thrice, three times', 'four times', and so on.
The suffix -iēns may also be spelled -iēs:,, etc.

equidem deciēs dīxī

Multiplicative numerals

Multiplicative numerals are declinable adjectives. 'single', 'double', 'treble', 'fourfold', and so on.
These numerals decline as 3rd declension adjectives:triplicem aciem instruxit

tabellās duplicēs tenentem

For completeness all the numbers have been given above. Not all of these numerals are attested in ancient books, however.
Based on this series of numerals there is a series of adverbs: simpliciter 'simply, frankly', dupliciter 'doubly, ambiguously', tripliciter 'in three different ways' etc., as well as verbs such as duplicāre 'to double', triplicāre 'to triple', quadruplicāre 'to make four times as much', and so on.

Proportional numerals

Proportional numerals are declinable adjectives. 'simple', 'twice as great', 'thrice as great', 'four times as great', and so on.
These are often used as nouns: simplum 'the simple sum', duplum 'double the amount of money' and so on.

duplam pecūniam in thēsaurōs repōnī

Linguistic details

Cardinal numbers

The numeral ūnus < Old Latin oinos ‘one’, with its cognates Old Irish óen ‘one’, Gothic ains ‘one’, Ancient Greek οἴνη oínē ‘ace on dice’, and the first part of Old Church Slavonic inorogŭ ‘Unicorn’, harks back to Proto-Indo-European *Hoi̯-no-s. The genitive forms ūnīus, ūnĭus and the dative form ūnī match the pronominal declension, the remaining forms conform with those of first and second declension adjectives. Nominative and accusative forms persist within the Romance languages as numeral and also in its secondarily acquired role as indefinite article, e. g. Old French and Occitan uns, une, un, Italian un, una, Spanish un, una, Portuguese um, uma, Romanian un, o.

The masculine nominative/accusative forms dŭŏ < Old Latin dŭō ‘two’ is a cognate to Old Welsh dou ‘two’, Greek δύω dýō ‘two’, Sanskrit दुवा duvā ‘two’, Old Church Slavonic dŭva ‘two’, that imply Proto-Indo-European *duu̯o-h₁, a Lindeman variant of monosyllabic *du̯o-h₁, living on in Sanskrit द्वा dvā ‘two’, and slightly altered in Gothic twai ‘two’, German zwei ‘two’ etc.; the feminine dŭae points to an ancestral form *duu̯ah₂-ih₁. Both forms bear a dual ending, which otherwise in Latin is preserved only in ambō ‘both’, and possibly in octō ‘eight’. The accusative forms dŭōs m., dŭās f., the genitive dŭom, classical dŭōrum m./n., dŭārum f., and the dative/ablative dŭōbus m./n., dŭābus f., are original Latin formations replicating nominal declension patterns; at times, duo stands in for other case forms, especially when combined with invariant numerals, e. g. duo et vīgintī ‘twenty-two’, duodētrīgintā ‘twenty-eight’.
Most Romance languages sustain an invariant form developed from the masculine accusative duōs > Spanish, Catalan, Occitan dos, French deux, Romansh duos, dus; Italian due seems to preserve the feminine nominative duae. Portuguese inflects masculine dois and feminine duas; Romanian has doi and două, respectively.

The masculine and feminine nominative form trēs ‘three’ and its cognates Gothic þreis ‘three’, Greek τρεῖς treîs ‘three’, Sanskrit त्रयः trayaḥ ‘three’ are based on Proto-Indo-European *trei̯-es; the original accusative form trīs, matching Umbrian trif, Gothic þrins, Old Irish trí, Greek τρίνς tríns < Proto-Indo-European *tri-ns, was being superseded from preclassical Latin onward. The neuter tria corresponds to Umbrian triia and Greek τρία tría. The genitive trium is a direct descendant of Proto-Indo-European *trii̯-om, unlike e. g. Greek τριῶν triôn with long -ōn < -o-om, taken from the second declension; the dative/ablative form tribus, as well as Umbrian tris < *trifos, sustains Proto-Indo-European *tri-bʰos. The Romance languages only preserve one invariant form reflecting Latin trēs > Spanish, Catalan, Occitan tres, Portuguese três, French trois, Romansh trais, treis, Romanian trei.

The invariant numeral quattuor ‘four’ does not fully correspond to any of its cognates in other languages, as Oscan petora ‘four’, Greek τέσσαρες téssares ‘four’, Old Irish cethair ‘four’, Gothic fidwôr ‘four’, Lithuanian keturì ‘four’, Old Church Slavonic četyre ‘four’ point to a Proto-Indo-European base *kʷetu̯or-, that should appear as *quetuor in Latin; the actual -a- has been explained as epenthetic vowel emerging from a zero-grade *kʷtu̯or-. The geminate -tt- might have been established to compensate the fluctuating quality of succeeding -u- between non-syllabic glide and full vowel apparent since Old Latin; in the postclassical form quattor this sound is dropped altogether, and in most Romance languages the second syllable is subject to syncope, which then is compensated by an additional vowel at the very end of the word, as in Spanish cuatro, Portuguese quatro, Italian quattro, French, Occitan, Catalan quatre, Romanian patru.

The cardinal number quīnque ‘five’, with its cognates Old Irish coíc ‘five’, Greek πέντε pénte ‘five’, Sanskrit पञ्च pañca ‘five’, leads back to Proto-Indo-European pénkʷe; the long -ī-, confirmed by preserved -i- in most Romance descendants, must have been transferred from the ordinal quīntus ‘fifth’, where the original short vowel had been regularly lengthened preceding a cluster with a vanishing fricative: quīntus < *quiŋxtos < *kʷuiŋkʷtos < *kʷeŋkʷ-to-s. The assimilation of antevocalic *p- to -kʷ- of the following syllable is a common feature of the Italic languages as well as the Celtic languages.