Cardinal numerals

The cardinal numerals are the ordinary numbers used for counting ordinary nouns ('one', 'two', 'three' and so on):

The conjunction et 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 (see Latin word order).

Most numbers are invariable and do not change their endings:

• regnāvit Ancus annōs quattuor et vīgintī (Livy)^[1]

'Ancus reigned for 24 years'

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 (or ūnius) and dative ūnī:

The first three numbers have masculine, feminine and neuter forms fully declined as follows (click on GL or Wh to change the table to the American order as found in Gildersleeve and Lodge, or Wheelock):

• omnēs ūnius aestimēmus assis (Catullus)

'let us value them (at the value) of a single as!'

• duo ex tribus fīliīs (Curtius)

'two of his three sons'

• dīvidunt tōtam rem in duās partīs (Cicero)

'they divide the whole thing into two parts'

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

• dā mī bāsia mīlle, deinde centum (Catullus)

'give me a thousand kisses, then a hundred'

• mīllia aliquantō plūra quam trecenta (Augustus)

'slightly more than 300,000'

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

• cum sex mīlibus equitum (Curtius)

'accompanied by six thousand(s) (of) cavalrymen'

Mīlle passūs '1000 paces' (plural mīlia passuum) is the Latin for a mile:

• quīcumque tē angariāverit mīlle passūs, vade cum illō et alia duo (Vulgate Bible)

'whoever compels you to walk a mile, go with him another two'

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

• non longius ab oppidō X mīlibus (Caesar)

'not further than 10 miles from the town'

Ordinal numerals

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

• prīmus 'first'
• secundus 'second'
• tertius 'third'
• vīcēsimus/vīcēnsimus 'twentieth'

Note: secundus only means 'second' in the sense of 'following'. The adjective alter, altera, alterum meaning 'other [of two]' 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 (Caesar)^[2]

'he arrived on the seventh day'

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.^[3]

• domī suae vir prīmārius (Cicero)

'the leading man of his family'

• secundāriī pānis quīnās sēlībrās (Pliny the Elder)

'five half-pounds of second-class bread'

• tertiārum (stannum) (Pliny the Elder)

'lead alloy containing one-third white metal'

• quārtāriōs vīnī (Livy)

'quarter-pints of wine'

• quīntārius numerus (Vitruvius)

'five-sixths' (taking a sextārius as the whole)

• oleī sextārius (Celsus)

'a pint of oil'

• octāvārium vectīgal (Justinian)

'an eighth-part tax'

Plūrāle tantum numerals

Certain nouns in Latin were plurālia tantum, i.e. nouns that were plural but which had a singular meaning, for example litterae 'a letter', castra 'a camp', catēnae 'a set of chains', vestīmenta '(a set of) clothes', hibernae 'winter quarters', nūptiae 'wedding', quadrīgae 'quadriga' etc. A special series of numeral adjectives was used for counting these, namely ūnī, bīnī, trīnī, quadrīnī, quīnī, sēnī, and so on. Thus Roman authors would write: ūnae litterae 'one letter', trīnae litterae 'three letters', quīna castra 'five camps', etc.

Except for the numbers 1, 3, and 4 and their compounds, the plurale tantum numerals are identical with the distributive numerals (see below).

• non dīcimus bīga ūna, quadrīgae duae, nūptiae trēs, sed prō eō ūnae bīgae, bīnae quadrīgae, trīnae nūptiae (Varro)

'We don't say una biga (one two-horse chariot), duae quadrigae (two four-horse chariots), tres nuptiae (three weddings) but instead unae bigae, binae quadrigae, trinae nuptiae'.

• Tullia mea vēnit ad mē ... litterāsque reddidit trīnās (Cicero)^[4]

'My daughter Tullia came to me ... and delivered (no fewer than) three letters'

• Octāvius quīnīs castrīs oppidum circumdedit (Caesar)^[5]

'Octavius surrounded the town with five camps'

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: singulī, bīnī, ternī, quaternī, quīnī, sēnī, and so on. The meaning of these is 'one each', 'two each' (or 'in pairs') and so on, for example

• ibī turrīs cum ternīs tabulātīs ērigēbat (Julius Caesar)

'there he began erecting towers with three storeys each'

• bīnī senātōrēs singulīs cohortibus praepositī (Livy)

'a pair of senators was put in charge of each group of soldiers'.

• lēgātī ternī in Āfricam ... et in Numidiam missī (Livy)^[6]

'three ambassadors were sent to Africa, and three to Numidia'

• in singulōs equitēs ... nummōs quīnōs vīcēnōs dedērunt (Livy)^[7]

'for each individual cavalryman they gave 25 coins'

The word singulī is always plural in this sense in the classical period.^[8]

The distributive numerals are also used for multiplying:^[9]

• ter terna, quae sunt novem (Macrobius)

'three threes, which are nine'

In numbers 13 to 19, the order may be inverted, e.g. dēnī ternī instead of ternī dēnī.^[10]

Distributive numerals + -ārius

Based on the distributive numerals are derived a series of adjectives ending in -ārius: singulārius 'unique', 'extraordinary', 'of one part', 'singular', bīnārius 'of two parts', ternārius 'of three parts', quaternārius '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 (Columella)

'four-foot ditches, that is, four foot long in every direction'

• quīnāria (fistula), dicta ā diametrō quīnque quadrantum (Frontinus)

'a five-digit pipe, named from its diameter of five digits'

• quīngēnāriae cohortēs (Curtius)

'five-hundred men battalions'

• quīngēnārius thōrāx (Pliny the Elder)

'a five-hundred pound suit of body armour'

• quīngēnāria poena (Gaius)

'a five-hundred as penalty' (an as was a bronze coin)

They can also be used for specifying age:

• exhērēdāta ab octōgēnāriō patre (Pliny the Younger)^[11]

'disinherited by her 80-year-old father'

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 (see Metres of Roman comedy).

The dēnārius was a silver coin originally worth ten assēs (but later sixteen 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.^[12]

Adverbial numerals

Adverbial numerals are (as the name states) 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. semel 'once', bis 'twice', ter 'thrice, three times', quater 'four times', and so on.

The suffix -iēns may also be spelled -iēs: quinquiēs, sexiēs, etc.

• equidem deciēs dīxī (Plautus)^[13]

'indeed I've said it ten times already'

Multiplicative numerals

Multiplicative numerals are declinable adjectives. simplex 'single', duplex 'double', triplex 'treble', quadruplex 'fourfold', and so on.

These numerals decline as 3rd declension adjectives:

• [Caesar] triplicem aciem instruxit (Caesar)

'(Caesar) arranged his soldiers in a triple line'

• tabellās duplicēs tenentem (Suetonius)

'holding a pair of writing tablets consisting of two leaves'

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.^[8]

Proportional numerals

Proportional numerals are declinable adjectives. simplus 'simple', duplus 'twice as great', triplus 'thrice as great', quadruplus '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.^[8]

• duplam pecūniam in thēsaurōs repōnī (Livy)^[14]

'double the amount of money to be replaced in the treasuries'

Cardinal numbers