Appendix:Latin cardinal numerals

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Cardinal numerals[edit]

When someone counts items, that person uses cardinal values. In grammatical terms, a cardinal numeral is a word used to represent such a countable quantity. The English words one, two, three, four, etc. are all examples of cardinal numerals.

In Latin, most cardinal numerals behave as indeclinable adjectives. They are usually associated with a noun that is counted, but do not change their endings to agree grammatically with that noun. The exceptions are ūnus (one), duo (two), trēs (three), and multiples of centum (hundred), all of which decline. Additionally, although mīlle (thousand) is an indeclinable adjective in the singular, it becomes a declinable noun in the plural. These exceptions are further explained in later sections.

Summary table[edit]

Smaller Cardinals Tens Hundreds
1 I ūnus, ūna, ūnum 11 XI ūndecim 10 X decem 100 C centum
2 II duo, duae, duo 12 XII duodecim 20 XX vīgintī 200 CC ducentī, -ae, -a
3 III trēs, tria 13 XIII tredecim 30 XXX trīgintā 300 CCC trecentī, -ae, -a
4 IV quattuor 14 XIV quattuordecim 40 XL quadrāgintā 400 CD quadringentī, -ae, -a
5 V quīnque 15 XV quīndecim 50 L quīnquāgintā 500 D quīngentī, -ae, -a
6 VI sex 16 XVI sēdecim 60 LX sexāgintā 600 DC sescentī, -ae, -a
7 VII septem 17 XVII septendecim 70 LXX septuāgintā 700 DCC septingentī, -ae, -a
8 VIII octō 18 XVIII duodēvīgintī 80 LXXX octōgintā 800 DCCC octingentī, -ae, -a
9 IX novem 19 XIX ūndēvīgintī 90 XC nōnāgintā 900 CM nōngentī, -ae, -a

Smaller cardinals[edit]

The smaller cardinal numerals, from ūnus (one) to vīgintī (twenty), have spellings and forms that are not easily predictable and therefore must be learned by students of Latin. Larger cardinal numerals follow more regular patterns of assembly.

ūnus[edit]

Inflection of ūnus ( I )
M F N MM FF NN
nom ūnus ūna ūnum ūnī ūnae ūna
gen ūnīus ūnīus ūnīus ūnōrum ūnārum ūnōrum
dat ūnī ūnī ūnī ūnīs ūnīs ūnīs
acc ūnum ūnam ūnum ūnōs ūnās ūna
abl ūnō ūnā ūnō ūnīs ūnīs ūnīs
voc ūnus ūna ūnum ūnī ūnae ūna

Inflection : The Latin ūnus (one) inflects like an irregular first and second declension adjective. The irregularities occur in the singular genitive, which ends in -īus instead of the usual or -ae, and in the singular dative, which ends in instead of the usual or -ae.

The choice of ending will agree with the gender of the associated noun: ūnus equus ("one horse"), ūna clāvis ("one key"), ūnum saxum ("one stone"). The ending will also agree with the grammatical case of the associated noun: ūnīus equī (genitive), ūnam clāvem (accusative), ūnī saxō (dative).

Plural : Although it may seem strange at first sight, ūnus does have a set of plural forms. These forms are used when the associated noun has a plural form, but an inherently singular meaning. For example, the Latin noun castra (camp) occurs only as a plural neuter form and takes plural endings, even though it identifies one object, hence: ūnōrum castrōrum ("of one camp").

Compounds : When ūnus is used to form compound numerals, such as ūnus et vīgintī ("twenty-one"), the case and gender agree with the associated noun, although the singular is used: vīgintī et ūnam fēminās vīdī . Unlike duo and trēs, the word ūnus is almost never used with mīlle (thousand) to indicate how many thousand.

duo[edit]

Inflection of duo ( II )
MM FF NN
nom duo duae duo
gen duōrum duārum duōrum
dat duōbus duābus duōbus
acc duōs / duo duās duo
abl duōbus duābus duōbus

Inflection : The Latin (two) has a highly irregular inflection. While some of the endings resemble those of a first and second declension adjective, others resemble those of a third declension adjective. In fact, its dative and ablative endings occur in only one other Latin word, ambō ("both"). This is a remnant of an earlier dual form present in anteclassical Latin.

The choice of ending will agree with the gender of the associated noun, which will necessarily be plural: duo equī ("two horses"), duae clāvēs ("two keys"), duo saxa ("two stones"). The ending will also agree with the grammatical case of the associated noun: duōs equōs (accusative), duārum clāvum (genitive), duōbus saxīs (dative).

Compounds : When duo is used to form compound numerals, such as duo et vīgintī or vīgintī duo ("twenty-two"), the case and gender agree with the associated noun. This is also the case when used with the plural of mīlle (thousand) to indicate how many thousands: duo mīlia ("two thousands"), duōrum mīlium ("of two thousands").

trēs[edit]

Inflection of trēs ( III )
MM FF NN
nom trēs trēs tria
gen trium trium trium
dat tribus tribus tribus
acc trēs trēs tria
abl tribus tribus tribus

Inflection : The Latin trēs (three) inflects like a plural third declension adjective with two endings in the nominative. Notice that the masculine and feminine endings are identical.

The choice of ending will agree with the gender of the associated noun, which will necessarily be plural: trēs equī ("three horses"), trēs clāvēs ("three keys"), tria saxa ("three stones"). The ending will also agree with the grammatical case of the associated noun: trēs equōs (accusative), trium clāvum (genitive), tribus saxīs (dative).

Compounds : When trēs is used to form compound numerals, such as trēs et vīgintī or vīgintī trēs ("twenty-three"), the case and gender agree with the associated noun. This is also the case when used with the plural of mīlle (thousand) to indicate how many thousands: tria mīlia ("three thousands"), trium mīlium ("of three thousands").

IV to XX[edit]

Smaller Cardinals
1 I ūnus, ūna, ūnum 11 XI ūndecim
2 II duo, duae, duo 12 XII duodecim
3 III trēs, tria 13 XIII tredecim
4 IV quattuor 14 XIV quattuordecim
5 V quīnque 15 XV quīndecim
6 VI sex 16 XVI sēdecim
7 VII septem 17 XVII septendecim
8 VIII octō 18 XVIII duodēvīgintī
9 IX novem 19 XIX ūndēvīgintī
10 X decem 20 XX vīgintī

The numerals quattuor (four) through vīgintī are all indeclinable, and never change their endings to match an associated noun. Each of these numerals has a single immutable form in all situations.

Many of these numerals are mirrored in English words (such as quadrangle, quintuplet, sextuple, octopus). The numerals for 7 through 10 appear in the English names of months (September, October, November, and December). These months were the seventh through tenth of the Roman calendar, since the Roman year began with mārtius (March).

Teens : Latin cardinals larger than decem (ten) but less than vīgintī (twenty) are constructed by addition. The ending -decim (a form of decem) is attached to the numerals ūnūs through novem. The resultant compound carries the same value as the mathematical sum of the components. For example quattuordecim (fourteen) is quattuor (four) + decem (ten). English does much the same by attaching -teen (a form of ten) to smaller numerals, such as the numeral fourteen which is four + ten.

In some of these compounds, a spelling and pronunciation change occurs during the attachment, so that sex + decem drops the -x and lengthens the e to yield sēdecim. This kind of change also occurs in English, as in five + ten which softens the sound of the v and drops the e to yield fifteen.

Exceptions : There are two exceptions to the general pattern for forming the teens. In Classical Latin, the numerals for 18 and 19 are more frequently written as subtractive compounds. So, although 18 may be written as octōdecim, it is more often written as duodēvīgintī (literally "two from twenty"). Likewise, the numeral for 19 may be written as novemdecim, but is more often encountered as ūndēvīgintī (one from twenty).

For more information about the subtractive pattern of construction, see the section on "counting backwards".

Larger cardinals[edit]

Tens[edit]

Multiples of ten
10 X decem 60 LX sexāgintā
20 XX vīgintī 70 LXX septuāgintā
30 XXX trīgintā 80 LXXX octōgintā
40 XL quadrāgintā 90 XC nōnāgintā
50 L quīnquāgintā 100 C centum

Hundreds[edit]

Inflection of ducentī ( CC )
MM FF NN
nom ducentī ducentae ducenta
gen ducentōrum ducentārum ducentōrum
dat ducentīs ducentīs ducentīs
acc ducentōs ducentās ducenta
abl ducentīs ducentīs ducentīs
voc ducentī ducentae ducenta

The numeral centum (100) is the only "hundred" that is indeclinable.

All multiples of centum, e.g. ducentī (200), trecentī (300), etc., decline as a plural adjective of the first and second declension.

Multiples of one hundred
100 C centum 1 600 DC sescentī, -ae, -a
200 CC ducentī, -ae, -a 700 DCC septingentī, -ae, -a
300 CCC trecentī, -ae, -a 800 DCCC octingentī, -ae, -a
400 CD quadringentī, -ae, -a 900 CM nōngentī, -ae, -a
500 D quīngentī, -ae, -a 1000 M mīlle, mīlia 2
1 centum does not inflect.
2 see the following section on mīlle.

mīlle[edit]

Inflection of mīlle ( M )
C (adj.) NN (noun)
nom mīlle mīlia
gen mīlle mīlium
dat mīlle mīlibus
acc mīlle mīlia
abl mīlle mīlibus
voc mīlle mīlia

The Latin mīlle (thousand) is irregular in that it has two forms. In the singular, it is an indeclinable adjective, but in the plural it is a noun that declines like a third declension neuter i-stem. Notice that the genitive plural ending is -ium.

Singular : In the singular, mīlle (thousand) functions as an adjective. This singular form is indeclinable, so its ending will remain the same rather than agree with the case or gender of the associated noun. However, the associated noun will necessarily be plural: mīlle equī ("thousand horses"), mīlle clāvēs ("thousand keys"), mīlle saxa ("thousand stones"). This is true regardless of the case or gender of the associated noun.

Plural : In the plural, mīlia functions as a noun, and will inflect according to how it is used in the sentence (subject, direct object, etc.). The associated noun being counted will necessarily be in the genitive plural, and so will not agree with the grammatical case of mīlia. Note that, if the numeral before mīlia is duo or trēs, then it will take a neuter form in the same grammatical case as mīlia : octō mīlia equōrum (nominative, "eight thousand of horses"), cum tribus mīlibus clāvum (ablative, "with three thousand of keys"), duōrum mīlium saxōrum (genitive, "of two thousand of stones").

Compound cardinals[edit]

Latin cardinal numerals larger than vīgintī (twenty), that are not multiples of ten, are assembled as compound words. The components of these compounds are the numerals ūnus (one) through novem (nine) and the multiples of decem (10), the multiples of centum (100), and mīlle (1000).

Compound numerals in Latin are assembled by one of two basic methods: additive or subtractive. Most compound numerals are additive, meaning that the value of the compound numeral is calculated by adding the values of the component words. However, a few Latin compound numerals are subtractive, meaning that the value of the compound numeral is calculated by subtracting the values of the component words. A large-valued compound numeral may incorporate both additive and subtractive components.

Additive compounds[edit]

Counting backwards[edit]

Tens +8 ( or –2 ) Tens +9 ( or –1 )
18 XVIII duodēvīgintī 19 XIX ūndēvīgintī
28 XXVIII duodētrīgintā 29 XXIX ūndētrīgintā
38 XXXVIII duodēquadrāgintā 39 XXXIX ūndēquadrāgintā
48 XLVIII duodēquīnquāgintā 49 XLIX ūndēquīnquāgintā
58 LVIII duodēsexāgintā 59 LIX ūndēsexāgintā
68 LXVIII duodēseptuāgintā 69 LXIX ūndēseptuāgintā
78 LXXVIII duodēoctōgintā 79 LXXIX ūndēoctōgintā
88 LXXXVIII duodēnōnāgintā 89 LXXXIX ūndēnōnāgintā
98 XCVIII nōnāgintā octō 99 XCIX ūndēcentum

Of the Latin compound numerals less than centum (100), seventeen are normally subtractive. All of these special cases represent values that are one or two less than a multiple of ten, and have names that subtract from a starting value rather than adding to that value. These seventeen exceptions are displayed in the table at right. Note that the compound numeral for 98 is not among the special cases, but instead is formed in the usual additive way. Subtractive compounds normally are written as single words (with no spaces) and are indeclinable.

Numerals representing cardinal values that are eight more (two less) than a multiple of ten are constructed literally as:

duo (two) + (from) + multiple of ten

Thus, the numeral for 38 is normally written as duodēquadrāgintā (two from forty), rather than as the expected trīgintā octō (thirty-eight) or octō et trīgintā (eight and thirty). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.

Numerals representing cardinal values that are nine more (one less) than a multiple of ten are constructed literally as:

ūnus (one) + (from) + multiple of ten

Thus, the numeral for 39 is normally written as ūndēquadrāgintā (one from forty), rather than as the expected trīgintā novem (thirty-nine) or novem et trīgintā (nine and thirty). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.

Grammar[edit]

Numbers are almost always treated as adjectives, and often, come before the noun. They may be used alone as substantive nouns, but as most are indeclinable, this tends to be ambiguous. Mille behaves differently; in the plural, as milia, the noun being counted must be in the genitive plural. For example, "two thousand soldiers" would be "duo milia militum" (literally, "two thousands of soldiers). Thus a mile is mille passūs (literally, "a thousand paces"), but two miles is duo milia passuum (literally, "two thousands of paces").

To denote one's age, which in English is expressed in the construction I am ... years old, in Latin one would most commonly say Habeo ... annos (literally, "I have ... years"). The numeral is in the accusative plural, if it declines.

See also[edit]