Appendix:Latin cardinal numerals

Cardinal numerals

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

1 - 10			11 - 20			x 10			x 100
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
10	X	decem	20	XX	vīgintī	100	C	centum	1000	M	mīlle

1–10

The smaller cardinal numerals, from ūnus (“one”) to decem (“ten”), are all simple (not made by combining two numbers).

ūnus

**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	ūne	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 -ī or -ae, and in the singular dative, which ends in -ī instead of the usual -ō 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

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

Inflection: The Latin duo (“two”) has a highly irregular inflection, derived in part from the old Indo-European dual number. While some of the endings resemble those of a first and second declension adjective, others resemble those of a third declension adjective. The inflection of ambō (“both”) is very similar.

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 clāvium (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

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

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 clāvium (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 X

1 - 10
1	I	ūnus, ūna, ūnum
2	II	duo, duae, duo
3	III	trēs, tria
4	IV	quattuor
5	V	quīnque
6	VI	sex
7	VII	septem
8	VIII	octō
9	IX	novem
10	X	decem

The numerals quattuor (“four”) through decem (“ten”) 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). 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”).

11 - 20

11 - 20
11	XI	ūndecim
12	XII	duodecim
13	XIII	tredecim
14	XIV	quattuordecim
15	XV	quīndecim
16	XVI	sēdecim
17	XVII	septendecim
18	XVIII	duodēvīgintī
19	XIX	ūndēvīgintī
20	XX	vīgintī

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 ūnus 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, in which the v is devoiced under the influence of the following t (and the purely orthographic e is dropped) 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".

20+

× 10

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

other numbers 20<x<100

Numbers inbetween multiples of 10 can be formed by two different ways. Let us take 22 as example:

vīgintī duo
duo et vīgintī

× 100

**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 up to nōngentī (“900”), 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 (mīllia) ²

¹ centum does not inflect. ² see the following section on mīlle.

mīlle

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

The Latin mīlle (“thousand”) is irregular in that it can function both as a numeral (adjective) and as a noun. When used as a noun, it declines like a third declension neuter i-stem with the genitive plural ending -ium, and even possesses a rare distinct singular ablative form mīllī.

Singular: In the singular, mīlle (“thousand”) can mimic other numerals by functioning as an indeclinable adjective whose ending will remain the same rather than agree with the case, gender or number of the associated head (such as a noun). The head itself declines for case and gender, but is always plural: mīlle equī (nominative masculine, "thousand horses"), mīlle clāvibus (ablative feminine, "with a thousand keys"), hōrum mīlle saxōrum (genitive neuter, "of these thousand stones"). This use agrees with the predicate in the plural: mīlle mīlitēs vēnērunt ("a thousand soldiers came").

Alternatively it can function as a neuter singular noun, which is also indeclinable with the exception of the existence of a rare ablative mīllī. In this usage it governs a partitive genitive and agrees with the predicate in the singular: mīlle mīlitum vēnit ("a thousand soldiers came").

A third and less preferred option combines the two uses by functioning as a neuter noun with plural predicate agreement, as in mīlle mīlitum vēnērunt, perhaps in a partitive sense "a thousand men from among the soldiers".

Plural: The plural form, mīlia, normally behaves as a declinable neuter noun of the third declension, inflects according to its grammatical function in the sentence (subject, direct object, etc.) and agrees with the predicate in the neuter plural. The associated noun being counted will necessarily be governed by mīlia in the genitive plural instead of agreeing with it as an adjective would: tot mīlia mīlitum capta ("that many thousand of soldiers were captured"). If further modified by the cardinal numerals duo or trēs ("two/three thousand"), or by distributive numerals like singulī and dēnī ("one/ten each"), or any other declinable adjective, the latter will appear in the same gender (neuter) and grammatical case as mīlia: fuērunt tria mīlia equōrum (nominative, "there were three thousand horses"), crepitus duōrum mīlium saxōrum (genitive, "the rumbling of two thousand stones"), in singulīs mīlibus nummum collocātīs (ablative, "in every thousand sesterces invested" - notice the irregular genitive plural).

However, if part of a compound numeral ("one thousand five hundred"), and/or when used with personal reference in the absence of a dependent genitive, it again functions as an adjective (either substantivized or dependent on the other numeral), and the predicate takes masculine agreement unless the personal reference is an exclusively feminine group: duo mīlia captī ("two thousand were captured"), duo mīlia quīngentī mīlitēs captī ("two thousand five hundred soldiers were captured"), tria mīlia quīngentae (mīlitēs) captae ("three thousand five hundred women (soldiers) were captured").

Compound cardinals

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

Counting backwards

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 or octō et nōnāgintā	99	XCIX	nōnāgintā novem or novem et nōnāgintā, one Classical attestation of ūndēcentum

Of the Latin compound cardinal numerals less than centum (“100”), sixteen 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 sixteen exceptions are displayed in the table at right. Note that in Classical Latin, the compound cardinal numerals for 98 and 99 are not among the special cases (with one counterexample in Pliny the Elder), but instead are 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”) + dē (“from”) + multiple of ten

Thus, the numeral for 48 is normally written as duodēquīnquāgintā (“two from fifty”), rather than as the expected quadrāgintā octō (“forty-eight”) or octō et quadrāgintā (“eight and forty”). 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:

ūn- (“one”) + dē (“from”) + multiple of ten

Thus, the numeral for 49 is normally written as ūndēquīnquāgintā (“one from fifty”), rather than as the expected quadrāgintā novem (“forty-nine”) or novem et quadrāgintā (“nine and forty”). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.

Grammar

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. Mīlle behaves differently; in the plural, as mīlia, the noun being counted must be in the genitive plural. For example, "two thousand soldiers" would be "duo mīlia mīlitum" (literally, "two thousands of soldiers). Thus a mile is mīlle passūs (literally, "a thousand paces"), but two miles is duo mīlia 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 Habeō ... annōs (literally, "I have ... years"). The numeral is in the accusative plural, if it declines. One may also express it through a genitive construction ... annōrum (of ... years) with the number declined in genitive, e.g. Andreās vīgintī ūnīus annōrum est (Andrew is of twenty-one years, meaning Andrew is 21 years old). The following unique words are however used for infants:

hornōtinus, a, um: 0-years-old^[1]
- mēnsuālis, e: 1-month-old^[2]
- bimēstris, e: 2-months-old^[3]
- trimēstris, e: 3-months-old^[4]
- quadrimēstris, e: 4-months-old^[5]
- quīnquemēstris, e: 5-months-old^[6]
- semēstris, e: 6-months-old^[7]
- (Late Latin) septemmēstris, e: 7-months-old^[8]
- (*octōmēstris?): 8-months-old
- (New Latin) novemmēstris, e: 9-months-old^[9]
- decemmēstris, e: 10-months-old^[10]
- (*undecemmēstris?): 11-months-old
anniculus, a, um: 1-year-old, yearling^[11]
bīmus, a, um: 2-years-old^[12]
trīmus, a, um: 3-years-old^[13]
quadrīmus, a, um: 4-years-old^[14]
(rare, Medieval Latin) quīnquīmus, a, um: 5-year-old^[15]

After that, one may also create a one-word adjective with the suffix -ennis, derived from annus, yielding to quīnquennis, sexennis, etc. Please note that all these words are adjectives on their own and thus need to agree with the name they refer to: e.g., Duōs habeō līberōs, maior nātū est Richardus trīmus, minor nātū est Marīa annicula. (I have two children, the eldest named Richard is three-years-old, the youngest Mary is one-year-old; more literally, the eldest is the three-year-old Richard, the youngest is the one-year-old Mary).

References

^ https://lsj.gr/wiki/hornotinus, in the sense of this year's
^ https://lsj.gr/wiki/mensualis, in the sense of a month old
^ https://lsj.gr/wiki/bimestris
^ https://lsj.gr/wiki/trimestris
^ https://lsj.gr/wiki/quadrimestris
^ https://lsj.gr/wiki/quinquemestris
^ https://lsj.gr/wiki/semestris, in the sense of six months old
^ https://lsj.gr/wiki/septemmestris
^ Found in 18th century law treatises about the legal rights of foeti
^ https://lsj.gr/wiki/decemmestris
^ https://lsj.gr/wiki/anniculus
^ https://lsj.gr/wiki/bimus
^ https://lsj.gr/wiki/trimus
^ https://lsj.gr/wiki/quadrimus
^ http://ducange.enc.sorbonne.fr/QUINQUIMUS