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, , , , 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, , , and multiples of , all of which decline. Additionally, although is an indeclinable adjective in the singular, it becomes a declinable noun in the plural. These exceptions are further explained in later sections.

1–10
The smaller cardinal numerals, from to, are all simple (not made by combining two numbers).

ūnus
Inflection: The Latin 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:  ("one horse"),   ("one key"),   ("one stone"). The ending will also agree with the grammatical case of the associated noun:  (genitive),   (accusative),   (dative).

Plural: Although it may seem strange at first sight, 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 occurs only as a plural neuter form and takes plural endings, even though it identifies one object, hence:   ("of one camp").

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

duo
Inflection: The Latin 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 is very similar.

The choice of ending will agree with the gender of the associated noun, which will necessarily be plural:  ("two horses"),   ("two keys"),   ("two stones"). The ending will also agree with the grammatical case of the associated noun:  (accusative),   (genitive),   (dative).

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

trēs
Inflection: The Latin 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:  ("three horses"),   ("three keys"),   ("three stones"). The ending will also agree with the grammatical case of the associated noun:  (accusative),   (genitive),   (dative).

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

IV to X
The numerals through  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, , ). The numerals for 7 through 10 appear in the English names of months (,, , and ). These months were the seventh through tenth of the Roman calendar, since the Roman year began with.

11 - 20
Latin cardinals larger than but less than  are constructed by addition. The ending (a form of ) is attached to the numerals  through. The resultant compound carries the same value as the mathematical sum of the components. For example is  +. English does much the same by attaching (a form of ) to smaller numerals, such as the numeral  which is  +.

In some of these compounds, a spelling and pronunciation change occurs during the attachment, so that +  drops the -x and lengthens the e to yield. This kind of change also occurs in English, as in +, in which the v is devoiced under the influence of the following t (and the purely orthographic e is dropped) to yield.

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, it is more often written as (literally "two from twenty"). Likewise, the numeral for 19 may be written as, but is more often encountered as.

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

other numbers 20<x100
Numbers inbetween multiples of 10 can be formed by two different ways. Let us take 22 as example:
 * vīgintī duo
 * duo et vīgintī

× 100
The numeral is the only "hundred" that is indeclinable.

All multiples of up to, e.g. , , etc., decline as a plural adjective of the first and second declension.

mīlle
The Latin 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.

Singular: In the singular, 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:  (nominative masculine, "thousand horses"),   (ablative feminine, "with a thousand keys"),    (genitive neuter, "of these thousand stones"). This use agrees with the in the plural:    ("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 . In this usage it governs a genitive and agrees with the predicate in the singular:    ("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 , perhaps in a partitive sense "a thousand men from among the soldiers".

Plural: The plural form,, 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 in the genitive plural instead of agreeing with it as an adjective would:     ("that many thousand of soldiers were captured"). If further modified by the cardinal numerals or  ("two/three thousand"), or by distributive numerals like  and  ("one/ten each"), or any other declinable adjective, the latter will appear in the same gender (neuter) and grammatical case as :     (nominative, "there were three thousand horses"),     (genitive, "the rumbling of two thousand stones"),      (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:   ("two thousand were captured"),      ("two thousand five hundred soldiers were captured"),      ("three thousand five hundred women (soldiers) were captured").

Compound cardinals
Latin cardinal numerals larger than, that are not multiples of ten, are assembled as compound words. The components of these compounds are the numerals through  and the multiples of, the multiples of , and.

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.

Counting backwards
Of the Latin compound cardinal numerals less than, 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:
 * + + multiple of ten

Thus, the numeral for 48 is normally written as, rather than as the expected  or. 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:
 * + + multiple of ten

Thus, the numeral for 49 is normally written as, rather than as the expected  or. 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, the noun being counted must be in the genitive plural. For example, "two thousand soldiers" would be " 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.  ūnīus annōrum est (Andrew is of twenty-one years, meaning Andrew is 21 years old). The following unique words are however used for infants: After that, one may also create a one-word adjective with the suffix -ennis, derived from , yielding to , , 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 līberōs,   est ,   est  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).
 * , a, um: 0-years-old
 * , e: 1-month-old
 * , e: 2-months-old
 * , e: 3-months-old
 * , e: 4-months-old
 * , e: 5-months-old
 * , e: 6-months-old
 * , e: 7-months-old
 * (*octōmēstris?): 8-months-old
 * , e: 9-months-old
 * , e: 10-months-old
 * (*undecemmēstris?): 11-months-old
 * , a, um: 1-year-old,
 * , a, um: 2-years-old
 * , a, um: 3-years-old
 * , a, um: 4-years-old
 * , a, um: 5-year-old