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In reviewing this question, a brief discussion arose in the comments about how many types of numbers Latin has. The suggestion was that the tradition states that there are four, and other types of number expressions are derived adjectives. (As an aside, many of the references use the word "numerals" for what I understand to be "numbers." I will leave that distinction aside for the moment and not comment on the potential discrepancies in what I quote or refer to below.)

I confirmed such a tradition of four types by consulting two sources I could easily access: Latin: An Intensive Course, by Floyd L. Moreland and Rita M. Fleischer and Allen and Greenough's New Latin Grammar for Schools and Colleges. The former has a chart in the appendix with columns headed "Cardinals," "Ordinals," "Distibutives," and "Adverbs." "Trīnī" is listed in parenthesis after "ternī" as a presumed alternative, but no other numbers are mentioned.

Allen and Greenough's New Latin Grammar says:

The Latin Numerals may be classified as follows:— I. NUMERAL ADJECTIVES:

Cardinal Numbers, answering the question how many? as, ūnus, one; duo, two, etc. Ordinal Numbers,1 adjectives derived (in most cases) from the Cardinals, and answering the question which in order? as, prīmus, first; secundus, second, etc. Distributive Numerals, answering the question how many at a time? as, singulī, one at a time; bīnī, two by two, etc.

II. NUMERAL ADVERBS, answering the question how often? as, semel, once; bis, twice, etc.

With respect to plurale tantum numbers, this refence makes these two clarifications in different sections (cardinals and distributives) without mentioning the form quadrīnī:

[*] a. For the declension of ūnus , see § 113. It often has the meaning of same or only. The plural is used in this sense; but also, as a simple numeral, to agree with a plural noun of a singular meaning: as, ūna castra, one camp (cf. § 137. b). The plural occurs also in the phrase ūnī et alterī, one party and the other (the ones and the others).

Instead of cardinals, to express simple number, when a noun plural in form but usually singular in meaning is used in a plural sense: as, bīna castra, two camps ( duo castra would mean two forts). With such nouns trīnī , not ternī , is used for three: as, trīna (not terna ) castra, three camps; terna castra means camps in threes.

After this discussion of the four types, the text goes on to describe "other numerals" of four other "types" and an other category that together cover ten different forms. Here are two sections of particular interest:

b. Temporals: bīmus , trīmus, of two or three years' age; biennis , triennis, lasting two or three years; bimēstris , trimēstris, of two or three months; bīduum, a period of two days; biennium, a period of two years.

[*] d. Other derivatives are: ūniō, unity; bīniō, the two (of dice); prīmānus of the first legion; prīmārius, of the first rank; dēnārius, a sum of 10 asses bīnus (distributive), double, etc.

This Wikipedia site (Latin Numerals) treats the numbers as nine types, including a separate set of plurale tantum numbers including quadrīnī, but excluding any reference to the "temporal derivatives" mentioned in Allen and Greenough and to "ūniō, unity; bīniō, the two (of dice); prīmānus of the first legion."

Why do we have all this confusion? With the exception of the adverbial numbers, all these expressions are basically equally adjectives derived from the cardinal numbers (with exceptions for some obvious words, like bis, singulī, prīmus, secundus, etc.).

In reading Caesar's Commentarii de Bello Gallico recently (the supposed first text for those starting extended reading in authentic classical Latin), I think I came across at least the following seven types of numbers: cardinal, ordinal, distributive, plurale tantum, adverbial, multiplicatives, and distributive + -ārius. Of course, some of these analyses are simply a matter of how one wishes to organize the material; however, it seems that I have had to consult at least two different sources to get a nearly complete picture, and I find the confusion between distributives and plural tantum numbers conceptually problematic.

Why does the tradition give us all this confusion, and why does it stop its description of numbers at four basic types given that so many other types seem to call for frequent use?

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    I cannot write up a full answer, but I would like to add that fractions seem to be a category of itself.
    – Canned Man
    Feb 22, 2022 at 21:48

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Different people will mean slightly different things by the word "numeral". If you want it to mean "a word or phrase directly related to a number or amount" or something similar, then there are indeed many more classes of Latin numerals than just four. But are the English words 'dozen', 'triplet', 'half', and 'three fifths' all numerals? Most people would say no, but a very broad definition would say yes.

One way to see things is to consider numerals to be the atoms of number-related expressions. Clearly 'three' and 'fifth' should be on the list of English numerals, but I don't think the 'three fifths' in itself needs to be listed. If you want to take a minimalist approach, then things composed in predictable ways from numerals should not be included as numerals. If you take this approach, then 'twenty-three' is not a numeral (predictable combination) but 'thirteen' is (unpredictable).

The Latin grammatical tradition lands somewhere between the two extremes: It identifies numerals as four (complete) lists of words which you cannot derive from each other but from which you can derive almost all number-related words you need. If you want, you could speak of the four classes as basic numerals and all else as derived numerals.

For example, the derivative suffix -arius is very productive and predictable, so it is most naturally placed in the derived rather than basic category. (They also seem to be less common than the basic ones, which may be something you want to factor in.)

Adjectives like triplus and triplex are not easily derived from the basic numerals, so why exclude them? I would categorize them similarly with biennis or unio or the English 'triplet' or 'double' — words that are related to numbers but that are not numbers in themselves. Drawing a line between "proper number words" and "other words related to numbers" (and thus defining the boundaries of what a numeral is) can be arbitrary. But it is practically useful to identify a set of core vocabulary and treat the rest as derivatives.

In the Latin grammatical tradition not all words related to numbers are numerals. If you feel they should be, then your use of the word "numeral" is untraditional. As with any nonstandard choice of terminology, it doesn't make you wrong but it can make communication difficult. Finally, I must add that I don't find defining the exact boundaries of the concept of a numeral all that useful.

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