7.4 Distributive numbers

Definition of distributive numbers

Distributive numbers answer the question "how many each?" They tell you how a quantity is divided equally among groups or individuals. Where a cardinal number like tres just means "three," the distributive terni means "three each" or "three apiece."

These numbers are adjectives, so they agree with their nouns in gender, number, and case. They always appear in plural forms, which makes sense since distribution inherently involves multiple recipients or groups.

Relationship to cardinal numbers

Distributive numbers are built from cardinal number stems, but they carry a different meaning. You use a cardinal when stating a total (tres pueri = "three boys") and a distributive when dividing among groups (terni pueri = "three boys each"). In contexts where a cardinal would be ambiguous about whether you mean a total or a per-group amount, the distributive removes that ambiguity.

Formation of distributive numbers

Regular patterns

Most distributives are formed by adding -ni, -nae, -na to the cardinal stem:

1. For simple stems, add -ni directly: quattuor → quaterni ("four each")
2. For cardinals ending in -em, replace that ending with -eni: septem → septeni ("seven each")
3. For higher compound numbers, combine distributives: viceni quini = "twenty-five each"

Irregular forms

The first three distributives are irregular and must be memorized:

• Singuli, -ae, -a ("one each") — not *unini
• Bini, -ae, -a ("two each") — not *duoni
• Terni (or trini), -ae, -a ("three each") — both forms are used interchangeably

At the higher end, centum becomes centeni ("a hundred each") and mille becomes milleni ("a thousand each").

Common distributive numbers

First ten distributives

• Singuli, -ae, -a: one each
• Bini, -ae, -a: two each
• Terni (trini), -ae, -a: three each
• Quaterni, -ae, -a: four each
• Quini, -ae, -a: five each
• Seni, -ae, -a: six each
• Septeni, -ae, -a: seven each
• Octoni, -ae, -a: eight each
• Noveni, -ae, -a: nine each
• Deni, -ae, -a: ten each

Multiples of ten

• Viceni, -ae, -a: twenty each
• Triceni, -ae, -a: thirty each
• Quadrageni, -ae, -a: forty each
• Quinquageni, -ae, -a: fifty each
• Sexageni, -ae, -a: sixty each
• Septuageni, -ae, -a: seventy each
• Octogeni, -ae, -a: eighty each
• Nonageni, -ae, -a: ninety each
• Centeni, -ae, -a: one hundred each

Declension of distributive numbers

Distributives decline like first/second declension plural adjectives (think boni, bonae, bona):

• Masculine: -i, -orum, -is, -os, -is (second declension plural)
• Feminine: -ae, -arum, -is, -as, -is (first declension plural)
• Neuter: -a, -orum, -is, -a, -is (second declension plural)

Since distributives describe quantities shared among groups, they only appear in plural forms. The neuter plural nominative/accusative always ends in -a (bina, terna, quaterna).

Usage in sentences

Adjectival function

Distributives modify plural nouns to show per-group quantities:

They agree with the noun in gender, number, and case, just like any other adjective. You can use them attributively (placed next to the noun) or predicatively.

With pluralia tantum (plural-only nouns)

This is one of the most important uses to remember. Latin has nouns that exist only in plural form, like castra ("camp"), litterae ("letter/epistle"), and nuptiae ("wedding"). With these nouns, you must use distributives instead of cardinals to express quantity:

• bina castra = "two camps" (not *duo castra, which would be confusing)
• trinae litterae = "three letters"

Without the distributive, there's no clear way to express "how many" of these plural-only nouns you mean.

Adverbial function

Distributives can combine with multiplicative adverbs to express repeated quantities. For example, bis deni literally "twice ten" can express "twenty." These constructions appear in contexts involving frequency or repeated cycles.

Comparison with other number types

Distributive vs. cardinal numbers

Distributive vs. ordinal numbers

Ordinals (primus, secundus, tertius) indicate position in a sequence. Distributives indicate per-group allocation. Ordinals typically modify singular nouns (tertius liber = "the third book"), while distributives modify plural nouns (terni libri = "three books each"). They use different suffixes: ordinals end in -us, -a, -um, while distributives end in -ni, -nae, -na.

Translation strategies

Translating distributives into English takes some flexibility. Here are the most common approaches:

• "each" or "apiece": bini → "two each" / "two apiece"
• "per": deni per mensem → "ten per month"
• "sets of": especially useful with pluralia tantum — ternae litterae → "three sets of letters" or simply "three letters"

Always check context. Sometimes a distributive is best rendered with a plain English number plus an explanatory phrase, especially when the "each" sense is already clear from the surrounding sentence.

Idiomatic expressions

Paired and naturally grouped items

Distributives often appear with things that come in natural sets. Binae manus ("two hands each") or bina scuta ("two shields each") emphasize the completeness of a set per person. You'll see this frequently in descriptions of soldiers' equipment or body parts.

Distributives in prose and poetry

In prose, distributives appear regularly in historical writing (describing how many troops were assigned to each legion) and in legal texts (specifying equal allocations). In poetry, they're less common because their forms can be metrically awkward, but poets do use them for emphasis or to highlight symmetry.

Historical development

Latin distributives trace back to Proto-Indo-European formations that used reduplication and suffixes to express distribution. By the Classical period, the forms had standardized into the -ni pattern familiar from textbooks. These Latin distributives later influenced how Romance languages handle distributive expressions, though most Romance languages lost the dedicated distributive adjective forms and replaced them with phrases like French chacun ("each one") plus a cardinal.