Distributive numbers in Latin express equal distribution among groups or individuals. They add precision to numerical relationships, indicating "X each" or "X apiece" in sentences. These numbers modify plural nouns and are crucial for describing allocations accurately.

Formed by adding -ni to cardinal number stems, distributive numbers have both regular and irregular patterns. They function as adjectives, agreeing with nouns in gender, number, and case, and can also serve as adverbs to express frequency or repetition of actions.

Definition of distributive numbers

• Distributive numbers represent a specific quantity distributed equally among multiple groups or individuals in Latin
• Serve a crucial role in expressing concepts of distribution, allocation, and equal division in Latin texts
• Enhance precision and clarity when describing numerical relationships in Latin grammar

Function in Latin grammar

• Express the idea of "X each" or "X apiece" in Latin sentences
• Indicate equal distribution of items among multiple recipients or groups
• Modify plural nouns to show how many of something each person or group receives
• Provide a concise way to express complex numerical relationships in Latin

Relationship to cardinal numbers

• Derived from cardinal numbers but convey a distinct distributive meaning
• Share numerical values with cardinals but add the concept of equal distribution
• Typically formed by adding the suffix -ni to the cardinal number stem
• Used in contexts where simple cardinal numbers would be ambiguous or insufficient

Formation of distributive numbers

Regular patterns

• Add the suffix -ni to the stem of cardinal numbers (quattuor → quaterni)
• Double the final consonant of the stem before adding -ni (sex → seni)
• Replace final -em of cardinals with -eni for numbers ending in -em (septem → septeni)
• Form higher numbers by combining lower distributives (viceni quini for "twenty-five each")

Irregular forms

• Singuli ("one each") instead of the expected unini
• Bini ("two each") instead of duoni
• Trini or terni ("three each") used interchangeably
• Centeni ("a hundred each") drops the -um from centum
• Milleni ("a thousand each") modifies mille significantly

Usage in sentences

Adjectival function

• Modify plural nouns to indicate distribution (pueri binas piras habent - "The boys have two pears each")
• Agree with the noun in gender, number, and case
• Often used with collective nouns to specify individual allocation
• Can be used attributively or predicatively in a sentence

Adverbial function

• Express frequency or repetition of actions (ter deni - "ten times each" or "thirty times")
• Modify verbs to indicate how often an action occurs for each subject
• Used in temporal expressions to denote recurring events or cycles
• Can be combined with other adverbs to create complex frequency expressions

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

Comparison with other number types

Distributive vs cardinal numbers

• Cardinals express simple quantity (tres - "three"), distributives indicate allocation (terni - "three each")
• Distributives always refer to plural groups, while cardinals can be singular or plural
• Distributives decline like adjectives, cardinals are often indeclinable
• Distributives emphasize equal division, cardinals focus on total quantity

Distributive vs ordinal numbers

• Ordinals indicate position or sequence (tertius - "third"), distributives show equal distribution
• Ordinals typically modify singular nouns, distributives modify plural nouns
• Ordinals use different suffixes (-us, -a, -um) compared to distributives (-ni, -nae, -na)
• Distributives express repetition or frequency, ordinals do not inherently convey this meaning

Idiomatic expressions

Paired nouns with distributives

• Used with naturally paired items (bina scuta - "two shields each")
• Express reciprocal actions or relationships (ternas litteras misimus - "we sent three letters each")
• Emphasize the completeness of sets (binae manus - "two hands each")
• Often found in descriptions of equipment or body parts

Distributives with plural-only nouns

• Required with plural-only nouns (pluralia tantum) instead of cardinals
• Used with words like castra (camp), nuptiae (wedding), litterae (letter)
• Convey precise quantities for these nouns (bina castra - "two camps")
• Help distinguish between singular and plural meanings of ambiguous nouns

Translation strategies

English equivalents

• Translate using "each" or "apiece" after the number (bini - "two each")
• Use the preposition "per" in some contexts (deni per mensem - "ten per month")
• Employ phrases like "sets of" for clarity (ternae litterae - "sets of three letters")
• Consider context to determine if distribution or simple quantity is meant

Context-dependent translations

• Adapt translation based on the specific usage in the Latin text
• Consider using cardinal numbers with explanatory phrases in some cases
• Translate as frequency adverbs when modifying verbs (bis deni - "twenty times")
• Maintain the distributive sense when crucial to the meaning of the passage

Declension of distributive numbers

Adjectival endings

• Follow the pattern of first and second declension adjectives
• Masculine and neuter use second declension endings (-i, -orum, -is, -os, -is)
• Feminine uses first declension endings (-ae, -arum, -is, -as, -is)
• Neuter plural nominative and accusative end in -a (bina, terna, etc.)

Agreement with nouns

• Match the gender, number, and case of the noun they modify
• Always used in plural form due to their distributive nature
• Can be used substantively, taking on the role of a noun
• Must agree with plural-only nouns in appropriate cases

Historical development

Origins in Proto-Indo-European

• Derived from Proto-Indo-European (PIE) distributive formations
• PIE used reduplication and suffixes to create distributive meanings
• Latin distributives evolved from these earlier forms
• Retained the fundamental concept of equal distribution from PIE

Evolution in Classical Latin

• Standardized forms emerged during the Classical period
• Replaced some earlier constructions for expressing distribution
• Integrated into the complex Latin number system
• Influenced the development of distributive expressions in Romance languages

Frequency in Latin literature

Prose usage

• Common in historical works for describing military formations
• Used in legal texts to specify equal distributions or allocations
• Found in philosophical writings to express logical relationships
• Employed in scientific and technical treatises for precise measurements

Poetic usage

• Less frequent in poetry due to metrical constraints
• Used for emphasis or to create specific rhythmic effects
• Found in descriptive passages to highlight symmetry or balance
• Employed metaphorically to convey concepts of equality or fairness