The numerals and derived numbers of the

Proto-Indo-European language Proto-Indo-European (PIE) is the reconstructed common ancestor of the Indo-European language family. No direct record of Proto-Indo-European exists; its proposed features have been derived by linguistic reconstruction from documented Indo-Eu ...

(PIE) have been reconstructed by modern linguists based on similarities found across all

Indo-European languages The Indo-European languages are a language family native to the northern Indian subcontinent, most of Europe, and the Iranian plateau with additional native branches found in regions such as Sri Lanka, the Maldives, parts of Central Asia (e. ...

. The following article lists and discusses their hypothesized forms.

Cardinal numbers

The

cardinal numbers In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case ...

are reconstructed as follows: Other reconstructions typically differ only slightly from Beekes and Sihler. A nineteenth-century reconstruction (by Brugmann) for ''thousand'' is . See also Fortson 2004. The elements (in the numerals "twenty" to "ninety") and (in "hundred") are reconstructed on the assumption that these numerals are derivatives of ''*deḱm̥(t)'' "ten". Lehmann believes that the numbers greater than ten were constructed separately in the dialect groups and that originally meant "a large number" rather than specifically "one hundred."

Gender of numerals

The numbers ''three'' and ''four'' had feminine forms with the suffix , reconstructed as and , respectively.

Numerals as prefixes

Special forms of the numerals were used as

prefix A prefix is an affix which is placed before the stem of a word. Particularly in the study of languages, a prefix is also called a preformative, because it alters the form of the word to which it is affixed. Prefixes, like other affixes, can b ...

es, usually to form bahuvrihis (like ''five-fingered'' in English):

Ordinal numbers

The

ordinal numbers In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the leas ...

are difficult to reconstruct due to their significant variation in the daughter languages. The following reconstructions are tentative: *"first" is formed with (related to some adverbs meaning "forth, forward, front" and to the

particle In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

"forth", thus originally meaning "foremost" or similar) plus various suffixes like (cf. Latin ''primus'', Russian ''perv-''). *"second": The daughter languages use a wide range of expressions, often unrelated to the word for "two" (including Latin and English), so that no PIE form can be reconstructed. A number of languages use the form derived from ''*h₂enteros'' meaning "the other f two (cf. OCS ''vĭtorŭ'', Lithuanian ''añtras'', Old Icelandic ''annarr'', modern Icelandic ''annar''). *"third" to "sixth" were formed from the cardinals plus the suffix : "third" etc. *"seventh" to "tenth" were formed by adding the thematic vowel to the cardinal: "eighth" etc. The cardinals ending in a syllabic nasal (seven, nine, ten) inserted a second nasal before the thematic vowel, resulting in the suffixes and . These and the suffix spread to neighbouring ordinals, seen for example in

Vedic upright=1.2, The Vedas are ancient Sanskrit texts of Hinduism. Above: A page from the '' Atharvaveda''. The Vedas ( or ; ), sometimes collectively called the Veda, are a large body of religious texts originating in ancient India. Composed ...

"eighth" and Lithuanian "ninth".

Reflexes

Reflexes In biology, a reflex, or reflex action, is an involuntary, unplanned sequence or action and nearly instantaneous response to a Stimulus (physiology), stimulus. Reflexes are found with varying levels of complexity in organisms with a nervous s ...

, or descendants of the PIE reconstructed forms in its daughter languages, include the following.

Reflexes of the cardinal numbers

In the following languages, reflexes separated by slashes mean: * Albanian: Tosk Albanian / Gheg Albanian * Armenian:

Classical Armenian Classical Armenian (, , ; meaning "literary anguage; also Old Armenian or Liturgical Armenian) is the oldest attested form of the Armenian language. It was first written down at the beginning of the 5th century, and most Armenian literature fro ...

/ Eastern Armenian /

Western Armenian Western Armenian ( ) is one of the two standardized forms of Modern Armenian, the other being Eastern Armenian. It is based mainly on the Istanbul Armenian dialect, as opposed to Eastern Armenian, which is mainly based on the Yerevan Arme ...

* English:

Old English Old English ( or , or ), or Anglo-Saxon, is the earliest recorded form of the English language, spoken in England and southern and eastern Scotland in the Early Middle Ages. It developed from the languages brought to Great Britain by Anglo-S ...

Modern English Modern English, sometimes called New English (NE) or present-day English (PDE) as opposed to Middle and Old English, is the form of the English language that has been spoken since the Great Vowel Shift in England England is a Count ...

* German:

Old High German Old High German (OHG; ) is the earliest stage of the German language, conventionally identified as the period from around 500/750 to 1050. Rather than representing a single supra-regional form of German, Old High German encompasses the numerous ...

/ New High German * Irish:

Old Irish Old Irish, also called Old Gaelic (, Ogham, Ogham script: ᚌᚑᚔᚇᚓᚂᚉ; ; ; or ), is the oldest form of the Goidelic languages, Goidelic/Gaelic language for which there are extensive written texts. It was used from 600 to 900. The ...

Modern Irish Irish (Standard Irish: ), also known as Irish Gaelic or simply Gaelic ( ), is a Celtic language of the Indo-European language family. It is a member of the Goidelic languages of the Insular Celtic sub branch of the family and is indigenous ...

* Ossetic:

Iron Iron is a chemical element; it has symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, forming much of Earth's o ...

/ Digor * Persian: Old Persian / Modern Persian * Tocharian: Tocharian A / Tocharian B

Cardinal numbers

Gender of numerals

Numerals as prefixes

Ordinal numbers

Reflexes

Reflexes of the cardinal numbers

Reflexes of the feminine numbers

Reflexes of the numeral prefixes

Reflexes of the ordinal numbers

Notes

References

Bibliography

Further reading