Proto-Indo-European numerals

The numerals and derived numbers of the Proto-Indo-European language (PIE) have been reconstructed by modern linguists based on similarities found across all Indo-European languages. The following article lists and discusses their hypothesized forms.

Cardinal numbers

The cardinal numbers are reconstructed as follows:

Number Reconstruction (Sihler)[1] Reconstruction (Beekes)[2]
one *Hoi-no-/*Hoi-wo-/*Hoi-k(ʷ)o-; *sem- *Hoi(H)nos ; sem-/sm̥-
two *d(u)wo- *du̯oh₁
three *trei- (full grade) / *tri- (zero grade) *trei̯es
four *kʷetwor- (o-grade) / *kʷetur- (zero grade)
(see also the kʷetwóres rule)
*kʷétu̯ōr
five *penkʷe *penkʷe
six *s(w)eḱs; originally perhaps *weḱs *(s)u̯éks
seven *septm̥ *séptm̥
eight *oḱtō, *oḱtou or *h₃eḱtō, *h₃eḱtou *h₃eḱteh₃
nine *(h₁)newn̥ *(h₁)néun
ten *deḱm̥(t) *déḱm̥t
twenty *wīḱm̥t-; originally perhaps *widḱomt- *du̯idḱm̥ti
thirty *trīḱomt-; originally perhaps *tridḱomt- *trih₂dḱomth₂
forty *kʷetwr̥̄ḱomt-; originally perhaps *kʷetwr̥dḱomt- *kʷeturdḱomth₂
fifty *penkʷēḱomt-; originally perhaps *penkʷedḱomt- *penkʷedḱomth₂
sixty *s(w)eḱsḱomt-; originally perhaps *weḱsdḱomt- *u̯eksdḱomth₂
seventy *septm̥̄ḱomt-; originally perhaps *septm̥dḱomt- *septm̥dḱomth₂
eighty *oḱtō(u)ḱomt-; originally perhaps *h₃eḱto(u)dḱomt- *h₃eḱth₃dḱomth₂
ninety *(h₁)newn̥̄ḱomt-; originally perhaps *h₁newn̥dḱomt- *h₁neundḱomth₂
hundred *ḱm̥tom; originally perhaps *dḱm̥tom *dḱm̥tóm
thousand *ǵʰeslo-; *tusdḱomti (originally "a massive number") *ǵʰesl-

Other reconstructions typically differ only slightly from Beekes and Sihler. A nineteenth-century reconstruction (by Brugmann) for thousand is *tūsḱmtiə.[3][4] See also Fortson 2004.[5]

The elements *-dḱomt- (in the numerals "twenty" to "ninety") and *dḱm̥t- (in "hundred") are reconstructed on the assumption that these numerals are derivatives of *deḱm̥(t) "ten".

Lehmann[6] believes that the numbers greater than ten were constructed separately in the dialect groups and that *ḱm̥tóm originally meant "a large number" rather than specifically "one hundred."

Gender of numerals

The numbers three and four had feminine forms with the suffix *-s(o)r-, reconstructed as *t(r)i-sr- and *kʷetwr̥-sr-, respectively.[5]

Numerals as prefixes

Special forms of the numerals were used as prefixes, usually to form bahuvrihis (like five-fingered in English):

Number Prefix (Fortson)[7]
one- (together, same) *sm̥-
two- *dwi-
three- *tri-
four- *kʷ(e)tru- or *kʷetwr̥-

Ordinal numbers

The ordinal numbers are difficult to reconstruct due to their variety in the daughter languages. The following reconstructions are tentative:[8]

  • "first" is formed with *pr̥h₃- (related to some adverbs meaning "forth, forward, front" and to the particle *prō "forth", thus originally meaning "foremost" or similar) plus various suffixes like *-mo-, *-wo- (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 [of two]" (cf. OCS vĭtorŭ, Lithuanuan añtras, Old Icelandic annarr)
  • "third" to "sixth" were formed from the cardinals plus the suffix *-t(ó)-: *tr̥-t(ó)- / *tri-t(ó)- "third" etc.
  • "seventh" to "tenth" were formed by adding the thematic vowel *-ó- to the cardinal: *oḱtow-ó- "eighth" etc.

The cardinals ending in a syllabic nasal (seven, nine, ten) inserted a second nasal before the thematic vowel, resulting in the suffixes *-mó- and *-nó-. These and the suffix *-t(ó)- spread to neighbouring ordinals, seen for example in Vedic aṣṭa- "eighth" and Lithuanian deviñtas "ninth".

Reflexes

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

Reflexes of the cardinal numbers

NumberReconstruction (Sihler)Reflexes[5][9]
one*Hoi-no-[10]Alb. njã > një (dialectal nji;njo), Lith. vienas, Latv. viens, Gaul. oinos, Gm. ein/eins, Eng. ān/one, Gk. oios, Av. aēuua, Ir. óin/aon, Kashmiri akh, Lat. ūnus, Kamviri ev, Osc. uinus, OCS edinŭ, ON einn, OPruss. aīns, Osset. iu/ieu, Pers. aiva-/yek, Pol. jeden, Roman. unu, Russ. odin, Ved. aika, Umbr. uns, Goth. ains, Welsh un
*sem-[11]Arm. mi/mek/meg, Alb. gjithë, Lith. sa, sav-as, Eng. sum/some, Gm. saman/zusammen, Gk. εἷς heis, Hitt. san, Av. hakeret, Ir. samail/samhail, Lat. semel, Lyc. sñta, Kamviri sâ~, Pers. hama/hamin, Russ. odin, yedin, perviy Ved. sakŕ̥t, Toch. sas/ṣe, Welsh hafal, ON sami, Goth. sama, Kurdish yek, ek, hev- as prefix.
two*du(w)o-[12]Hitt. dā-, Luv. tuwi-, Lyc. tuwa, Ved. dvā(u), Av. duua, Pers. duva/do, Osset. dyuuæ/duuæ, Kashmiri zū', Kamviri dü, Gk. δύω dúō, Lat. duō, Osc. dus, Umbr. tuf, ON tveir, Goth. twai, Eng. twā/two, Gm. zwêne/zwei, Gaul. vo, Ir. dá/dó, Welsh dau, Arm. erkow/yerku/yergu, Toch. wu/wi, OPruss. dwāi, Latv. divi, Lith. dù, OCS dŭva, Pol. dwa, Russ. dva, Alb. dy;di/dy;dў, Kurdish du.
three*trei-[13]Hitt. teriyaš (gen. pl.), Lyc. trei, Ved. tráyas, Av. θrāiiō, Pers. çi/se, Osset. ærtæ/ærtæ, Kashmiri tre, Kamviri tre, Gk. τρεῖς treĩs, Lat. trēs, Osc. trís, Umbr. trif, ON þrír, Goth. þreis, Eng. þrēo/three, Gm. drī/drei, Gaul. treis, Ir. treí/trí, Welsh tri, Arm. erek῾/yerek῾/yerek῾, Toch. tre/trai, OPruss. tri, Latv. trīs, Lith. trỹs, OCS trije, Pol. trzy, Russ. tri, Alb. tre/tre. se`(thr>s).
four*kʷetwor-[14]Lyc. teteri, Ved. catvāras, Av. caθuuārō, Pers. /čahār, Osset. cyppar/cuppar, Kashmiri tsor, Kamviri što, Gk. téttares, Lat. quattuor, Osc. petora, Umbr. petor, ON fjórir, Goth. fidwor, Eng. fēower/four, Gm. feor/vier, Gaul. petor, Ir. cethir/ceathair, Welsh pedwar, Arm. čork῾/čors/čors, Toch. śtwar/śtwer, OPruss. keturjāi, Latv. četri, Lith. keturì, OCS četyre, Pol. cztery, Russ. četyre, Alb. katër;katrë/katër, Kurdish char, chwar.
five*pénkʷe[15]Luv. panta, Ved. pañca, Av. panca, Pers. panča/panj, Osset. fondz/fondz, Kashmiri pā.~tsh Kamviri puč, Gk. πέντε pénte, Lat. quīnque, Osc. pompe, Umbr. pumpe, ON fimm, Goth. fimf, Eng. fīf/five, Gm. fimf/fünf, Gaul. pempe, Ir. cóic/cúig, Welsh pump, Arm. hing/hing/hink, Toch. päñ/piś, OPruss. pēnkjāi, Latv. pieci, Lith. penkì, OCS pętĭ, Pol. pięć, Russ. pjat', Alb. pesë/pes(ë);pês, Kurdish penc.
six*s(w)eḱs[16]Ved. ṣáṣ, Av. xšuuaš, Pers. /šeš, Osset. æxsæz/æxsæz, Kashmiri śe, Kamviri ṣu, Gk. ἕξ héks, Lat. sex, Osc. sehs, Umbr. sehs, ON sex, Goth. saíhs, Eng. siex/six, Gm. sëhs/sechs, Gaul. suex, Ir. sé/sé, Welsh chwech, Arm. vec῾/vec῾/vec῾, Toch. ṣäk/ṣkas, OPruss. usjai, Latv. seši, Lith. šešì, OCS šestĭ, Pol. sześć, Russ. šest', Alb. gjashtë/gjasht(ë);xhasht, Kurdish shesh.
seven*septm̥[17]Hitt. šipta-, Ved. saptá, Av. hapta, Pers. hafta/haft, Osset. avd/avd, Kashmiri sath, Kamviri sut, Gk. ἑπτά heptá, Lat. septem, Osc. seften, ON sjau, Goth. sibun, Eng. seofon/seven, Gm. sibun/sieben, Gaul. sextan, Ir. secht/seacht, Welsh saith, Arm. ewt῾n/yot῾/yot῾ě, Toch. ṣpät/ṣukt, OPruss. septīnjai, Lith. septynì, Latv. septiņi, OCS sedmĭ, Pol. siedem, Russ. sem', Alb. shtatë/shtat(ë), Kurdish heft.
eight*h₃eḱtō[18]Lyc. aitãta-, Ved. aṣṭā(u), Av. ašta, Pers. ašta/hašt, Osset. ast/ast, Kashmiri ā.ṭh, Kamviri uṣṭ, Gk. ὄκτω oktō, Lat. octō, Osc. uhto, ON átta, Goth. ahtau, Eng. eahta/eight, Gm. ahto/acht, Gaul. oxtū, Ir. ocht/ocht, Welsh wyth, Arm. owt῾/ut῾ě, Toch. okät/okt, OPruss. astōnjai, Latv. astoņi, Lith. aštuonì, OCS osmĭ, Pol. osiem, Russ. vosem', Alb. tëte/tet(ë), Kurdish hesht.
nine*(h₁)newn̥[19]Lyc. ñuñtãta-,[20] Ved. nava, Av. nauua, Pers. nava/noh, Kashmiri nav, Kamviri nu, Gk. ἐννέ(ϝ)α enné(w)a, Lat. novem, Osc. nuven, Umbr. nuvim, ON níu, Goth. niun, Eng. nigon/nine, Gm. niun/neun, Gaul. navan, Ir. nói/naoi, Welsh naw, Arm. inn/inn/inně, TochA. ñu, OPruss. newīnjai, Latv. deviņi, Lith. devynì, OCS devętĭ, Pol. dziewięć, Russ. devjat', Alb. nëntë;nëndë/nând(ë);non(t), Kurdish neh, no.
ten*deḱm̥(t)[21]Ved. dáśa, Av. dasa, Pers. daθa/dah, Osset. dæs/dæs, Kashmiri da.h, Kamviri duc, Gk. δέκα déka, Lat. decem, Osc. deken, Umbr. desem, ON tíu, Goth. taíhun, Eng. tīen/ten, Gm. zëhen/zehn, Gaul. decam, Ir. deich/deich, Welsh deg, Arm. tasn/tas/dasě, Toch. śäk/śak, OPruss. desīmtan, Latv. desmit, Lith. dẽšimt, OCS desętĭ, Pol. dziesięć, Russ. desjat', Alb. dhjetë/dhet(ë), Kurdish deh, de.
twenty*wīḱm̥t-Ved. viṁśatí-, Av. vīsaiti, Pers. /bēst, Kashmiri vuh, Kamviri vici, Doric ϝίκατι wíkati, Lat. vīgintī, Gaul. vocontio, Ir. fiche/fiche, M. Welsh ugein(t), Arm. k῾san/k῾san/k῾san, Toch. wiki/ikäṃ, Lith. dvi-de-šimt, Alb. njëzet/njizet, Kurdish bist.
thirty*trīḱomt-Skr. triṅśat, Gk. τριάκοντα triákonta, Lat. trīgintā, Ir. /tríocha, Lith. tris-de-šimt, Kurdish sih, si.
forty*kʷetwr̥̄ḱomt-Skr. catvāriṅśat, Gk. τεσσεράκοντα tessarákonta, Lat. quadrāgintā, Lith. keturias-de-šimt, Kurdish chil.
fifty*penkʷēḱomt-Skr. pañcāśat, Gk. πεντήκοντα pentêkonta, Lat. quinquāgintā, Ir. /caoga, Lith. penkias-de-šimt, Kurdish pe`nci, penca.
sixty*s(w)eḱsḱomt-Skr. ṣaṣṭih, Gk. ἐξήκοντα exêkonta, Lat. sexāgintā, Ir. /seasca, Lith. šešias-de-šimt, Russ. šest'desjat, Kurdish shest.
seventy*septm̥̄ḱomt-Skr. saptatih, Gk. heptákonta, Lat. septuāgintā, Ir. /seachtó, Lith. septynias-de-šimt, Russ. sem'desjat, Kurdish hefte`, hefta.
eighty*h₃eḱtō(u)ḱomt-Skr. aśītih, Gk. ὀγδοήκοντα ogdοêkonta, Lat. octāgintā, Ir. /ochtó, Lith. aštuonias-de-šimt, Russ. vosem'desjat, Kurdish heshte`, heshta.
ninety*(h₁)newn̥̄ḱomt-Skr. navatih, Gk. ἐνενήκοντα enenêkonta, Lat. nonāgintā, Ir. /nócha, Lith. devynias-de-šimt, Russ. devjanosto, Kurdish not, newet.
hundred*ḱm̥tom[22]Ved. śatám, Av. satəm, Pers. /sad, Osset. sædæ, Kashmiri śath, Gk. ἑκατόν hekatón, Lat. centum, ON hundrað, Goth. hund, Eng. hundred/hundred, Gm. hunt/hundert, Gaul. cantam, Ir. cét/céad, Welsh cant, Toch. känt/kante, Latv. simts, Lith. šim̃tas, OCS sŭto, Pol. sto, Russ. sto/sotnja, Kurdish sed.
thousand*(sm̥-)ǵʰéslo-Skr. sahasram, Av. hazarəm, Pers. /hazār, Gk. khilioi, Lat. mīlle, Kurdish hezar.
*tusdḱomtiON þúsund, Goth. þusundi, Eng. þusend/thousand, Gm. þūsunt/tausend, TochA. tmāṃ, TochB. tmāne/tumane, Lith. tūkstantis, Latv. tūkstots, OCS tysǫšti, Pol. tysiąc, Russ. tys'ača
*wel-tyo-[23]Toch. wälts/yaltse; OCS velьjь/velikъ

In the following languages, reflexes separated by slashes mean:

Reflexes of the feminine numbers

NumberReconstructionReflexes[5]
three*t(r)i-sr-Ved. tisrás, Av. tišrō, Gaul. tidres, Ir. teoir/?
four*kʷetwr̥-sr-Ved. cátasras, Av. cataŋrō, Lith. keturios, Ir. cetheoir/?

Reflexes of the numeral prefixes

NumberReconstructionReflexes (with examples)[7][24]
one- (together, same)*sm̥-Ved. sa-kŕ̥t "once", Gk. há-ploos "one-fold, simple", Lat. sim-plex "one-fold"
two-*dwi-Ved. dvi-pád- "two-footed", Gk. dí-pod- "two-footed", Archaic Lat. dui-dent "a sacrificial animal with two teeth", Lith. dvi-kojis "two-footed"
three-*tri-Ved. tri-pád- "three-footed", Gk. trí-pod- "three-footed (table)", Lat. tri-ped- "three-footed", Lith. tri-kojis "three-footed", Gaul. tri-garanus "having three cranes", Alb. tri-dhjetë "thirty" (three ten)
four-*kʷ(e)tru-Ved. cátuṣ-pád- "four-footed", Av. caθru-gaoša- "four-eared", Gk. tetrá-pod- "four-footed", Lat. quadru-ped- "four-footed", Lith. ketur-kojis "four-footed"

Reflexes of the ordinal numbers

NumberReconstructionReflexes
first*pr̥h₃-wó-Ved. pūrviyá-, OCS prĭvŭ,[8] Pol. pierwszy, Russ. pervyj, Toch. parwät/parwe
*pr̥h₃-mó-Goth. fruma, Lith. pìrmas,[8] Latv. pirmais, Lat. prīmus, Osc. perum
other formsEng. fyrst/first,[8]

Hitt. para, Lyc. pri, Av. pairi, vienet-as, paoiriia, Osset. fyccag, farast/farast, Kamviri pürük, Gk. prōtos, Umbr. pert, ON fyrstr, Gm. furist/Fürst "prince, ruler"; fruo/früh "early", Ir. er/air, Welsh ar, OPruss. pariy, Alb. i parë

second*(d)wi-teró-Skr. dvitīya, Gk. deúteros, Russ. vtoroj
third*tri-t(y)ó-Ved. tr̥tīya-, Gk. trítos, Lat. tertius,[8]

Alb. (i) tretë, Lith. trečias < *tretias, Russ. tretij

fourth*kʷetwr̥-tó-Gk. tétartos, Eng. feorþa/fourth, OCS četvirĭtŭ,[8]

Alb. (i) katërt, Lat. quartus, Lith. ketvirtas, Russ. chetv'ortyj

fifth*penkʷ-tó-Av. puxδa-, Gk. pémptos,[8]

Lat. quīntus, Alb. (i) pestë, Lith. penktas, Russ. p'atyj

sixth*sweḱs-tó-Gk. héktos, Lat. sextus,[8]

Alb.(i) gjashtë, Lith. šeštas, Russ. šestoj

seventh*septm̥-(m/t)ó-Gk. hébdomos, Lat. septimus, OCS sedmŭ,[8]

Lith. septintas, sekmas, Russ. sed'moj

eighth*h₃eḱtōw-ó-Gk. ógdo(w)os, Lat. octāvus,[8]

Russ. vos'moj, Lith. aštuntas, ašmas

ninth*(h₁)newn̥-(n/t)ó-Lat. nōnus,[8]

Gk. énatos, Russ. dev'atyj, Lith. devintas

tenth*deḱm̥-(m/t)ó-Ved. daśamá-, Av. dasəma-, Lat. decimus,[8]

Gk. dékatos, Lith. dešimtas, Russ. desjatyj

See also

Notes

  1. Sihler (1995:40224)
  2. Beekes (1995:21216)
  3. Brugmann (1892:48)
  4. Meillet:372)
  5. Fortson (2004:131)
  6. Lehmann (1993:252255)
  7. Fortson (2004:131132)
  8. Fortson (2004:132)
  9. Gvozdanovic (1991)
  10. BLAŽEK, Václav. "Indo-European "one" and "first"". In: Sborník prací Filosofické fakulty Brněnské university, A 47. Brno: MU, 1999. p. 7-27. A 47. ISBN 80-210-2098-9.
  11. de Vaan, Michiel. "Proto-Indo-European *sm and *si ‘one’". In: The Precursors of Proto-Indo-European. Leiden, The Netherlands: Brill|Rodopi, 2019. pp. 203–218. doi: https://doi.org/10.1163/9789004409354_015
  12. BLAŽEK, Václav. "Indo-European "two"". In: Sborník prací Filosofické fakulty brněnské university. Brno: Masarykova universita, 1998. p. 5-25. A 46. ISBN 80-210-1796-1.
  13. BLAŽEK, Václav. "Indo-European "three"". In: Lingua Posnaniensis, Polsko: neznámý, 1998, vol. 40, No 1, p. 33-45. ISSN 0079-4740.
  14. BLAŽEK, Václav. "Indo-European "four"." In: Indogermanische Forschungen, Berlin: Walter de Gruyter, 1998, vol. 103, No 1, p. 112-134. ISSN 0019-7262.
  15. BLAŽEK, Václav. "Indo-European "five"". In: Indogermanische Forschungen, Berlin-NY: Walter de Gruyter, 2000, vol. 105, No 1, p. 102-120. ISSN 0019-7262.
  16. BLAŽEK, Václav. "Indo-European "six"". In: Sborník prací Filosofické fakulty brněnské university. Brno: Masarykova universita, 2000. p. 5-18. A 48. ISBN 80-210-2350-3.
  17. Blažek, Václav. "Indo-European ‘Seven’". In: Journal of Indo-European Studies, Monograph Series 22 (1997): 9-29.
  18. BLAŽEK, Václav. "Indo-european "eight"". In: Historische Sprachforschung. SRN: neznám, 1998, vol. 111, No 1, p. 209-224. ISSN 0935-3518.
  19. BLAŽEK, Václav. "Indo-European "nine"". In: Historische Sprachforschung. Göttingen: Vanderhoeck & Ruprecht, 1999. vol. 112, No 2, p. 188-390. ISSN 0935-3518.
  20. "This numeral ... is obviously derived from the word for "nine". (...) The etymological connection with PIE *newn ... is evident ...". Eichner, Heiner. "Anatolian". In: Gvozdanovic, Jadranka (ed.). Indo-European numerals. Trends in linguistics: Studies and monographs n. 57. Berlin; New York: Mouton de Gruyter. 1991. p. 87. ISBN 3-11-011322-8
  21. BLAŽEK, Václav. "Indo-European "ten"". In: Bygone voices reconstructed. On language origins and their relationships: In honor of Aharon Dolgopolski. Ed. by Vitalij V. Shevoroshkin & Harald U. Sverdrup. Copenhagen: Underskoven Publishers ApS, 2009. pp. 113-123. ISBN 978-87-91947-33-9.
  22. BLAŽEK, Václav. "Indo-European "hundred"". In: History of Language. Melbourne: Association for the History of Language, 1999, 5.2, No 2, p. 71-82. ISSN 1441-5542.
  23. Douglas Q. Adams, A Dictionary of Tocharian B, 2nd ed., 2013, ISBN 9401209367 s.v. yaltse
  24. Fortson (2004:120)

References

Further reading

  • Bammesberg, Alfred (1995). “Latin quattuor and Its Prehistory”. In: Journal of Indo-European Studies (JIES) 23 (1-2): 213-222.
  • Beekes, Robert S. P. (1987). “The Word for ‘Four’ in Proto-Indo-European”. In: Journal of Indo-European Studies (JIES) 15 (1/2): 215-219.
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