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The Latin cardinal numbers starting at ten are decem, undecim, duodecim… Does the -decim (roughly "-teen") come from decem or from the same root? (I faintly recall decem and δέκα coming from something like *dekm.) It seems very plausible for semantic reasons and similarity, but I would like to understand the situation better. Can someone explain the relation between decem and -decim? Assuming they have a common origin, why does one have E and the other I? Is this case exceptional? Are there similar vowel changes in Latin that would help understand this case by analogy? I can't think of any such vowel changes in the last syllable, or even a short E becoming a short I, so I am really short of other similar examples. Are there attested spelling variants like duodecem that might shed light on the issue?

  • Maybe the same kind of apophony that gave us -cidere from cadere when a preverb is attached? Although it seemed to leave short e unchanged: cfr. perlegere, subvenire... – giobrach Aug 30 '17 at 17:17
  • @giobrach Possibly. Weakening of a stem vowel before a prefix is not unusual, but I failed to locate more analogous cases (short E to short I, or in the last syllable). I do think this is a part of the same general phenomenon, but I don't see enough context to put it in. – Joonas Ilmavirta Aug 30 '17 at 17:35
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    The i seems more common: ūndecim, duodecim, but also decimus; the latter is also attested with u > decumanus. – Draconis Sep 1 '17 at 0:40
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It might be a type of metathesis: *undecem > *undicem > undecim. This is apparently irregular, but metathesis often is. I don't know for sure, but I was able to find a source that suggests this, although it indicates that we don't have any attestation of the pre-metathesis form *undicem:

12.1.11.1. In Latin 'eleven' to 'seventeen' are all indeclinable compounds of 'one', 'two', etc. and 'ten', which appears as -decim. By normal vowel weakening *-decem > *-dicem, cf. auspicem < *auispecem acc. sg. to auspex. The metathesis must have been due to the combined pressure of decem and the ordinals, viz. decimus : decem :: undecimus : undecim in place of *undicimus : *undicem

(Robert Coleman, 1992. "Italic", Chapter 12 of Indo-European Numerals, p. 396-397, edited by Jadranka Gvozdanovic)

Coleman seems to indicate that the dating of this hypothesized change from *undicem > undecim is a bit unclear.

  • Metathesis never crossed my mind, but it makes sense. To me decem > dicem > decim sounds more plausible than a direct decem > decim. – Joonas Ilmavirta Sep 3 '17 at 10:16
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De Vaan writes, s.v. "decem":

In -decim, the i is not well explained. It is often believed to be due to a metathesis of *-dicem > *-decim, but a metathesis of two vowels is extremely rare in IE languages, and hence unlikely. The numerals in decim probably have -dec- from decern 'ten' and -im on the model of the ordinal numbers in -decimus. The ordinal *dekamo- yields decumo- or decimo-, and from it, decumanus is derived.

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