> I am a high school math teacher with a historical question. Bill Dunham >suggested I ask you. Why in both the Romance and Germanic languages are >eleven and twelve so different from the rest of the teens, and why is >fifteen in the Romance languages different from the rest of the teens?
Eves suggest the origin of words like eleven and twelve likely goes back to the use of a number base other than 10 (here, perhaps 12 or 20). The same may be true of Romance words for the lower teens, though they do not all change at the same point. In French, e.g., we have seize (16) but dix-sept (17). The latter is surely a base ten name; what of the former? The Romance languages (at least French) also use a few words suggestive of a base twenty system. The French word for twenty (vingt) is clearly not a two-tens word, though thirty (trente), forty (quarante) and fifty (cinquante) probably are base ten. Sixty is also, but 70 is rendered as sixty-ten (soixante-dix), 71 as sixty-eleven. Eighty is not eight-tens, but four-twenties (quatre-vingt).
Check the first chapter of Howard Eves, _An Introduction to the History of Mathematics_, for this and some other interesting stuff on number names.
Doug Hale UT Permian Basin email@example.com