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Re: Types of numerals

From:tomhchappell <tomhchappell@...>
Date:Tuesday, January 17, 2006, 16:29
--- In conlang@yahoogroups.com, R A Brown <ray@C...> wrote:
> Tom Chappell wrote: >> --- In conlang@yahoogroups.com, John Vertical > [snip] >>>That there are no primitive non-cardinals >>>relating to numbers other than 1 or 2. >> But I think there are, though they may be rare. >> What about English "quarter"? > English "half" is surely a better example.
John was asking for words related to numbers other than 1 or 2.
> English "quarter" is derived through Old French from > Latin 'quartarius' = "a fourth part", which in turn is derived from > the ordinal 'quartus'. So I don't think "quarter" is a 'primitive'.
Clearly, diachronically speaking, "quarter" is derived, as you detailed. But, synchronically speaking, "quarter" is not derived from any modern English word; (in particular, not from "four" or "fourth"); and that is what I meant.
> Most languages seem to have a word for 1/2 which is not related to > their word for 2.
I think we suspected as much.
> But 1/4 seems generally (always?) to be derived from a word for 4,
Interesting. I didn't know that.
> either in the language itself
(English is not an example)
> or, as in English, from another language.
Yes, English is an example of this. I imagine many of us suspected it, but I (for one) didn't know the details until you wrote them in. Thank you.
>> What about the Ancient Egyptian words for "2/3" and "1/3", >> whatever they were? (Does someone know? > AFAIK there were not separate root words for these. > You may be thinking of the fact that
You are, clearly, correct about the source of my mistake.
> in writing fractions were expressed as sums of "unit fractions" > (reciprocals) (1/n).
I knew that; I think this was in "the Giant Golden Book of Mathematics" I got when I was eight or so.
> My understanding is that the unit fractions were expressed by the > symbol _r_ (which, inter alia, was the word for "part" - (the > Egyptians only expressed consonants, never vowels) - followed by > the numeral. So 1/3 would be: rIII.
I didn't know that. Thanks for telling me.
> To do more complicated fractions you just added unit fractions, so > for example, 2/5 would be expressed by; rIII rXIIIII (1/3 + 1/15).
I knew about the (1/3 + 1/15), but didn't know about the "rIII rXV".
> (I've used the familiar Roman symbols for 10 & 1 instead of the > Egyptian symbols).
Can we even type in hieroglyphs and/or hieratic and/or demotic script?
> There was, however, a symbol for 2/3 -
Yes, I knew that; and that was the source of my error.
> - but it wasn't a 'primitive'.
I didn't know that. Thanks for telling me.
> It was the symbol for _r_ (which was a stylized mouth, as the word > for mouth was also _r_), with two small vertical lines beneath > signifying the _dual ending_. In other words, it was the dual of > the word for "part", i.e. 'two parts'. But it came to have the > specialized meaning of "two parts (of three)", i.e. 2/3. It is read > as _rwjj_ (IPA values) or _rwy_, depending upon the transliteration > system used.
I didn't know _any_ of that. Thanks for telling me; I'm glad I know now.
>>>> "Two-thirds" was indeed "lexicalized" in Ancient >>>> Egyptian, so I've read; > No - a specialized meaning given to the dual of the lexical word for > "part" - see above.
Yes, I see now.
> On the other hand, Classical Latin did have a lexeme meaning 2/3 - > it was the masculine noun _bes_ (genitive: _bessis_ )
Yes, a previous poster gave a URL which tells the Latin lexemes for each of 1/12, 1/6, 1/4, 1/3, 5/12, 1/2, 7/12, 2/3, 3/4, 5/6, 11/12; as well as, IIRC, 1/144, 1/72, 1/48, 1/36, 1/24.
>>>> and I wager "three-fourths" is lexicalized in >>>> some natlangs, as well. > You mean, like the Latin _dodrans_ (gen. _dodrantis_)
Yes, indeed. Thanks.
>> Does anyone know for sure? > I know that one for sure :-)
Thanks, Ray. Tom H.C. in MI