Re: [HM] Esimo

Arturo Mena (amena@ucv.cl)
Mon, 26 Apr 1999 23:23:35 -0500

Prof. Lueneburg wrote:
>
> In Tartaglia's writings and also in Bombelli's "Algebra", I find
> the suffix "esimo" used as a word of its own meaning the denominator
> of a fraction. Nunes in his "Libro de Algebra en Arithmetica y
> Geometria" which is written in Spanish also uses esimo (also written
> essimo) in that sense. My question is: Is esimo still used in that
> sense in Italian, Spanish (or Portugese)? If not, when was it given up?
>
> Another question in that context. In former times, the words "frazione"
> and "rotto" were both used to mean fraction in Italian. As I was told
> by Italian colleagues, the word rotto is not used any more in that
> sense. When was this usage given up?
>

In Spanish, as far as I know, the answer is almost the same given by Romulo
Lins:

"esimo" and "ecimo" are used (with a marked accent on "e", each time the
stress is made on the third syllab counting backwards. I'll use a ' ))

un de'cimo= one tenth
un vige'simo = one twentieth (of)

cente'simo = 100th
mile'sino
diezmile'simo...
millone'simo
and so on for powers of 10.

For other fractions we use 'avos':

'un doceavo' = 1/12.

Fractions up (down!) to 1/9 have special names:

1/2 = un medio
1/3 = un tercio
1/4 = un cuarto
1/5 = un quinto
1/6 = un sexto
1/7 = un se'ptimo
1/8 = un octavo
1/9 = un noveno

Note that the same words are used as ordinals: second, third, etc. In
that case, you may use the word "nono" for "noveno"- but seldom do.

Then we have the common latin roots for ordinals:
the tenth: el de'cimo
the eleventh: el unde'cimo, el de'cimo primero
the 12th : el duode'cimo, el de'cimo segundo
the 13th: el de'cimo tercero
the 20th: el vige'simo
the 34th: el trige'simo,
then cuadrage'simo, quincuage'simo, sexage'simo, septuage'simo, octage'simo,
nonage'simo, cente'simo.

If referring to money, avos is also used, depending on the country and the
currency: some use, for instance, "centavos", in Chile we have had "centavos"
and "cente'simos" - at different times.

In any case, we use, for instance, "vige'simo", mainly when referrinfg to
lottery games (the same number is sold in twenty pieces).
In common speech, people tend to use "avos" instead of the more elaborated
latin expressions; for instance, one prefer to say "el onceavo" instead of
"el unde'cimo", to express "the eleventh"; "el treintaicincoavo" instead
of "el trige'simo quinto").
Roots like "sesqui" are still present in Spanish; but , as far as I know,
you don't really use them (I have used them in my Linear Algebra class -
for "sesquilinear" (sesquilineal, in Spanish) and when my country
celebrated 150 years of independence).

I believe that with other roots tha situation is similar in other languages.
For instance, we alternate between the greek "bi" (as in "bilingu~e", that
is, bilingual) and the latin "di" (as in "dia'logo", i.e., dialogue).

Every math teacher or instructor uses the word "ene'simo" ("n-e'simo").

For fractions, we use "fraccio'n". Interestingly enough, the word
"quebrado", that was used up to the sixties, is vanishing in this area
as a subproduct, I believe, of the changing of Secondary Curricula in
Math. (In any case, the latin word "fractura", means, precisely, "quebrar",
that is, to break.
What is even more interesting is that, in former times, that is what an
algebraist was suppose to mend: according to Don Quixote, an algebraist
took care of the broken arm or leg of, if memory serves, a "bachiller
Piero Sa'nchez").

-From frankly not-rainy Chile

Arturo Mena