Post by Massimo MancaHo un problema a tradurre in italiano un passo di Boezio, cioè il 2,
26 dell'__Institutio arithmetica_. Mi interessa in particolare la
traduzione di _numerus antelongior_. La questione è questa: per numero
eteromeco si intende un numero che è il prodotto di due fattori la cui
differenza è uguale a uno, per esempio quelli appartenenti alla
sequenza 2, 6, 12, 20, 30, 42. heteromekos viene tradotto da Boezio
in latino con una perifrasi "numerus parte altera longior"; gli
antelongiores sono numeri che derivano dal prodotto di fattori la cui
differenza è maggiore di uno, per es. 15=3x5. In greco si dicono
"promeci"; esiste una terminologia matematica moderna per questo
genere di numeri? Ho trovato una traduzione francese "oblong", ma
"oblungo" mi suona così così.
Mah, mi sembra di aver capito che i numeri "oblunghi" in realtà
corrispondano agli eteromechi, non ai promechi (in inglese anche "pronic":
"Pronic numbers are also known as oblong or heteromecic"-CRC Concise
Encyclopedia of Mathematics, pag. 2396).
Io invece ho sottomano una traduzione inglese del passo di Boezio che citavi
[Michael Masi, Boethian Number Theory : a Translation of the De Institutione
Arithmetica (with Introduction and Notes), Amsterdam: Rodopi, 1983] -che,
tra l'altro, talvolta traduce gli eteromechi come "longilateral numbers",
oltre che con la perifrasi "longer by one side"- ma, in questo caso, non è
molto d'aiuto, come puoi leggere:
"27. Concerning »antelongior« numbers and the terminology of the number
longer by one side.
So, if numbers differ by only a unity, when they are multiplied together,
the numbers described above are created, unless you multiply by some other
number, as three times 7 or three times 5 or in some other manner, and their
sides do not differ by only a unity. Then they are not called by the term
longer by one side, but »antelongior.«
By Pythagoras, or by the heirs of his wisdom, they are described with no
other number than by two. They call this the principle of alternity and say
that the same nature always follows identical to itself and becomes no other
except through ungenerated primal unity. The binary number, the first real
number, is different from unity because at first it is separated from it by
a unity. And so this is the principle of alternity because it is dissimilar
from unity, the first and always same substance. Rightly is it said
therefore that these numbers are longer by one side because of the sides of
such a figure which precede each other by a single adjacent numerical value.
There is an argument, however, that alternity may justly be constituted in
the binary number which is said by some persons to be only from two, and
among these persons there is no lack of reason in such argument. But again,
it has been demonstrated that the odd number alone is produced from unity,
and that the even number is produced only by duality, that is by the binary
number. The median of any number is one if it is an odd number: if the
number is even, this equality is divided into equal halves. So it must be
said that of the even numbers there is an odd number participating, and that
if it participates in the immutable substance of its nature, then the even
number is formed from unity and the even number is full of the nature of the
other and because of that, it is completed in duality".
Insomma io fossi in te lascerei "antelongior" oppure, basandomi sulla
terminologia greca, scriverei direttamente promeco.
Un saluto,
Nico