[HM] Euclid and the unique factorization theorem

Christian Marinus Taisbak (marinus@private.dk)
Fri, 17 Dec 1999 20:17:27 +0100

I have treated the subject "Euclid and The unique factorization theorem"
in a talk at the Liverpool conference "Science Matters" July 8-12 1996,
the proceedings of which must be about to appear, to believe professor
C.J. Tuplin.

In my dissertation "Division and Logos" (Odense University Press, 1971,
Odense, Denmark), p. 109, I helped Euclid to a formulation of the theorem,
using the concept (treated at length in Elements IX) apo monados arithmoi
hexes analogon, --- in my terminology "continui ab unitate":

Any number is the least that is measured by some numbers, each of which
belongs to a "continui ab unitate" characterized by a prime number. And
it will not be measured by any other number belonging to any "continui ab
unitate" characterized by a prime number which is different from the
original primes.

(It is worth while to compare this wording with that of IX.14, on which it
is modelled.)

Greetings from stormy Copenhagen

Christian Marinus Taisbak <marinus@private.dk>
Mathematical Sciences in Antiquity
Copenhagen University, Institute for Greek & Latin