Subject: Re: [HM] Euclid and the unique factorization theorem
From: Christian Marinus Taisbak (marinus@private.dk)
Date: Fri Feb 04 2000 - 13:58:26 EST
Could Euclid have stated the prime factorization theorem ?
In my book "Division and Logos" (Odense University Press, 1971), p. 109
I made up a formulation which Euclid *could* have used, in two parts:
1) Any number is the least that is measured by some numbers, each of
which belongs to a "continui ab unitate" (apo monados hexes analogon
cf Elements ix.8 ff) characterized by a prime number.
2) If a number is the least that is measured by some numbers, each of
which belongs to a "continui ab unitate" characterized by a prime
number, then it will not be measured by any greater member of those
"continui ab unitate", 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.
In the proceedings (forthcoming ?) from the Liverpool conference
(1996 July 12 ..) I treated this matter again.
Marinus, at Varronian point 8 (Aquarii 15).
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