Date: Wed, 1 Feb 1995 20:32:38 -0500
From: [Permission pending]
To: rusin@math.niu.edu
Subject: Re: Bezout's Theorem

Thanks for your comment on my Bezout post.

I should have said Bezout's Lemma in the first place or maybe
Bezout's Identity. Both of which I have actually seen in print.

As several responders mentioned, Bezout's Theorem is a well-known
result in algebraic geometry, namely,


``If two projective curves C and D in P_2 of degrees m and n have no
  common component, then they have precisely mn points of intersection
  counting multiplicities.''

However Dipankar wrote:

See, for example, Kirwan ``Complex Algebraic Curves'' LMSST #23,
Cambridge (chap 3).  Kirwan notes that the reason for associating
B{\'e}zout's name to the theorem ``is not entirely clear, since
although B{\'e}zout gave a proof of the theorem, it was neither
correct nor the first proof to be given''.

The following is another response of some interest. At least it
tells something about Bezout:

I have read in some place, that in fact, the lemma you mention, has been
brought
to the attention of mathematicians
by " Bachet de Meziriac"  contemporary of Fermat, Pascal.... and
known above all by his book "Problemes plaisans (sic) et delectables", title
easy to translate. That book is a collection of nice problems in arithmetic,
wri
tten for
amusement. In that time, there was no TV...
 Perhaps, B d M has learnt the lemma from Diophante (?).
But, by tradition,  the lemma in question is said "de Bezout".
Bezout, French mathematician  lived during the 19th century.
Fans of the history of mathematics may give more informations....
--
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* Yvon SIRET                                                       *
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I also found reference in at least one place to the fact that
an integral domain in which every finitely generated ideal is
principle is called a Bezout ring.

[sig deleted]