Re: [HM] Re: porisms
Claire Czinczenheim (c.czinczenheim@mail.ac-lille.fr)
Thu, 28 Jan 1999 16:12:21 +0100
I think I missed your first message, but here is what I know about
porisms:
It is used in medieval Greek manuscripts, usually in marginalia, to
indicate a corollary following a theorem.
There is a Lost Book of Porisms, by Euclid, which Chasles tried to
reconstruct last century, following definitions and explanations given
by Pappus: it is something intermediate between problem and theorem,
where you do not have only to construct an object, but also to exhibit
it. That has caused many to wonder about the meaning of the word. The
best source is Heath's Thirteen Books of Euclid's Elements (Dover),
volume I, introduction. Ian Mueller (Philosophy of Mathematics and
Deductive Structure in Euclid's Elements) thinks that the problem: to
find the center of a circle (III 1) is what the Greeks called a porism,
because you do not construct, you look for something that was defined
before. And I think he points to two other such places in the Elements.
I would be glad to follow the discussion on this subject.
Claire Czinczenheim
----------
> De : Jim Propp <propp@math.mit.edu>
> A : historia-matematica@chasque.apc.org
> Objet : [HM] Re: porisms
> Date : mercredi 27 janvier 1999 23:45
>
> While we're on the subject: Where can I learn what a "diorism" is?
>
> Thanks,
>
> Jim Propp
> Department of Mathematics
> University of Wisconsin