Subject: Re: [HM] Pythagorean Theorem
From: Avinoam Mann (MANN@vms.huji.ac.il)
Date: Tue Mar 07 2000 - 18:57:54 EST
On Wed, 8 Mar 2000, Mike Kallaher wrote:
> Recently, there have been several questions regarding the first
> mention of a particular term. In my geometry class yesterday, one student
> asked:When was the Pythagorean Theorem first called the Pythagorean
> Theorem?
> Does anyone have an answer?
>
> Mike Kallaher
>
Proclus writes: 'If we listen to those who like to record antiquities, we
shall find them attributing this theorem to Pythagoras and saying that he
sacrificed an ox on its discovery. For my part, though I marvel at those
who first noted the truth of this theorem, I admire more the author of
the _Elements_, not only for the very lucid proof by which he made it
fast, but also because in the sixth book he laid hold of a theorem even
more general than this and secured it by irrefutable scientific
arguments'. (Morrow's edition, pp.337-8.)
Thus, at the 5th century that theorem was attributed to Pythagoras, so
probably was called at least occasionally Pythagoras' Theorem. Moreover,
it's usually assumed that by 'those who like...', Proclus refers to
Eudemus, 4th century BC. So the attribution is very early. Though
Proclus' source may be later than Eudemus, earlier he refers to 'Eudemus
and his school' (p. 332).
The way that Proclus writes, one gets the impression that he was not
convinced that that attribution is correct. He also seems to imply that
the proof in the _Elements_ is Euclid's own, and that the pre-Euclidean
proofs were not completely satisfactory.
A recent message in this forum, answering my query about 'Oliver Byrne's
proof', suggests that not everybody found Euclid's proof as lucid as
Proclus did. I certainly did not the first time I saw it, in high school,
it was the first proof of that theorem that I've seen.
Avinoam Mann
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