Subject: Re: [HM] Was Euclid trained by a pupil of Plato?
From: Alexander Jones (ajones@chass.utoronto.ca)
Date: Wed Jan 12 2000 - 09:29:35 EST
> I have a question. There is a brief discussion of the School of
> Alexandria at this URL:
>
> http://www.drury.edu/faculty/ess/philsci/Alexandria1.html
>
> A reference for the page is given:
>
> A Short History of Scientific Ideas to 1900 by Charles Singer (Oxford:
> Clarendon Press, 1959)
>
> An excerpt is:
>
> "Among the first to be called to the Alexandrian Academy was
> Euclid (ca. 330 - 260). Euclid was trained in Athens, PROBABLY
> [my caps] by a pupil of Plato."
>
> Do math historians generally agree about this?
>
> Ralph Gainey
No. Nothing in Singer's notice is well established; in fact we really don't
*know* anything about Euclid except that he is earlier than, or conceivably
contemporary with, Apollonius (active about 200 B.C.) since Apollonius
cites his work on the "locus on three and four lines" in the preface to the
conics. Pappus alleges in Collection Book 7 that Apollonius studied with
Euclid's pupils in Alexandria. Whether he had good authority in this, or
(as I suspect) guessed it from Apollonius' remarks, this is the only
testimony explicitly linking Euclid to Alexandria, and it doesn't actually
say that Euclid himself worked there.
Proclus has three things to say about Euclid in the second introduction to
his commentary on Elements Book I. First, that Euclid "came not long after"
a number of mathematical writers connected with the Academy, including
Philip of Mende (who is usually assumed to be the same as Philip of Opus,
who edited Plato's Laws after Plato's death). Secondly, that he was a
contemporary of Ptolemy I. Thirdly, that Euclid belonged to the Platonic
sect. The explicit bases of these assertions are:
1. Euclid's Elements brings together, systematizes, and tightens the
contributions of the people that Proclus says were his predecessors
(Proclus names Theaetetus and Eudoxus).
2. Archimedes, who lived after Ptolemy I's time, mentions Euclid; and there
is an anecdote [the "royal road" one] involving a conversation between
Euclid and Ptolemy I.
3. The Elements leads up to the construction of the "Platonic" figures in
Book 13.
It goes without saying that argument 3 is worthless. As for argument 2, the
works of Archimedes as we have them (i.e. with some losses, and undoubted
revisions and textual damage) only mention Euclid once, in a cross
reference that could very easily be a later insertion. Proclus might have
had something more solid than this in an Archimedean writing that hasn't
come down to us, but we can't be sure of that. The anecdote is scarcely
admissible evidence.
Alexander Jones
Graduate Coordinator and Associate Chair
Department of Classics, University of Toronto
97 St George Street, Toronto, ON M5S 2E8 Canada
tel. (416) 978-0483
fax (416) 978-7307
http://www.chass.utoronto.ca/~ajones
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