FOM: Conics

Alasdair Urquhart urquhart at
Thu Mar 1 14:10:02 EST 2001

The proposition about tangents to an ellipse is proved
by Apollonius (fl. 247-222 BC) in his Conics, Book III, Proposition 48
(reference in Heath's History of Greek Mathematics,
Volume 2, p. 157).  Heath says earlier in his history that
the elementary propositions proved by Apollonius in his
Books I to IV were well known, so the proposition on
tangents was very likely already contained in 
Euclid's lost work on conics.  Pappus said (Heath Vol. II, p. 116)
that Euclid credited Aristaeus with the results on conics that he systematized,
so the answer to the historical question may be "Aristaeus", who seems
to have flourished somewhere between 350 and 300 BC.


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