Subject: Re: [HM] History of the Conics
From: Luigi Borzacchini (gibi@pascal.dm.uniba.it)
Date: Mon Mar 06 2000 - 04:56:45 EST
>
> I'm wondering how Apollonius (or someone else?) first made the
> connection between the shapes--parabola, ellipse, hyperbola--and the
> slicing of a cone to generate those shapes.
> Also, can anyone recommend an informative book on the subject?
> Thanks.
>
Probably it must be ascribed to Menaechmus (mid IV century BC),
because from Eutocius we know how he connected the Delian problem to some
properties (we could call 'analytic') of conics (along two ways, one based
on the parabola and one on the hyperbola).
This means that he was already able to find these properties from the
orthogonal slicing of the cone, and then that the connection you are looking
for was already known.
In the past there has been two hypotheses about the earlier history of
conics theory. The first is that the starting point was the Delian problem.
The second hypothesis considers the discovery an autonomous development of
solid geometry.
I find more convincing the first, because Menaechmus was a disciple of
Eudoxus, and then it had to be well acquainted with Archytas' solution of
the Delian problem, written in terms of the two mean proportionals,so that
the discovery of the conics was on the line of an evolution of Archytas'
solution of this problem.
Luigi Borzacchini
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