[HM] A question about angle trisection

Robin Hartshorne (robin@math.berkeley.edu)
Sun, 6 Sep 1998 19:43:50 -0700 (PDT)

I have been reading The Analytic Art by F. Viete, English translation
by T. R. Witmer (1983). In the translator's introduction, p. 7, the
traslater suggests that the results that Viete may be most proud of
are his trisection of the angle, finding two or more proportionals,
constructing the heptagon, and others. He points to the end of Viete's
"Introduction to the analytic art" where Viete himself says that with
his art now he can solve these problems.

The trisection that Viete gives in " A Supplement to goemetry"
Prop. IX is almost identical to the one that Archimedes gives in his
book of lemmata, and I have seen the same construction also referred
to the mathematical collection of Pappus, though I did not verify the
reference myself.

So my question is, is it possible that Viete was unaware of these
sources and thought that he had discovered this construction himself?
Otherwise why whould he be so proud of it?

By the way, I suppose the construction of the heptagon is original
to Viete, and that he has sufficient reason to be proud of that one.

Greetings from Berkeley

Robin Hartshorne