Warning! The translation of Viete that you are using is not always
reliable, and there is a reliable translation in the doctoral thesis of
Richard Ferrier
Thomas Aquinas College
10000 N. Ojai Road
Santa Paula, CA 93060
Fax 805-525-4417
e-mail: 75402.1336@compuserve.com
2nd Warning! We will be in Berkeley -- Emily & I -- towards the end of
October. Perhaps we can have a luncheon chat. Invite Martin Davis. If
all else fails, and I don't think it will, I can bring the translation
from our library.
Best wishes from Annapolis,
Sam Kutler
>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