On Mon, 26 Jun 2000, Amaya García Pérez wrote:
> I would like to find more information about
> the "mesolabium", the device used in the Renaissance
> to find more than one mean-proportionals between two
> string lengths.
>
The mesolabium is mentioned on four accasions in Salinas's _De musica_ 3,
where the invention is attributed to Archimedes. Actually, it has a more
venerable history than that, pertaining to the problem of the duplication
of the cube, which is described in Vitruvius's _De architectura_, Book IX,
pr. 14, as having been solved by Archytas (by a cylindrical diagram) and
by Eratosthenes "by means of the mesolabium," a diagram of which appears
as Plate K in Granger's translation for the Loeb Classical Library. A full
discussion of the mathematics (together with numerous diagrams) may be
found in Sir Thomas Heath's _History of Greek Mathematics_, vol. 1, pp.
244-70.
I hope this information will be of assistance.
Sincerely yours,
Thomas J. Mathiesen
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