Subject: [HM] New Archimedes URL
From: Ralph Gainey (sesame@mcn.org)
Date: Tue Jan 04 2000 - 01:24:51 EST
David E. Smith's introduction to Archimedes' treatise "Geometrical
Solutions Derived From Mechanics" [recovered in the Palimpsest] is
now available:
http://www.mcn.org/2/sesame/archimedes.html
He discusses in detail the contents of the treatise, and concludes
by saying, "In general, therefore, the greatest value of the work
lies in the following:
1. It throws light upon the hitherto only suspected relations of
Archimedes and Eratosthenes.
2. It shows the working of the mind of Archimedes in the discovery
of mathematical truths, showing that he often obtained his results
by intuition or even by measurement, rather than by an analytic
form of reasoning, verifying these results later by strict analysis.
3. It expresses definitely the fact that Archimedes was the discoverer
of those properties relating to the sphere and cylinder that have
been attributed to him and that are given in his other works without
a definite statement of their authorship.
4. It shows that Archimedes was the first to state the volume of the
cylinder segment mentioned, and it gives an interesting description
of the mechanical method by which he arrived at his result."
RLG
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