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The Project Gutenberg EBook of Geometrical Solutions Derived from Mechanics
by Archimedes
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Title: Geometrical Solutions Derived from Mechanics
A Treatise of Archimedes
Author: Archimedes
Release Date: April, 2005 [EBook #7825]
[Yes, we are more than one year ahead of schedule]
[This file was first posted on May 20, 2003]
Edition: 10
Language: English
Character set encoding: ASCII
*** START OF THE PROJECT GUTENBERG EBOOK GEOMETRICAL SOLUTIONS ***
Gordon Keener
% gbn0305181551: Archimedes, Geometrical Solutions Derived from Mechanics. Gordon Keener <gkeener@nc.rr.com>. 1909c. 5/19/2003. ok.
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\usepackage[greek,english]{babel}
\usepackage{wrapfig}
\usepackage{graphicx}
\title{Geometrical Solutions Derived from Mechanics}
\author{A Treatise of Archimedes}
\date{\vspace{\baselineskip}
{\small Recently discovered and translated from the Greek
by}\\ Dr. J. L. Heiberg\\ {\small Professor of Classical Philology at
the University of Copenhagen}\\
\vspace{\baselineskip} {\small with an introduction by}\\ David Eugene
Smith\\ {\small President of Teachers College, Columbia University, New York}\\
\vspace{\baselineskip}
{\small English version translated from the German by}\\ Lydia
G. Robinson\\ {\small and reprinted from ``The Monist,'' April,
1909}\\
\vspace{\baselineskip}
{\small Project Gutenberg edition:\\
gbn0305181551: Archimedes, Geometrical Solutions Derived from Mechanics.
Gordon Keener $<$gkeener@nc.rr.com$>$. 1909c. 5/19/2003. ok.}
}
\begin{document}
\maketitle
\vfill\pagebreak
\section*{Introduction}
If there ever was a case of appropriateness in discovery, the finding
of this manuscript in the summer of 1906 was one. In the first place
it was appropriate that the discovery should be made in
Constantinople, since it was here that the West received its first
manuscripts of the other extant works, nine in number, of the great
Syracusan. It was furthermore appropriate that the discovery should be
made by Professor Heiberg, \emph{facilis princeps} among all workers
in the field of editing the classics of Greek mathematics, and an
indefatigable searcher of the libraries of Europe for manuscripts to
aid him in perfecting his labors. And finally it was most appropriate
that this work should appear at a time when the affiliation of pure
and applied mathematics is becoming so generally recognized all over
the world. We are sometimes led to feel, in considering isolated
cases, that the great contributors of the past have worked in the
field of pure mathematics alone, and the saying of Plutarch that
Archimedes felt that ``every kind of art connected with daily needs
was ignoble and vulgar''\footnote{Marcellus, 17.} may have
strengthened this feeling. It therefore assists us in properly
orientating ourselves to read another treatise from the greatest
mathematician of antiquity that sets clearly before us his
indebtedness to the mechanical applications of his subject.
Not the least interesting of the passages in the manuscript is the
first line, the greeting to Eratosthenes. It is well known, on the
testimony of Diodoros his countryman, that Archimedes studied in
Alexandria, and the latter frequently makes mention of Konon of Samos
whom he knew there, probably as a teacher, and to whom he was indebted
for the suggestion of the spiral that bears his name. It is also
related, this time by Proclos, that Eratosthenes was a contemporary of
Archimedes, and if the testimony of so late a writer as Tzetzes, who
lived in the twelfth century, may be taken as valid, the former was
eleven years the junior of the great Sicilian. Until now, however, we
have had nothing definite to show that the two were ever
acquainted. The great Alexandrian savant,---poet, geographer,
arithmetician,---affectionately called by the students Pentathlos, the
champion in five sports,\footnote{His nickname of \emph{Beta} is well
known, possibly because his lecture room was number 2.} selected by
Ptolemy Euergetes to succeed his master, Kallimachos the poet, as head
of the great Library,---this man, the most renowned of his time in
Alexandria, could hardly have been a teacher of Archimedes, nor yet
the fellow student of one who was so much his senior. It is more
probable that they were friends in the later days when Archimedes was
received as a savant rather than as a learner, and this is borne out
by the statement at the close of proposition I which refers to one of
his earlier works, showing that this particular treatise was a late
one. This reference being to one of the two works dedicated to
Dositheos of Kolonos,\footnote{We know little of his works, none of
which are extant. Geminos and Ptolemy refer to certain observations
made by him in 200 B. C., twelve years after the death of
Archimedes. Pliny also mentions him.} and one of these (\emph{De
lineis spiralibus}) referring to an earlier treatise sent to
Konon,\footnote{\selectlanguage{greek} T\~wn pot\`i K\'onwna
\'apustal\'entwn jewrhm\'atwn.} we are led to believe that this was
one of the latest works of Archimedes and that Eratosthenes was a
friend of his mature years, although one of long standing. The
statement that the preliminary propositions were sent ``some time
ago'' bears out this idea of a considerable duration of friendship,
and the idea that more or less correspondence had resulted from this
communication may be inferred by the statement that he saw, as he had
previously said, that Eratosthenes was ``a capable scholar and a
prominent teacher of philosophy,'' and also that he understood ``how
to value a mathematical method of investigation when the opportunity
offered.'' We have, then, new light upon the relations between these
two men, the leaders among the learned of their day.
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