Geometric Algebra
"Geometric Algebra" is the term introduced by the historian H. Zeuthen in
1886 (Geschichte der Mathematik im Altertum und Mittelaiter, Ch 4, and
Lehre von den Kegelschnitten, 1886, Ch 1) to describe the type of algebra-like identities developed in Book II of Euclid, in the technique of
application of areas, and in the second-order relations of the conics. [Katz,
p. 64 says Book II, I.43-45, and VI.27-30.] This term, and the underlying
hypothesis, has been generally accepted by historians of mathematics.
Recently the case against geometric algebra has flared into a controversy
among historians. It is quite instructive to read the papers on this topic
and to try to form your opinion about the issues. While doing so you will
learn that scholars can be deeply divided about the proper interpretation
of the same text.
Here are a few references to get you going:
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Wilbur
Knorr, The Ancient Tradition of Geometric Problems (1986), pp. 203-204.
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S. Unguru, "History of ancient mathematics: Some reflections on the
state of the art," Isis, 70(1979), 555-565, for a survey of the argument.
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If you have comments, send email to V. Frederick Rickey at
fred-rickey@usma.edu .