[snip]
> What I would like to know is what the situation is at the moment: Is
> Greshon considered to be the first discoverer or do people disagree?
> Are there any new articles that I might consult about this?
>
In Vol 22, No 4, 1995 of the Aust. Math. Soc. Gazette, Hussein Tahir
draws attention to an explicit use of mathematical induction in Pappus'
Collection, Book 4, on the arbelos. Pappus computes the relationship
between the diameters and distances above the baseline of each of an
infinite chain of circles, each tangent to the next, inscribed in the
arbelos. In modern notation, let the n-th circle have diameter d_n and
have centre h_n above the baseline. Pappus result is that h_n=nd_n.
According to Tahir, Pappus quotes Archimedes, Book of Lemmas,
Proposition 6 for the case n=1; then he showed that if the statement
is true for for n-1, then it is true for n. The Reference is to Pappus,
'La Collection Math/ematique', translated by Paul Ver Eeke, Paris:
Albert Blanchard, 1933.
__________________________________________
Associate Professor Phill Schultz
Director of Postgraduate Studies,
Department of Mathematics and Statistics,
The University of Western Australia,
Nedlands, 6907, Australia
Phone:(08)9380-3381 Fax:(08)9380-1028
e-mail schultz@maths.uwa.edu.au