Dear Mary Catherine,
I suppose you already know the greatest work about mathematical
discovery, "The method" (included in the famous "rediscovered"
palimpsest), where Archimedes exposes his way to the finding of 15 of
his theorems. Van der Waerden in "Einfall und Ueberlegung" discusses
one of them: the volume of the sphere. You have also a short
discussion on Archimedes' method in Polya's "Mathematics and
plausible reasoning". You may find interesting to have a look at the
VIIth book of Pappus' "Mathematical collection", devoted to clarify
the so called "mysterious method of Greek geometers". "The method of
analysis" by Hintikka and Remes discusses genially this topic. There
is also an article about it in Thomas Nickles (ed.) "Scientific
discovery, logic, and rationality": Peggy Marchi's "The method of
analysis in mathematics".
Saludos a todos desde Sevilla en mi primera salida al forum
(especialmente a mi apreciado amigo el profesor Ubiratan D'Ambrosio).
M.Carmen Hernandez-Martin
Facultad de Filosofia
Universidad de Sevilla
Espan~a