Analysis as Analysis of Figures: The Logic of the Analytical Method

Abstract

Perhaps the most misleading thing about the current discussions of analysis and synthesis in Pappus is that they do not bring out clearly what the analyses of Greek geometers were analyses of. The prominence given to the directional problem in fact encourages a misleading interpretation. It tends to suggest that what is being analysed is the deductive leap from axioms to the theorem to be proved, which is analysed into a sequence of steps of deduction (and analogously for constructions in the case of problematical analysis). We shall call this the propositional interpretation or the analysis-of-proofs view. It is our thesis that although it is possible in principle to look upon the method of analysis in these terms, it embodies a wrong emphasis and is consequently badly misleading as to what the actual practice of Greek geometers was and also as to the terminology they employed.