Algorithm and Demonstration in the Sixteenth-Century Ars Magna

Abstract

This chapter is a study of the use of algorithms, by sixteenth-century French and Italian algebraists, to persuade and to prove. It argues that practitioners of the ars magna saw the generality and persuasiveness of demonstrations in the repeatability of procedures. The crucial locus of persuasion was the worked example, which played a key role in both arithmetical and geometrical demonstration in the mid-sixteenth century. Discussing examples from Girolamo Cardano, Guillaume Gosselin, and Simon Stevin, the chapter shows how mathematicians of the late sixteenth century assimilated algorithms to regnant literary forms of geometrical demonstration so that worked examples could take the argumentative place of diagrams. François Viète, in turn, employed the range of persuasive techniques offered by his predecessors.