The legitimation of geometrical procedures before 1590

Abstract

Sixteenth- and seventeenth-century mathematicians were not the first to struggle with the interpretation of exactness of geometrical constructions; also in the classical Greek period there existed a rich variety of constructional procedures and many opinions on their acceptability. It appears that these opinions never converged to a clear communis opinio. This lack of uniformity and the relative scarcity of sources meant that sixteenth-century mathematicians had no clear classical examples in developing their ideas about the exactness of geometrical constructions. Therefore, it is not necessary to survey the classical ideas on the legitimacy of constructions here; rather I can restrict myself to dealing with those few classical sources that actually influenced the early modern debates. Besides, and fortunately, I can refer to an excellent recent study on the classical tradition of geometrical problem solving, Wilbur Knorr’s The ancient tradition of geometric problems.₁

Knorr 1986