Renaissance: Series of problems asvarietas

Abstract

In the present paper I wish to discuss three texts published by two mathematical authors, Oronce Fine and his student Jean Borrel. These three texts are typical of the time and are examples of the transformation occurring in the genres of mathematical books. This had direct consequences on the ways and the purpose of presenting series of problems followed by further mathematical authors. Oronce Fine's contribution has been to present commercial problems as Euclidean problems on proportions, as well as to replace the university quadrivium by four practical disciplines: practical arithmetic, practical geometry, cosmography, sundials. The two books by his disciple Borrel reflect the view on mathematics promoted by Oronce Fine: we can recognize mathematics in every aspect of the world. Borrel is also very concerned with distinctions in the human world: variety in the Opera geometrica and in the Logistica corresponds to redefinition of professional roles according to Fine's program. In particular, Borrel wants to stress the role of a new category of mathematicians, specialized in the practical disciplines Fine taught at the College Royal, the g eometers. They dealt with practical problems by using classical humanistic education and practical mathematics, exactly what jurists did: Through the crucial rhetorical notion of varietas he is able to illustrate, in the Opera geometrica, the multifarious mathematical competence required for jurists. Among geometers, Borrel distinguishes a group of people, the logisticians, dealing in particular with the computational side. The readership of his Logistica was also, by and large, constituted by jurists. In fact many jurists were logisticians or needed competence in this art, and many logisticians had a training in law. The texts by the two authors examined here show a use of series of problems as varieties at two levels: the level of the presentation of examples for a rule, mostly in the main part of the text, and the level of a list of cases at the end on the book.