THE RENAISSANCE

Regiomontanus's comments on the utility of mathematics provide more insight into his understanding of the discipline. He begins conventionally enough, listing, by way of claiming that he neglects to mention them, those practical pursuits to which mathematics is important, including architecture, commerce, and military matters.48 Emphasis on practical utility was generally characteristic of those Italian humanists who considered mathematics in a positive light. Andrea Brenta, for example, focuses on Archimedes's ability to delay the overrunning of Syracuse by Marcus Marcellus's troops (a story told by Valerius Maximus).49 Aeneas Silvius Piccolomini, in his The Education of Boys, also relates that story, along with accounts of generals whose knowledge of eclipses allowed them to soothe their soldiers' terror during those unsettling events.50

Regiomontanus, however, quickly moves on to a more specific kind of utility: understanding the Aristotelian corpus. For example, "I think there is no one who is able to learn the seventh [book] of the Physics without [End Page 57] understanding proportions."51 According to Regiomontanus, important sections of De caelo et mundo, the Meteora, the Physics, and the Metaphysics all require that the reader be fluent with mathematics. The idea that a grounding in mathematics was necessary for the study of philosophy was one propounded by a number of Byzantine educators, particularly John Argyropoulos, who probably taught mathematics in conjunction with the works of Aristotle.52 In a letter to his son, Argyropoulos's pupil Alamanno Rinucinni explained the importance of mathematical studies: