Aristarchus’s De magnitudinis et distantiis solis et lunae was translated into Latin and printed by Federico Commandino in 1572. All subsequent editions of Aristarchus’ treatise, published by John Wallis (1688), Fortia d’ Urban (1823) and Thomas Heath (1913), followed Commandino’s work. In this article, through a philological approach to the geometric diagrams, I tracked down one of the Greek sources used by Commandino for preparing his Latin version. Commandino pays particular attention to drawing figures. This article sheds light on the (...) interaction between mathematical skills and the drawing of geometric diagrams implemented in his Latin edition of Aristarchus’ book. (shrink)

In the third century b.c.e., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made better (...) measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. (shrink)

In this paper I present two cases, taken from the history of science, in which mathematics and physics successfully interplay. These cases provide, respectively, an example of the successful application of mathematics in astronomy and an example of the successful application of mechanics in mathematics. I claim that an illustration of these cases has a twofold value in the context of the applicability debate. First, it enriches the debate with an historical perspective which is largely omitted in the contemporary discussion. (...) Second, it reveals a component of the applicability problem that has received little attention. This component concerns the successful application of physical principles in mathematical practice. With the help of the two examples, in the final part of the paper I address the following question: are successful applications of mathematics to physics and successful applications of physics to mathematics two sides of the same problem? (shrink)