Abstract

Study over the past decade by the Archimedes Palimpsest Project of the Method of Mechanical Theorems, recovered in 1998, has produced evidence that the ancient Greek mathematician Archimedes may have made informal use of actual infinity in his method of discovering geometric theorems. This runs contrary to the Greek tradition of rigorous proof which allows only for the use of potential infinity. We will examine the relevant argument, Proposition 14, compare it with the more traditional Greek infinitary argument known as the method of exhaustion, and consider the questions arising about the Greek attitude toward infinity.