The Concept of Infinity in Ancient Greek Mathematics

TL;DRAbstract

It was for a long time believed that the Greeks did not deal directly with actual infinity, considering it less than rigorous, and instead preferred a concept of unlimited extendability. However, the recent interpretation by Dr. Reviel Netz of an argument found in Archimedes' Method of Mechanical Theorems has resulted in a recognition that the Greeks acknowledged and were capable of using actual infinity in mathematical argument. With this in mind, the paper will examine the infinitary arguments presented prior to Archimedes' work in Euclid, specifically book XII of the Elements, with a view to establishing the context behind Archimedes' use of actual infinity. This work will have ramifications for future research planned on the later interpretation of Euclid's infinitary arguments and their successors in the calculus of Newton and Leibniz.

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