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Eudoxes... not only based the method on rigorous demonstration... but he actually applied the method to find the volumes of any pyramid, of the cone, proving that any pyramid is one third part of the prism which has the same base and equal height, and that any cone is one third part of the cylinder which has the same base and equal height. Archimedes, however, tells us the remarkable fact that these two theorems were first discovered by Democritus, though he was not able to prove them , asking whether we are to regard them as equal or unequal... Democritus was already close on the track of infinitesimals. (en) |
