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The Principle of Booidancy by Archimedes
Archimedes was a greek mathematician who is one of the greatest thinkers of ancient times. He figured out calculus in some ancient form that was able to cope with problems of curvature. To figure out properties of curved shapes, he imagined them as palpable weights,. And he imagined weighing them in his mind against shapes whose volume or area he already knew. Ehe solves problems about volumes two different ways. First, he discovers them with the method of weighing in his mind, and then he proves them with geometry that he invents.