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The Origins of Infinitesism
An ancient manuscript was discovered, rediscovered in the Vatican library early in the 1900s. It contains a complete description of this non rigorous but essential piece of Archimedes work. In order to make exhaustion work you actually have to know what the answer is. And he had to know that the pie he was talking about, so to speak, for the sphere was the same pie as the one you get for the circle.