"The method of not erring is sought by all the world. The logicians profess to guide it, the geometricians alone attain it, and apart from science, and the imitations of it, there are no true demonstrations."

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Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

— Archimedes