"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."

Source: On the Equilibrium of Planes. Treatise by Archimedes, Book 1, Propositions 6 & 7, The Law of the Lever,