I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

Give me but a firm spot on which to stand, and I shall move the earth.

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.

The centre of gravity of any cylinder is the point of bisection of the axis.

Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.

Eureka! [I have found it!] On discovery of a method to test the purity of gold.

There are things which seem incredible to most men who have not studied Mathematics.