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

Many people believe that the grains of sand are infinite in multitude ... Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe

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.

Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.

Give me a place to stand, and a lever long enough, and I will move the world.

The perimeter of the earth is about 3,000,000 stadia and not greater.

Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.