Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.

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

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

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

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

Spoken of the young Archimedes: . . . [he] was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.

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