Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.

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

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.

The diameter of the earth is greater than the diameter of the moon and the diameter of the sun is greater than the diameter of the earth.

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

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.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!