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

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

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

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.

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