In the discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.

Wherever there is number, there is beauty.

The light of the Sun is the pure energy of intellect.

A true philosopher is married to wisdom; he needs no other bride.

It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.

[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it.

In the discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.