He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.

The knowledge which we have acquired ought not to resemble a great shop without order, and without an inventory; we ought to know what we possess, and be able to make it serve us in need.

It is a good thing to proceed in order and to establish propositions. This is the way to gain ground and to progress with certainty.

For, above all, I hold a notion of possibility and necessity according to which there are some things that are possible, but yet not necessary, and which do not really exist. From this it follows that a reason that always forces a free mind to choose one thing over another (whether that reason derives from the perfection of a thing, as it does in God, or from our imperfection) does not eliminate our freedom.

Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.

It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour.

I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.