Of all things, good sense is the most fairly distributed: everyone thinks he is so well supplied with it that even those who are the hardest to satisfy in every other respect never desire more of it than they already have.
Each problem that I solved became a rule which served afterwards to solve other problems.
If I found any new truths in the sciences, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.
. . . thus each truth discovered was a rule available in the discovery of subsequent ones.
It is very certain that, when it is not in our power to determine what is true, we ought to act according to what is most probable.
I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.
I thought the following four [rules] would be enough, provided that I made a firm and constant resolution not to fail even once in the observance of them. The first was never to accept anything as true if I had not evident knowledge of its being so; that is, carefully to avoid precipitancy and prejudice, and to embrace in my judgment only what presented itself to my mind so clearly and distinctly that I had no occasion to doubt it. The second, to divide each problem I examined into as many parts as was feasible, and as was requisite for its better solution. The third, to direct my thoughts in an orderly way; beginning with the simplest objects, those most apt to be known, and ascending little by little, in steps as it were, to the knowledge of the most complex; and establishing an order in thought even when the objects had no natural priority one to another. And the last, to make throughout such complete enumerations and such general surveys that I might be sure of leaving nothing out. These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.
When writing about transcendental issues, be transcendentally clear.
If we possessed a thorough knowledge of all the parts of the seed of any animal (e.g. man), we could from that alone, be reasons entirely mathematical and certain, deduce the whole conformation and figure of each of its members, and, conversely if we knew several peculiarities of this conformation, we would from those deduce the nature of its seed.
Cogito Ergo Sum. "I think, therefore I am."
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
Perfect numbers like perfect men are very rare.
Omnia apud me mathematica fiunt.
With me everything turns into mathematics.
It is not enough to have a good mind. The main thing is to use it well.
If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.
... the two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.
Intuition is the undoubting conception of a pure and attentive mind, which arises from the light of reason alone, and is more certain than deduction.
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also as to those which I have intentionally omitted so as to leave to others the pleasure of discovery.