No doubt you know that Galileo had been convicted not long ago by the Inquisition, and that his opinion on the movement of the Earth had been condemned as heresy. Now I will tell you that all things I explain in my treatise, among which is also that same opinion about the movement of the Earth, all depend on one another, and are based upon certain evident truths. Nevertheless, I will not for the world stand up against the authority of the Church. ...I have the desire to live in peace and to continue on the road on which I have started.

Analytical geometry was invented by Descartes and the first exposition of it was given in 1637: that exposition was both difficult and obscure, and to most of his contemporaries, to whom the method was new, it must have been incomprehensible. Wallis made the method intelligible to all mathematicians.

I should like you to consider that these functions (including passion, memory, and imagination) follow from the mere arrangement of the machine's organs every bit as naturally as the movements of a clock or other automaton follow from the arrangement of its counter-weights and wheels.

I suppose the body to be nothing but a statue or machine made of earth, which God forms with the explicit intention of making it as much as possible like us.

In order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things.

Thus, all unknown quantities can be expressed in terms of a single quantity, whenever the problem can be constructed by means of circles and straight lines, or by conic sections, or even by some other curve of degree not greater than the third or fourth.But I shall not stop to explain this in more detail, because I should deprive you of the pleasure of mastering it yourself, as well as of the advantage of training your mind by working over it, which is in my opinion the principal benefit to be derived from this science. Because, I find nothing here so difficult that it cannot be worked out by anyone at all familiar with ordinary geometry and with algebra, who will consider carefully all that is set forth in this treatise.

I think, therefore I am.

Good sense is, of all things among men, the most equally distributed; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess.

In my opinion, all things in nature occur mathematically.

No more useful inquiry can be proposed than that which seeks to determine the nature and the scope of human knowledge. ... This investigation should be undertaken once at least in his life by anyone who has the slightest regard for truth, since in pursuing it the true instruments of knowledge and the whole method of inquiry come to light. But nothing seems to me more futile than the conduct of those who boldly dispute about the secrets of nature ... without yet having ever asked even whether human reason is adequate to the solution of these problems.

The entire method consists in the order and arrangement of the things to which the mind's eye must turn so that we can discover some truth.

So blind is the curiosity by which mortals are possessed, that they often conduct their minds along unexplored routes, having no reason to hope for success, but merely being willing to risk the experiment of finding whether the truth they seek lies there.

Staying as I am, one foot in one country and the other in another, I find my condition very happy, in that it is free.

M. Desargues puts me under obligations on account of the pains that it has pleased him to have in me, in that he shows that he is sorry that I do not wish to study more in geometry, but I have resolved to quit only abstract geometry, that is to say, the consideration of questions which serve only to exercise the mind, and this, in order to study another kind of geometry, which has for its object the explanation of the phenomena of nature... You know that all my physics is nothing else than geometry.

What I have given in the second book on the nature and properties of curved lines, and the method of examining them, is, it seems to me, as far beyond the treatment in the ordinary geometry, as the rhetoric of Cicero is beyond the a, b, c of children.

René Descartes is more widely known as a philosopher than as a mathematician, although his philosophy has been controverted while his mathematics has not. ...In accordance with the ideals of his age, when experimental science was first seriously challenging arrogant speculation, Descartes set a greater store by his philosophy than his mathematics. But he fully appreciated the power of his new method in geometry.