René Descartes Quotes

An optimist may see a light where there is none, but why must the pessimist always run to blow it out?

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

I could give here several other ways of tracing and conceiving a series of curved lines, each curve more complex than any preceding one, but I think the best way to group together all such curves and them classify them in order, is by recognizing the fact that all points of those curves which we may call "geometric," that is, those which admit of precise and exact measurement, must bear a definite relation to all points of a straight line, and that this relation must be expressed by a single equation. If this equation contains no term of higher degree than the rectangle of two unknown quantities, or the square of one, the curve belongs to the first and simplest class, which contains only the circle, the parabola, the hyperbola, and the ellipse; but when the equation contains one or more terms of the third or fourth degree in one or both of the two unknown quantities (for it requires two unknown quantities to express the relation between two points) the curve belongs to the second class; and if the equation contains a term of the fifth or sixth degree in either or both of the unknown quantities the curve belongs to the third class, and so on indefinitely.

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.

Loosely translated: With me, everything turns into mathematics.

Mais apud me omnia fiunt Mathematicè in Natura

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.

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.

Me tenant comme je suis, un pied dans un pays et l'autre en un autre, je trouve ma condition très heureuse, en ce qu'elle est libre.

Mr. Clerselier has written me that you are expecting from him my Meditations... in order to present them to the queen of the land. ...If I had only been as wise as they say the savages persuaded themselves that the monkeys were, I never would have become known as a maker of books: Since it is said that they imagined that the monkeys could indeed speak, if they wanted to, but that they chose not to so lest they be forced to work. And since I had not the same prudence to abstain from writing, I now have neither as much liesure nor as much peace as I would have had if I had kept quiet. But since the mistake has already been made, and since I am now known by an infinity of people at the academy, who look askance at my writings and scour them for means of harming me, I do have great hope of being known to persons of great merit, whose power and virtue could protect me.

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.

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.

Several years have now passed since I fi rst realized how numerous were the false opinions that in my youth I had taken to be true, and thus how doubtful were all those that I had subsequently built upon them. And thus I realized that
once in my life I had to raze everything to the ground and begin again from the
original foundations, if I wanted to establish anything firm and lasting in the sciences.