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

It is frequently stated that Descartes was the first to apply algebra to geometry. This statement is inaccurate, for Vieta and others had done this before him. Even the Arabs sometimes used algebra in connection with geometry.

In the Greek geometry the idea of motion was wanting but with Descartes it became a very fruitful conception. ...This geometric idea of co-ordinate representation, together with the algebraic idea of two variables in one equation having an indefinite number of simultaneous values, furnished a method for the study of loci, which is admirable for the generality of its solutions. Thus the entire conic sections of Apollonius is wrapped up and contained in a single equation of the second degree.

His Geometry is not easy reading. An edition appeared subsequently with notes by his friend De Beaune, which were intended to remove the difficulties.

His philosophy has long since been superseded by other systems, but the analytical geometry of Descartes will remain a valuable possession forever.

His decipherment of Nature might be crude, yet he had the courage to insist that the mechanical sense could be made of the workings of Nature, throughout the realms of physics, chemistry, and even physiology. By reasserting the unity and rationality of Nature, he did as much as any man to put seventeenth-century scientists back on the intellectual road first trodden by the Greeks.

In the theory of the state of the seventeenth century, the monarch is identified with God and has in the state a position exactly analogous to that attributed to God in the Cartesian system of the world.

As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition.

The primary property of matter was indeed distinctly announced by Descartes in what he calls the "First Law of Nature": "That every individual thing, so far as in it lies, perseveres in the same state, whether of motion or of rest."

By... confounding the properties of matter with those of space he arrives at the logical conclusion, that if the matter within a vessel could be entirely removed the space within the vessel would no longer exist. In fact he assumes that all space must be always full of matter.