So far the development of algebra and geometry had been mutually independent, except for a few isolated applications of geometrical constructions to the solution of algebraical problems. Certain minds had long suspected the advantages which would accrue from the unrestricted application of algebra to geometry, but it was not until the advent of the philosopher Rene Descartes that the co-ordination was effected.

Kepler divined its possibility; but his thoughts, derailed (so to speak) by the false analogy of magnetism, brought him no farther than to the .rough draft of the scheme of vortices expounded in detail by Rene Descartes in his Principia Philosophiae (1644).

Francis Schooten (Commentary on Descartes) assigns the invention of the curve to Rene Descartes and the first publication on this subject after Descartes to Marin Mersenne.

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Considered as a history of algebra, this work is strongly objected to by Jean Etienne Montucla on the ground of its unfairness as against the early Italian algebraists and also Franciscus Vieta and Rene Descartes and in favour of Harriot; but Augustus De Morgan, while admitting this, attributes to it considerable merit.

Hoffmann, Rene Descartes (1905); Elizabeth S.