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These protests were evidently justified by common sense: yet they missed the speculative radicalism and depth of the Cartesian doctrines, which had struck the keynotes of all modern philosophy and science: for they assumed, for the first time in history, the transcendental point of view.

The Cartesian philosophy swings around the proposition that only through universal doubt can we at last reach truth. Spinoza soon went beyond this and made his plea for faith in a universal Good. Five years went by years of work at his lenses, helping his friends in their farm work, and several hours daily devoted to study and writing. Spinoza's manuscripts were handed around by his pupils.

Normals are treated, not in connexion with tangents, but as minimum or maximum straight lines drawn to the curves from different points or classes of points. Certain propositions of great difficulty enable us to deduce quite easily the Cartesian equations to the evolutes of the three conics. He was also a master of the theory of epicycles and eccentrics.

The space between the planets was divided off into definite points in a series of Cartesian co-ordinates, the sun being the origin, and the plane of the elliptic being the X-Y plane. The OX line was taken pointing toward one of the brightest of the fixed stars that was in the plane of the elliptic.

And Fontenelle offers what he regards as a formal Cartesian proof of the permanence of natural forces. If the Ancients had better intellects than ours, the brains of that age must have been better arranged, formed of firmer or more delicate fibres, fuller of "animal spirits."

But he had grown up in the same intellectual climate in which that idea was produced; he had been nurtured both on the dissolving, dialectic of Bayle, and on the Cartesian enunciation of natural law. And his work contributed to the service, not of the doctrine of the past, but of the doctrine of the future. For he attempted to extend the Cartesian theory to social facts.

It is the Cartesian doubt the maxim that assent may properly be given to no propositions but such as are perfectly clear and distinct which, becoming incarnate, so to speak, in the Englishmen, Anthony Collins, Toland, Tindal, Woolston, and in the wonderful Frenchman, Pierre Bayle, reached its final term in Hume.

It was thus that both the Cartesian and Spinozan systems of philosophy had their birth-place on Dutch soil. Réné Descartes sought refuge from France at Amsterdam in 1629, and he resided at different places in the United Provinces, among them at the university towns of Utrecht, Franeker and Leyden, for twenty years.

And now that he had shaken off the Ghetto, or rather been shaken off by it, he had scandalized no less shockingly that Christendom to which the Ghetto had imagined him apostatizing: he had fearlessly contradicted every system of the century, the ruling Cartesian philosophy no less than the creed of the Church, and his plea for freedom of thought had illustrated it to the full.

I was pleased with the Cartesian opinion, that the idea of God is distinguished from all other ideas by involving its reality; but I was not wholly satisfied. I began then to ask myself, what proof I had of the outward existence of anything? Of this sheet of paper for instance, as a thing in itself, separate from the phaenomenon or image in my perception.