Essentially, therefore, Descartes's process is that known later as the process of isoperimeters, and often attributed wholly to Schwab.2 In 16J5 appeared the Arithmetica Infinitorum of John Wallis, where numerous problems of quadrature are dealt with, the curves being now represented in Cartesian co-ordinates, and algebra playing an important part.
In Germany a few Cartesian lecturers taught at Leipzig and Halle, but the system took no root, any more than in Switzerland, where it had a brief reign at Geneva after 1669.
From the real or fancied rapprochements between Cartesianism and Jansenism, it became for a while impolitic, if not dangerous, to avow too loudly a preference for Cartesian theories.
To attach a clear and definite meaning to the Cartesian doctrine of God, to show how much of it comes from the Christian theology and how much from the logic of idealism, how far the conception of a personal being as creator and preserver mingles with the pantheistic conception of an infinite and perfect something which is all in all, would be to go beyond Descartes and to ask for a solution of difficulties of which he was 1 Ouvres, vi.
The most important formulae are those which correspond to the use of rectangular Cartesian co-ordinates.
It is to her that the Principles of Philosophy were dedicated; and in her alone, according to Descartes, were united those generally separated talents for metaphysics and for mathematics which are so characteristically co-operative in the Cartesian system.
Although the systematic framework of the thought and the terminology used are both derived from the Cartesian philosophy, the intellectual milieu of the time, the early work enables us, better than the Ethics to realize that the inspiration and starting-point of his thinking is to be found in the religious speculations of his Jewish predecessors.
But this example, combined with the Cartesian principles, set many active and ingenious spirits to work to reconstruct the whole of medicine on a physiological or even a mechanical basis - to endeavour to form what we should now call physiological or scientific medicine.
John Wallis, in addition to translating the Conics of Apollonius, published in 1655 an original work entitled De sectionibus conicis nova methodo expositis, in which he treated the curves by the Cartesian method, and derived their properties from the definition in piano, completely ignoring the connexion between the conic sections and a cone.
The original texts, of theses discussed in the schools, and of systematic expositions of Cartesian philosophy for the benefit of the student.