SKETCH OF REN& DESCARTES. 839 



tinct that they can not be doubted." Descartes attached less 

 importance to the geometrical 'and mathematical methods of 

 which he was the inventor than to his moral and metaphysical 

 speculations. But, while the latter have been sifted and riddled 

 in discussion, and have suffered under the revolutions of thought, 

 the mathematical principles he established and the methods he 

 introduced remain. In geometry he gave demonstrations of gen- 

 eral principles, under which solutions adapted to one problem 

 could be applied to all like it. In algebra, for the old clumsy 

 notation and nomenclature, always suggesting material relations, 

 he substituted the beautiful, convenient system, purely abstract, 

 by the aid of which that branch of the science has marched to 

 almost universal application and perfection. And in the applica- 

 tion of algebra to geometry, he introduced the method of abscissas 

 and ordinates, by means of which any curve and any condition 

 of form can be computed by a process as beautiful as it is direct. 



The Meditations on the First Philosophy, which appeared in 

 manuscript in 1640, consists of six parts, in the first of which the 

 author expounds his philosophy of doubt; in the second, he 

 reaches the certainty of his own being, through the use of his 

 famous maxim, cogito, ergo sum (I think, therefore I am) ; in the 

 third, he deduces an argument to prove the existence of God from 

 the idea of an infinite and sovereignly perfect being ; in the fourth, 

 he draws a distinction between speculative reasoning, for which 

 the light of nature is sufficient, and doctrines of faith and the con- 

 duct of life, which rest on another foundation ; in the fifth, he 

 explains the corporeal nature, and brings forward another argu- 

 ment for the existence of God ; and in the sixth he treats of the 

 distinctions between intellect and imagination, the difference yet 

 intimate connection of soul and body, errors of the senses and the 

 means of avoiding them, and the reasons upon which we can con- 

 clude concerning the existence of material things, which he, how- 

 ever, regarded as inferior to the evidence on which we predicate 

 the existence of God and the soul. The book in this form was 

 submitted to the criticisms of a number of distinguished students, 

 whose objections were printed and bound with the main treatise 

 when it was published in 1641, and with them the replies of the 

 author, considerably swelling the bulk of the volume. 



The Principles of Philosophy, 1644, contained an exposition of 

 the principles of knowledge as developed in the Meditations ; an 

 explanation of the primary laws of nature, the properties of mat- 

 ter, space, motion, etc. ; the system of the world, the sky, and 

 celestial bodies ; and a treatise on the Earth. The statement of 

 the three laws of nature, the seven secondary laws of impact 

 (which are pronounced by later science to a large extent incor- 

 rect), and the famous theory of Vortices, by which Descartes at- 



