Rules for the Direction of the Mind: Discourse on the Method : Meditations on First Philosophy : Objections Against the Meditations and Replies : The GeometryIs it possible to be certain of anything? If so, how? The father of modern philosophy and the founder of rational method in philosophical thought, René Descartes (1596-1650) sought the answers to these questions and in doing so, addressed the most important of methods of thinking and understanding truth. In Discourse on Method, he applies a scientific approach to philosophy that comprises four principles: to accept only what reason recognizes as "clear and distinct"; to analyze complex ideas by dividing them into smaller elements; to reconstruct the ideas; and to make accurate and complete enumerations of the data. His Meditations proceed according to this method, exploring the mind/body distinction, the nature of truth and error, the existence of God, and the essence of material things. |
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Page 333
... equation having four roots , namely three true roots , 2 , 3 , and 4 , and one false root , 5 . It is evident from the above that the sum of an equation having several roots is always divisible by a binomial consisting of the unknown ...
... equation having four roots , namely three true roots , 2 , 3 , and 4 , and one false root , 5 . It is evident from the above that the sum of an equation having several roots is always divisible by a binomial consisting of the unknown ...
Page 336
... equation to whole numbers , and often in rationalizing the terms . Thus , given x3 - √3x2 + 34x 8 -27√3 = 0 , let there be required another equation in which all the terms are expressed in rational numbers . Let y = x √3 and multiply ...
... equation to whole numbers , and often in rationalizing the terms . Thus , given x3 - √3x2 + 34x 8 -27√3 = 0 , let there be required another equation in which all the terms are expressed in rational numbers . Let y = x √3 and multiply ...
Page 339
... equation into two others , each of the second degree , whose roots will be the same as those of the original equation . Instead of + x1 ± px2 ± qx ± r = 0 , write the two equations զ + x2 - yx + 3y2 ± } p ± = 0 2y and զ + x2 + yx + ...
... equation into two others , each of the second degree , whose roots will be the same as those of the original equation . Instead of + x1 ± px2 ± qx ± r = 0 , write the two equations զ + x2 - yx + 3y2 ± } p ± = 0 2y and զ + x2 + yx + ...
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¹Cf able absolutely infinite action affect affirm angles argument attribute believe called ceived certainly chiliagon clear and distinct clearly and distinctly conceived conic sections consequently consider contrary corporeal curve deceived Demonst deny Descartes desire determined dioptrics Discourse on Method discover doubt dream easily efficient cause endeavour equal equation error essence everything evil existence existence of God explained external body fact faculty false fear finite follows formal cause given greater hatred Hence human body human mind hyperbola idea imagine infinite intellect judge judgment knowledge latus rectum less lines matter means Meditation merely method mode motion nature necessarily never nevertheless object opinions parabola perceive perfect philosophy possess proposition prove Q.E.D. Corol Q.E.D. PROP Q.E.D. Schol reality reason reply say Prop scholium sense sorrow soul substance syllogism tain term thinking thing thought tion triangle true truth understand unless words