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René Descartes. René Descartes ( / deɪˈkɑːrt / day-KART or UK: / ˈdeɪkɑːrt / DAY-kart; French: [ʁəne dekaʁt] ⓘ; Latinized:Renatus Cartesius; [note 3] [11] 31 March 1596 – 11 February 1650) [12] [13] [14] : 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern ...
The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation. and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting In the plane the equation is. If we stretch the curve in the direction by a factor of this becomes.
La Géométrie. The work was the first to propose the idea of uniting algebra and geometry into a single subject [2] and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was ground-breaking.
Descartes' rule of signs. In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for getting information on the number of positive real roots of a polynomial. It asserts that the number of positive roots is at most the number of sign changes in the sequence of polynomial's ...
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
General Scholium. The General Scholium ( Latin: Scholium Generale) is an essay written by Isaac Newton, appended to his work of Philosophiæ Naturalis Principia Mathematica, known as the Principia. It was first published with the second (1713) edition of the Principia and reappeared with some additions and modifications on the third (1726 ...
Deductive reasoning. Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and " Socrates is a man" to ...
Cartesian doubt is a systematic process of being skeptical about (or doubting) the truth of one's beliefs, which has become a characteristic method in philosophy. [3] : 403 Additionally, Descartes' method has been seen by many as the root of the modern scientific method. This method of doubt was largely popularized in Western philosophy by ...
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