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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 ...
Descartes' rule of signs and its generalizations. Descartes' rule of signs asserts that the difference between the number of sign variations in the sequence of the coefficients of a polynomial and the number of its positive real roots is a nonnegative even integer. It results that if this number of sign variations is zero, then the polynomial ...
René Descartes ( / deɪˈkɑːrt / day-KART or UK: / ˈdeɪkɑːrt / DAY-kart; French: [ʁəne dekaʁt] ⓘ; [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 philosophy and science. Mathematics was ...
Rules 13–24 deal with what Descartes terms "perfectly understood problems", or problems in which all of the conditions relevant to the solution of the problem are known, and which arise principally in arithmetic and geometry. Rules 25–36 deal with "imperfectly understood problems", or problems in which one or more conditions relevant to the ...
Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences ( French: Discours de la Méthode pour bien conduire sa raison, et chercher la vérité dans les sciences) is a philosophical and autobiographical treatise published by René Descartes in 1637. It is best known as the source of the famous quotation ...
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.
t. e. Cartesianism is the philosophical and scientific system of René Descartes and its subsequent development by other seventeenth century thinkers, most notably François Poullain de la Barre, Nicolas Malebranche and Baruch Spinoza. [1] Descartes is often regarded as the first thinker to emphasize the use of reason to develop the natural ...
t. e. La Géométrie was published in 1637 as an appendix to Discours de la méthode ( Discourse on the Method ), written by René Descartes. In the Discourse, Descartes presents his method for obtaining clarity on any subject. La Géométrie and two other appendices, also by Descartes, La Dioptrique ( Optics) and Les Météores ( Meteorology ...