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Learn how to count the roots of a polynomial by examining sign changes in its coefficients, as described by René Descartes in his La Géométrie. See examples, proofs, generalizations and related topics.
Deductive reasoning is the process of drawing valid inferences from true premises. Learn about the logical features, rules, and applications of deductive reasoning, as well as its contrast with ampliative reasoning and psychological theories.
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 ...
[6] [7] Descartes did not provide the reasoning through which he found this relation. [8] Japanese mathematics frequently concerned problems involving circles and their tangencies, [9] and Japanese mathematician Yamaji Nushizumi stated a form of Descartes' circle theorem in 1751. Like Descartes, he expressed it as a polynomial equation on the ...
The folium of Descartes is an algebraic curve named after René Descartes, who challenged Pierre de Fermat to find its tangent line. Learn about its history, properties, graphing methods, and relation to the trisectrix of Maclaurin.
René Descartes (/ d eɪ ˈ k ɑːr t / day-KART or UK: / ˈ d eɪ k ɑːr t / DAY-kart; French: [ʁəne dekaʁt] ⓘ; [note 3] [11] 31 March 1596 – 11 February 1650) [12] [13]: 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science.
Learn how logarithms were invented by John Napier and Henry Briggs in the 16th and 17th centuries, and how they were used to simplify calculations in trigonometry, astronomy, and navigation. Discover the origins and applications of natural logarithms, common logarithms, and slide rules.
Learn the definition, examples, properties and algorithms of discrete logarithms in mathematics and cryptography. Discrete logarithms are the inverse of modular exponentiation and are hard to compute in general groups.
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