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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.
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.
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 ...
Learn about René Descartes' famous treatise on his method of doubt and his famous statement "I think, therefore I am". The web page also covers the book's organization, content, and influence in 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.
This enhancement of Descartes' work was primarily carried out by Frans van Schooten, a professor of mathematics at Leiden and his students. Van Schooten published a Latin version of La Géométrie in 1649 and this was followed by three other editions in 1659−1661, 1683 and 1693.
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.
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