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La Géométrie
''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''), were published with the ''Discourse'' to give examples of the kinds of successes he had achieved following his method (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience). The work was the first to propose the idea of uniting algebra and geometry into a single subject 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. It also contributed to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publishing
Publishing is the activities of making information, literature, music, software, and other content, physical or digital, available to the public for sale or free of charge. Traditionally, the term publishing refers to the creation and distribution of Printing, printed works, such as books, comic books, newspapers, and magazine, magazines to the public. With the advent of digital information systems, the scope has expanded to include electronic publishing, digital publishing such as E-book, e-books, Magazines, digital magazines, Electronic publishing, websites, social media, music, and video game publisher, video game publishing. The commercial publishing industry ranges from large multinational conglomerates such as News Corp, Pearson PLC, Pearson, Penguin Random House, and Thomson Reuters to major retail brands and thousands of small independent publishers. It has various divisions such as trade/retail publishing of fiction and non-fiction, educational publishing, and Academi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative numbers, signed distances to the point from two fixed perpendicular oriented lines, called ''coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the ''Origin (mathematics), origin'' and has as coordinates. The axes direction (geometry), directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1637 In Science
The year 1637 in science and technology involved some significant events. Mathematics * René Descartes promotes intellectual rigour in '' Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences'' and introduces the Cartesian coordinate system in its appendix ''La Géométrie'' (published in Leiden). * Pierre de Fermat conjectures Fermat's Last Theorem. Publications * May – Chinese encyclopedist Song Yingxing publishes his ''Tiangong Kaiwu'' ("Exploitation of the Works of Nature"). Births * February 12 – Jan Swammerdam, Dutch naturalist, pioneer of comparative anatomy and entomology (died 1680) * François Mauriceau, French obstetrician (died 1709) Deaths * June 24 – Nicolas-Claude Fabri de Peiresc, French astronomer (born 1580) * May 19 – Isaac Beeckman, Dutch philosopher and scientist (born 1588) * Henry Gellibrand, English mathematician (born 1597 Events January–March * January 4 – Japan's Chancellor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Literature
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1637 Books
Events January–March * January 5 – Pierre Corneille's tragicomedy ''Le Cid'' is first performed, in Paris, Kingdom of France, France. * January 16 – The siege of Nagpur ends in the modern-day Maharashtra state of India, as Kok Shah, the Gonds of Deogarh, King of Deogarh, surrenders his kingdom to the Mughal Empire. * January 23 – John Maurice, Prince of Nassau-Siegen arrives from the Netherlands to become the Governor of Dutch Brazil, and extends the range of the colony over the next six years. * January 28 – Qing invasion of Joseon: The Manchu armies of China complete their invasion of northern Korea with the surrender of Injo of Joseon, King Injo of the Joseon, Joseon Kingdom. * February 3 – Tulip mania collapses in the Dutch Republic. * February 15 – Ferdinand III, Holy Roman Emperor, Ferdinand III becomes Holy Roman Emperor upon the death of his father, Ferdinand II, Holy Roman Emperor, Ferdinand II, although his formal coronatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Rabuel
Claude Rabuel (1669 – 1729) was a French Jesuit mathematician. He analyzed Descartes's '' Géométrie.'' Rabuel was professor at the Collège de la Trinité in Lyon. Works * From Biblioteca europea di informazione e cultura ** From Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ... References 1669 births 1729 deaths 18th-century French Jesuits 18th-century French mathematicians {{France-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hudde's Rules
In mathematics, Hudde's rules are two properties of polynomial roots described by Johann Hudde. 1. If ''r'' is a double root of the polynomial equation ::a_0x^n + a_1x^ + \cdots + a_x + a_n = 0 :and if b_0, b_1, \dots, b_, b_n are numbers in arithmetic progression, then ''r'' is also a root of ::a_0b_0x^n + a_1b_1x^ + \cdots + a_b_x + a_nb_n = 0. :This definition is a form of the modern theorem that if ''r'' is a double root of ''ƒ''(''x'') = 0, then ''r'' is a root of ''ƒ'' '(''x'') = 0. 2. If for ''x'' = ''a'' the polynomial ::a_0x^n + a_1x^ + \cdots + a_x + a_n :takes on a relative maximum or minimum value, then ''a'' is a root of the equation ::na_0x^n + (n-1)a_1x^ + \cdots + 2a_x^2 + a_x = 0. :This definition is a modification of Fermat's theorem in the form that if ''ƒ''(''a'') is a relative maximum or minimum value of a polynomial ''ƒ''(''x''), then ''ƒ'' '(''a'') = 0, where ''ƒ'' ' is the derivative of ''ƒ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Hudde
Johannes (van Waveren) Hudde (23 April 1628 – 15 April 1704) was a mathematician, burgomaster (mayor) of Amsterdam between 1672 – 1703, and governor of the Dutch East India Company. Hudde initially studied law at the University of Leiden, until he turned to mathematics under the influence of Frans van Schooten. He contributed to the theory of equations in his posthumous ''De reductione aequationum'' of 1713, in which he was the first to take literal coefficients in algebra as indifferently positive or negative. In the Latin translation that Van Schooten made of Descartes' La Géométrie, Hudde, together with Johan de Witt and Hendrik van Heuraet, published work of their own. Hudde's contribution consisted of describing an algorithm for simplifying the calculations necessary to determine a double root to a polynomial equation. And establishing two properties of polynomial roots known as Hudde's rules, that point toward algorithms of calculus. As a "burgemeester" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frans Van Schooten
Frans van Schooten Jr. also rendered as Franciscus van Schooten (15 May 1615 – 29 May 1660) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes. He translated La Géométrie in Latin and wrote commentaries and explanations to it. Because most contemporary scientists and mathematicians in Europe knew the invention of analytic geometry through Van Schooten's edition, with its extensive commentaries by Johannes Hudde, Johan de Witt, and Hendrik van Heuraet, he had a significant influence on the science and mathematics of Europe at the time; especially on the invention of calculus by Gottfried Leibniz and Isaac Newton. Life Van Schooten's father, was a professor of mathematics at the University of Leiden, having Christiaan Huygens, Johann van Waveren Hudde, and René de Sluze as students. Van Schooten met Descartes in 1632 and read his ''Géométrie'' (an appendix to his ''Discours de la méthode'') while it was still unpublished. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Descartes' Rule Of Signs
In mathematics, Descartes' rule of signs, described by René Descartes in his ''La Géométrie'', counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of the polynomial's coefficients (omitting zero coefficients), and the difference between the root count and the sign change count is always even. In particular, when the number of sign changes is zero or one, then there are exactly zero or one positive roots. A linear fractional transformation of the variable makes it possible to use the rule of signs to count roots in any interval. This is the basic idea of Budan's theorem and the Budan–Fourier theorem. Repeated division of an interval in two results in a set of disjoint intervals, each containing one root, and together listing all the roots. This approach is used in the fastest algorithms today for computer computation of real roots of polynomials (see real-root is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Theorem
In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f(x) is a polynomial, then x - a is a factor of f(x) if and only if f (a) = 0 (that is, a is a root of the polynomial). The theorem is a special case of the polynomial remainder theorem. The theorem results from basic properties of addition and multiplication. It follows that the theorem holds also when the coefficients and the element a belong to any commutative ring, and not just a field. In particular, since multivariate polynomials can be viewed as univariate in one of their variables, the following generalization holds : If f(X_1,\ldots,X_n) and g(X_2, \ldots,X_n) are multivariate polynomials and g is independent of X_1, then X_1 - g(X_2, \ldots,X_n) is a factor of f(X_1,\ldots,X_n) if and only if f(g(X_2, \ldots,X_n),X_2, \ldots,X_n) is the zero polynomial. Factorization of polynomials Two problems where the factor theorem is commonly applied are those of factoring a polyn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
