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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'', he 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 the mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publishing
Publishing is the activity of making information, literature, music, software and other content available to the public for sale or for free. Traditionally, the term refers to the creation and distribution of printed works, such as books, newspapers, and magazines. With the advent of digital information systems, the scope has expanded to include electronic publishing such as E-book, ebooks, academic journals, micropublishing, Electronic publishing, websites, blogs, video game publisher, video game publishing, and the like. Publishing may produce private, club, commons or public goods and may be conducted as a commercial, public, social or community activity. The commercial publishing industry ranges from large multinational conglomerates such as Bertelsmann, RELX, Pearson plc, Pearson and Thomson Reuters to thousands of small independents. It has various divisions such as trade/retail publishing of fiction and non-fiction, educational publishing K–12, (k-12) and Academic publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratrix
In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and Ehrenfried Walther von Tschirnhaus, E. W. Tschirnhaus, which are both related to the circle. Quadratrix of Dinostratus The quadratrix of Dinostratus (also called the ''quadratrix of Hippias'') was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis. Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it effected a mechanical solution of squaring the circle. Pappus of Alexandria, Pappus, in his ''Collections'', treats its history, and gives two methods by which it can be generated. # Let a helix be drawn on a right circular cylinder (geometry), cylinder; a screw surface is then obtained by drawing line (geometry), lines from every point of t ... [...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–June * January 24 – Battle of Turnhout: Maur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Literature
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Books
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...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, France. * January 16 – The siege of Nagpur ends in what is now the Maharashtra state of India, as Kok Shah, the 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 – The Manchu armies of China complete their invasion of northern Korea with the surrender of King Injo of the Joseon Kingdom. * February 3 – Tulip mania collapses in the Dutch Republic. * February 15 – Ferdinand III becomes Holy Roman Emperor upon the death of his father, Ferdinand II, although his formal coronation does not take place until later in the year. * February 18 – Eighty Years' War – Battle off Lizard Point: Off the coast of Corn ... [...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 digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ... 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 burgomaster (mayor) of Amsterdam between 1672 – 1703, a mathematician and governor of the Dutch East India Company. As a "burgemeester" of Amsterdam he ordered that the city canals should be flushed at high tide and that the polluted water of the town "secreten" should be diverted to pits outside the town instead of into the canals. He also promoted hygiene in and around the town's water supply. "Hudde's stones" were marker stones that were used to mark the summer high water level at several points in the city. They later were the foundation for the "NAP", the now Europe-wide system for measuring water levels.J.P.M KwaaHet Normal Amsterdam Peil (NAP)(Dutch) Mathematical work Hudde studied law at the University of Leiden, but turned to mathematics under the influence of his teacher Frans van Schooten. From 1654 to 1663 he worked under van Schooten. ''La Géométrie'' (1637) by René Descartes provid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 coefficients (omitting the zero coefficients), and that the difference between these two numbers is always even. This implies, in particular, that if the number of sign changes is zero or one, then there are exactly zero or one positive roots, respectively. By a homographic transformation of the variable, one may use Descartes' rule of signs for getting a similar information on the number of roots in any interval. This is the basic idea of Budan's theorem and Budan–Fourier theorem. By repeating the division of an interval into two intervals, one gets eventually a list of disjoint intervals containing together all real roots of the polynomial, and containing each exactly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Theorem
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor (x - \alpha) if and only if f(\alpha)=0 (i.e. \alpha is a root). Factorization of polynomials Two problems where the factor theorem is commonly applied are those of factoring a polynomial and finding the roots of a polynomial equation; it is a direct consequence of the theorem that these problems are essentially equivalent. The factor theorem is also used to remove known zeros from a polynomial while leaving all unknown zeros intact, thus producing a lower degree polynomial whose zeros may be easier to find. Abstractly, the method is as follows:. # Deduce the candidate of zero a of the polynomial f from its leading coefficient a_n and constant term a_0. (See Rational Root Theorem.) # Use the factor theorem to conclude that (x-a) is a factor of f(x). # Compute the polynomial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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