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fermat

The dispute on the latter point between Fermat and Descartes was continued, even after the philosopher's death, as late as 1662.

00In another question connected with this, the problem of drawing tangents to any curve, Descartes was drawn into a controversy with Pierre (de) Fermat (1601-1663), Gilles Persone de Roberval (1602-1675), and Girard Desargues (1593-1661).

00Fermat and Descartes agreed in regarding the tangent to a curve as a secant of that curve with the two points of intersection coinciding, while Roberval regarded it as the direction of the composite movement by which the curve can be described.

00Pierre De Fermat >>

00Between Roberval and Descartes there existed a feeling of ill - will, owing to the jealousy aroused in the mind of the former by the criticism which Descartes offered to some of the methods employed by him and by Pierre de Fermat; and this led him to criticize and oppose the analytical methods which Descartes introduced into geometry about this time.

00no number of the form 4n+3, or 4n - I, can be the sum of two squares), and goes on to a d, practically, the condition stated by Fermat, "and the double of it [n] increased by one, when divided by the greatest square which measures it, must not be divisible by a prime number of the form 4n - 1," except for the omission of the words "when divided.

00A reprint of 1670 is only valuable because it contains P. de Fermat's notes; as far as the Greek text is concerned it is much inferior to the other.

00In the theory of numbers he furnished solutions of many of P. Fermat's theorems, and added some of his own.

00Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study.

00Other editions have been published, of which we may mention Pierre Fermat's (1670), T.

00It was proposed by Pierre de Fermat to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians.

00A solution was also given by Fermat in his Relation.

00Diophantine problems were revived by Gaspar Bachet, Pierre Fermat and Euler; the modern theory of numbers was founded by Fermat and developed by Euler, Lagrange and others; and the theory of probability was attacked by Blaise Pascal and Fermat, their work being subsequently expanded by James Bernoulli, Abraham de Moivre, Pierre Simon Laplace and others.

00This problem was proposed by Pierre de Fermat first to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians.

00Now the direction and phase of the light are those of the ray which reaches the eye; and by Fermat's principle, established by Huygens for undulatory motion, the path of a ray is that track along which the disturbance travels in least time, in the restricted sense that any alteration of any short reach of the path will increase the time.

00As, however, our terrestrial optical apparatus is now all in motion along with the matter, we must dealt .with the rays relative to the moving system, and to these also Fermat's principle clearly applies; thus V+ (lu'--mv'-Fnw') is here the velocity of radiation in the direction of the ray, but relative to the moving material system.

00To Legendre is due the theorem known as the law of quadratic reciprocity, the most important general result in the science of numbers which has been discovered since the time of P. de Fermat, and which was called by Gauss the " gem of arithmetic."

00Pappus gives somewhat full particulars of the propositions, and restorations were attempted by P. Fermat (Ouvres, i., 1891, pp. 3-51), F.

00He was a great mathematician in an age which produced Descartes, Fermat, Huygens, Wallis and Roberval.

00The cycloid was a famous curve in those days; it had been discussed by Galileo, Descartes, Fermat, Roberval and Torricelli, who had in turn exhausted their skill upon it.

00The mathematical theory of probability and the allied theory of the combinatorial analysis were in effect created by the correspondence between Pascal and Fermat, concerning certain questions as to the division of stakes in games of chance, which had been propounded to the former by the gaming philosopher De Mere.

00Daguerre for the invention of photography, the grant for the publication of the works of P. Fermat and Laplace, the acquisition of the museum of Cluny, the development of railways and electric telegraphs, the improvement of the navigation of the Seine, and the boring of the artesian wells at Grenelle.

00Sir Christopher Wren, the famous architect, determined the length of the arc and its centre of gravity, and Pierre Fermat deduced the surface of the spindle generated by its revolution.

00At the same time he challenged Roberval and Fermat to construct the tangent; Roberval failed but Fermat succeeded.

00It was further investigated by John Wallis, Christiaan Huygens (who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661).

00The extraordinary advances made by him in this branch of knowledge were owing to his happy method of applying mathematical analysis to physical problems. As a pure mathematician he was, it is true, surpassed in profundity by more than one among his pupils and contemporaries; and in the wider imaginative grasp of abstract geometrical principles he cannot be compared with Fermat, Descartes or Pascal, to say nothing of Newton or Leibnitz.

00Hesse, "they are, like P. Fermat's theorems, riddles to the present and future generations."

00PIERRE DE FERMAT (1601-1665), French mathematician, was born on the 17th of August 1601, at Beaumont-de-Lomagne near Montauban.

00Fermat's Theorem, if p is prime and a is prime to p then a p-1 -1 is divisible by p, was first given in a letter of 1640.

00Fermat's Problem is that x n +y n =z n is impossible for integral values of x, y and z when n is greater than 2.

00Fermat was for some time councillor for the parliament of Toulouse, and in the discharge of the duties of that office he was distinguished both for legal knowledge and for strict integrity of conduct.

00He left a son, Samuel de Fermat (1630-1690) who published translations of several Greek authors and wrote certain books on law in addition to editing his father's works.

00The Opera mathematica of Fermat were published at Toulouse, in 2 vols.

00The Ouvres of Fermat have been re-edited by P. Tannery and C. Henry (Paris, 1891-1894).

00See Paul Tannery, "Sur la date des principales decouvertes de Fermat," in the Bulletin Darboux (1883); and "Les Manuscrits de Fermat," in the Annales de la faculte des lettres de Bordeaux.

00cute to see that the theorem, first referred to in Fermat's notebook in 1637 (!

00The dispute on the latter point between Fermat and Descartes was continued, even after the philosopher's death, as late as 1662.

00In another question connected with this, the problem of drawing tangents to any curve, Descartes was drawn into a controversy with Pierre (de) Fermat (1601-1663), Gilles Persone de Roberval (1602-1675), and Girard Desargues (1593-1661).

00Fermat and Descartes agreed in regarding the tangent to a curve as a secant of that curve with the two points of intersection coinciding, while Roberval regarded it as the direction of the composite movement by which the curve can be described.

00Pierre De Fermat >>

00Between Roberval and Descartes there existed a feeling of ill - will, owing to the jealousy aroused in the mind of the former by the criticism which Descartes offered to some of the methods employed by him and by Pierre de Fermat; and this led him to criticize and oppose the analytical methods which Descartes introduced into geometry about this time.

00no number of the form 4n+3, or 4n - I, can be the sum of two squares), and goes on to a d, practically, the condition stated by Fermat, "and the double of it [n] increased by one, when divided by the greatest square which measures it, must not be divisible by a prime number of the form 4n - 1," except for the omission of the words "when divided.

00A reprint of 1670 is only valuable because it contains P. de Fermat's notes; as far as the Greek text is concerned it is much inferior to the other.

00In the theory of numbers he furnished solutions of many of P. Fermat's theorems, and added some of his own.

00Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study.

00Other editions have been published, of which we may mention Pierre Fermat's (1670), T.

00It was proposed by Pierre de Fermat to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians.

00A solution was also given by Fermat in his Relation.

00Diophantine problems were revived by Gaspar Bachet, Pierre Fermat and Euler; the modern theory of numbers was founded by Fermat and developed by Euler, Lagrange and others; and the theory of probability was attacked by Blaise Pascal and Fermat, their work being subsequently expanded by James Bernoulli, Abraham de Moivre, Pierre Simon Laplace and others.

00This problem was proposed by Pierre de Fermat first to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians.

00Now the direction and phase of the light are those of the ray which reaches the eye; and by Fermat's principle, established by Huygens for undulatory motion, the path of a ray is that track along which the disturbance travels in least time, in the restricted sense that any alteration of any short reach of the path will increase the time.

00As, however, our terrestrial optical apparatus is now all in motion along with the matter, we must dealt .with the rays relative to the moving system, and to these also Fermat's principle clearly applies; thus V+ (lu'--mv'-Fnw') is here the velocity of radiation in the direction of the ray, but relative to the moving material system.

00To Legendre is due the theorem known as the law of quadratic reciprocity, the most important general result in the science of numbers which has been discovered since the time of P. de Fermat, and which was called by Gauss the " gem of arithmetic."

00Pappus gives somewhat full particulars of the propositions, and restorations were attempted by P. Fermat (Ouvres, i., 1891, pp. 3-51), F.

00He was a great mathematician in an age which produced Descartes, Fermat, Huygens, Wallis and Roberval.

00The cycloid was a famous curve in those days; it had been discussed by Galileo, Descartes, Fermat, Roberval and Torricelli, who had in turn exhausted their skill upon it.

00The mathematical theory of probability and the allied theory of the combinatorial analysis were in effect created by the correspondence between Pascal and Fermat, concerning certain questions as to the division of stakes in games of chance, which had been propounded to the former by the gaming philosopher De Mere.

00Daguerre for the invention of photography, the grant for the publication of the works of P. Fermat and Laplace, the acquisition of the museum of Cluny, the development of railways and electric telegraphs, the improvement of the navigation of the Seine, and the boring of the artesian wells at Grenelle.

00Sir Christopher Wren, the famous architect, determined the length of the arc and its centre of gravity, and Pierre Fermat deduced the surface of the spindle generated by its revolution.

00At the same time he challenged Roberval and Fermat to construct the tangent; Roberval failed but Fermat succeeded.

00It was further investigated by John Wallis, Christiaan Huygens (who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661).

00The extraordinary advances made by him in this branch of knowledge were owing to his happy method of applying mathematical analysis to physical problems. As a pure mathematician he was, it is true, surpassed in profundity by more than one among his pupils and contemporaries; and in the wider imaginative grasp of abstract geometrical principles he cannot be compared with Fermat, Descartes or Pascal, to say nothing of Newton or Leibnitz.

00Hesse, "they are, like P. Fermat's theorems, riddles to the present and future generations."

00PIERRE DE FERMAT (1601-1665), French mathematician, was born on the 17th of August 1601, at Beaumont-de-Lomagne near Montauban.

00His great work De maxims et minimis brought him into conflict with Rene Descartes, but the dispute was chiefly due to a want of explicitness in the statement of Fermat (see Infinitesimal Calculus).

00Fermat's Theorem, if p is prime and a is prime to p then a p-1 -1 is divisible by p, was first given in a letter of 1640.

00Fermat's Problem is that x n +y n =z n is impossible for integral values of x, y and z when n is greater than 2.

00Fermat was for some time councillor for the parliament of Toulouse, and in the discharge of the duties of that office he was distinguished both for legal knowledge and for strict integrity of conduct.

00He left a son, Samuel de Fermat (1630-1690) who published translations of several Greek authors and wrote certain books on law in addition to editing his father's works.

00The Opera mathematica of Fermat were published at Toulouse, in 2 vols.

00The Ouvres of Fermat have been re-edited by P. Tannery and C. Henry (Paris, 1891-1894).

00See Paul Tannery, "Sur la date des principales decouvertes de Fermat," in the Bulletin Darboux (1883); and "Les Manuscrits de Fermat," in the Annales de la faculte des lettres de Bordeaux.

00Fermat, Roberval and Desargues took exception in their various ways to the methods employed in the geometry, and to the demonstrations of the laws of refraction given in the Dioptrics and Meteors.

01Fermat, Roberval and Desargues took exception in their various ways to the methods employed in the geometry, and to the demonstrations of the laws of refraction given in the Dioptrics and Meteors.

01

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