8 résultats
178044931(Paris, Moutard, Panckoucke, 1780). 4to. Extract from ""Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IX. Pp. 593-624 and 2 folded engraved plates. Clean and fine.
178044931Paris Moutard Panckoucke 1780. 4to. Extract from "Mémoires fe Mathematique et de Physique Présentés à l'Academie des Sciences par divers Savans" Tome IX. Pp. 593-624 and 2 folded engraved plates. Clean and fine. <br/><br/><em>First appearance of an importent papwer in the history of analytic geometry."In this article Tinseau gave an interesting generalization of the Pythagorean theorem for space of three dimensions: the square of the area of a plane surface is equal to the sum of the squares of the projection of this surface upon three mutually perpendicular coordinate planes.To Tinseau it appears that the use of the word "conoid" in the modern sense is due."Boyer "History of Analytic Geometry p. 207."Two of the three memoirs that constitute Tinseau’s oeuvre deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface contact curves of circumscribed cones or cylinders various surfaces attached to a space curve the determination of the osculatory plane at a point of a space curve problems of quadrature and cubature involving ruled surfaces the study of the properties of certain special ruled surfaces particularly conoids and various results in the analytic geometry of space. In these two papers the equation of the tangent plane at a point of a surface was first worked out in detail the equation had been known since Parent methods of descriptive geometry were used in determining the perpendicular common to two straight lines in space and the Pythagorean theorem was generalized to space the square of a plane area is equal to the sum of the squares of the projections of this area on mutually perpendicular planes. DSB. Although Tinseau published very little his papers are of great interest as additions to Monge’s earliest works. Indeed Tinseau appears to have been Monge’s first disciple. </em> unknown
175042900(Petropoli (St. Petersbourg), 1750). 4to. Uncut, without wrappers. Extracted from ""Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tom. I. ad Annum 1747 et 1748. Pp. 3-19 a. 1 engraved plate., and pp. 20-48.
175042900Petropoli St. Petersbourg 1750. 4to. Uncut without wrappers. Extracted from "Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae" Tom. I. ad Annum 1747 et 1748. Pp. 3-19 a. 1 engraved plate. and pp. 20-48. <br/><br/><em>First printing of both papers. The second is important as it contains Euler'is second proof of the Euler-Fermat theorem which Euler presents as a consequence of the theorem that abp = apbp mod p. This paper also includes results about possible divisors of a2n b2n and Euler uses this to show again that F5 is not prime. - Enestroem No. 133 a. 134. </em> unknown
177041596(Berlin, Haude et Spener, 1770). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome V, pp. 203-221, 1 plate and pp. 222-288, 1 engraved plate.
177041596Berlin Haude et Spener 1770. 4to. No wrappers as issued in "Mémoires de l'Academie Royale des Sciences et Belles-Lettres" Tome V pp. 203-221 1 plate and pp. 222-288 1 engraved plate. <br/><br/><em>Both papers first edition. The first paper is Euler's discussion of "Cramers Paradox" and it contains his inventions of 2 kinds of curves "Cusps of first kind" or keratoid cusp and "Cups of second kind" or ramphoid cusp. - Enestroem E 169.The second paper contains Euler's famous proof of "The fundamental Theorem of Algebra". - Enestroem E 170. </em> unknown
177946989Paris, Ph.-D. Pierres, 1779. 4to. Nice recent vellum, titlelabel with gilt lettering on spine. (4),XXVIII,471 pp. Wide-margined, clean and fine.
177946989Paris Ph.-D. Pierres 1779. 4to. Nice recent vellum titlelabel with gilt lettering on spine. 4XXVIII471 pp. Wide-margined clean and fine. <br/><br/><em>First edition of Bezout's main work - a fundamental contribution to algebraic geometry - in which he prooved the so called ´Bezout's theorem. The theorem was essentially stated by Isaac Newton in his proof of lemma 28 of volume 1 of his Principia where he claims that two curves have a number of intersection points given by the product of their degrees.Bézout's theorem is a statement in algebraic geometry concerning the number of common points or intersection points of two plane algebraic curves. The theorem claims that the number of common points of two such curves X and Y is equal to the product of their degrees. The work stimulated many investigations in the modern theory of elimination including Cauchy’s refinements of elimination procedure and Sylvester’s work on resultants and inertia forms. Bezout’s theorem is crucial to the study of the intersection of manifolds in algebraic geometry."It was not until 1779 that Bezout published his Théorie des équations algébriques his major work on elimination theory. Its best-known achievement is the statement and proof of Bezout’s theorem: "The degree of the final equation resulting from any number of complete equations in the same number of unknowns and of any degrees is equal to the product of the degrees of the equations." Bezout following Euler defined a complete polynomial as one that contains each possible combination of the unknowns whose degree is no more than the degree of the polynomial. Bezout also computed that the degree of the resultant equation is less than the product of the degrees for various systems of incomplete equations. Here we shall consider only the complete case.The proof makes one marvel at the ingenuity of Bezout who like Euler not only could manipulate formulas but also had the ability to choose those manipulations that would be fruitful. He was compelled to justify his nth-order results by a naive "induction" from the observed truth of the statements for 1 2 3 ···. Also numbered subscripts had not yet come into use and the notations available were clumsy."DSB. </em> hardcover
