RIEMANN, Bernhard. "On the Hypotheses Which Lie at the Bases of Geometry" (MAJOR paper in the history of mathematics) in "Nature"

Riemann, Cornu, Maxwell, many others

Verlag: Macmillan & Co., London, 1873

Beschreibung

RIEMANN, Bernhard (1826-1866). "On the Hypotheses Which Lie at the Bases of Geometry" (MAJOR paper in the history of mathematics); CORNU, Marie Alfred. "New Experiments for the Determination of the Velocity of Light"; James Clerk Maxwell "On Loschmidt's experiments on diffusion In relation to the kinetic theory of gases"; James Clerk Maxwell, "Molecules", and many others, in "Nature", volume 8, 1873. [++] This is a full volume of the journal "Nature" containing the following important papers: RIEMANN, Bernhard. "On the Hypotheses Which Lie at the Bases of Geometry" pp, 14-17 and 36-37("Ueber die Hypothesen, welche der Geometrie zu Grunde liegen", translated by William Kingdom Clifford). AND CORNU, Marie Alfred. "New Experiments for the Determination of the Velocity of Light", (pp., 184-186, 1873). AND James Clerk Maxwell "On Loschmidt's experiments on diffusion In relation to the kinetic theory of gases" (pp. 298-300, 1873). AND James Clerk Maxwell, "Molecules" (pp. 437-441, 1873). And Thomas Xavier de Colmar, "The Arithmometer" pp 320-321, August 21, 1873 (with an illustration of the device). And much else! [++] All in "Nature", London and New York, Macmillan and Co., volume 8, May-October 1873; xii, 572pp. The volume is newly and beautifully rebound in half-leather and cloth boards the binding has just a touch of "antiquing" here and there to make it appear not-brand-new even though it is, making it a lovely and inspired piece of bookbinding. [++] This paper by Riemann (first delivered in 1854 and first printed in 1867) was first printed in English in 1873, translated by WK Clifford, is absolutely foundational, establishing the field of Riemannian geometry and setting the stage for Einstein's general theory of relativity. ("In 1853, Gauss asked Riemann, his student, to prepare a Habilitationsschrift on the foundations of geometry. Over many months, Riemann developed his theory of higher dimensions and delivered his lecture at Göttingen in 1854 entitled "Ueber die Hypothesen, welche der Geometrie zu Grunde liegen". It was not published until twelve years later in 1868 by Dedekind, two years after his death. Its early reception appears to have been slow, but it is now recognized as one of the most important works in geometry.Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in his theorema egregium. The fundamental objects are called the Riemannian metric and the Riemann curvature tensor. For the surface (two-dimensional) case, the curvature at each point can be reduced to a number (scalar), with the surfaces of constant positive or negative curvature being models of the non-Euclidean geometries."--Wikiwand' [++] "At the end of 1853 [Riemann] submitted his Habilitationsschrift on Fourier series and a list of three possible subjects for his Habilitationsvortrag. Against Riemann s expectation Gauss chose the third: Über die Hypothesen, welche der Geometrie zu Grunde liegen . It was thus through Gauss s acumen that the splendid idea of this paper was saved for posterity. Both papers were posthumously published in 1867, and in the twentieth century the second [the English translation offered here) became a great classic of mathematics. Its reading on 10 June 1854 was one of the highlights in the history of mathematics: young, timid Riemann lecturing to the aged, legendary Gauss, who would not live past the next spring, on consequences of ideas the old man must have recognized as his own and which he had long secretly cultivated. W. Weber recounts how perplexed Gauss was, and how with unusual emotion he praised Riemann s profundity on their way home."--Complete Dictionary of Scientific Biography online.

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Bibliografische Details

• Titel: RIEMANN, Bernhard. "On the Hypotheses Which Lie at the Bases of Geometry" (MAJOR paper in the history of mathematics) in "Nature"
• Verlag: Macmillan & Co., London
• Erscheinungsjahr: 1873
• Einband: Hardcover
• Zustand: Fine
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