1869Best.-Nr. 41671Kjøbenhavn Copenhagen Bianco Luno1869. 4to. Uncut and unopened in orig. printed wrappers. Off-print from: Vidensk. Selsk. Skr. 5 Række naturvidenskabelig og matematisk Afd. 8 Bd. V. Pp. 203-248. A mint copy. First printing off-print in original printed wrappers of this groundbreaking paper."A further remarkable result of Lorenz' optical researches on the basis of his fundamental wave equation was the well-known formula Lorents-Lorenz formula for the refraction constant R. His first paper on the refraction constant in which he also gave an experimental verification of his formula in the case of water dates from 1869. In 1870 H. A. Lorentz arrived at the same result independently of Lorenz." D.S.B. VIII:501. unknown

Herman H. J. Lynge & Søn A/S · Dänemark2.500,00 DKK≈ 334,46 €

HERMITE, CHARLES - HERMITE'S THEOREM PROOVING THE TRANSCENDALITY OF eBiblio.com

Sur la fonction exponentielle. Suite. Sur la fonction exponentielle. Suite. 4 Parts all.

1873Best.-Nr. 47891Paris: Gauthier-Villars 1873. 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences" Vol 77 Nos 1 2 4 a. 5 4 entire issues offered. Hermite's paper: pp.18-24; 74-79; 226-233; 285-293. With halftitle and titlepage to vol. 77. First apperance of Hermite's epoch-making memoir in which he proved the transcendence of e and thus initiated a new era in number theory. A decade later Lindemann used the method of Hermite's work to establish the transcendence of pi. Parkinson "Breakthroughs" 1873 M. unknown

Herman H. J. Lynge & Søn A/S · Dänemark8.500,00 DKK≈ 1.137,16 €

D'ALEMBERT, JEAN LE ROND - D'ALEMBERT'S THEOREM - THE FUNDAMENTAL THEOREM OF ALGEBRABiblio.com

Recherches sur le Calcul Intégral. Premier - Seconde Partie. Suite des Recherches sur le Calcul Intégral. = Troisieme Partie. Additons aux Recherches sur le Calcul Integral. Errata pour les Mémoires imprimés dans les Volumes de 1746 .

1848Best.-Nr. 46603Berlin Haude et Spener 1848-52. 4to. No wrappers as extracted from "Mémoires de l'Academie Royale des Sciences et Belles-Lettres" tome II 1846 tome IV tome VI a. tome VI. Pp. 182-224 pp. 249-291 pp. 361- 378 pp. 413-416 and 1 folded engraved plate. First apperance of d'Alembert's 3 importent papers on the Calculus of Integration a branch of mathematical science which is greatly indepted to him. He here gives the proof of THE FUNDAMENTAL THEOREM OF ALGEBRA called d'Alembert's theorem and later corrected by Gauss 1799.The theorem is based on these three assumptions:Every polynomial with real coefficients which is of odd order has a real root. This is a corollary of the intermediate value theorem. Every second order polynomial with complex coefficients has two complex roots. For every polynomial p with real coefficients there exists a field E in which the polynomial may be factored into linear terms.Also with an importent paper by Leonhard Euler "Mémoire sur l'Effet de la Propagation successive de la Lumiere dans l'Apparition tant des Planetes que des Cometes" Memoir on the effect of the successive propogation of light in the appeareance of both comets and planets. Pp. 141-181 and 2 folded engraved plates. - The paper is founded on Euler's theory of light as waves and not as particles. It is from the same year as his fundamental work on light as waves: "Nova Theoria" - Enestroem E 104. unknown

Herman H. J. Lynge & Søn A/S · Dänemark7.500,00 DKK≈ 1.003,37 €

IVORY, JAMES - THE INTRODUCTION OF IVORY'S THEOREMBiblio.com

On the Attraction of homogenous Ellipsoides. Read June 15 1809.

1809Best.-Nr. 42620London W. Bulmer and Co. 1809. 4to. No wrappers as extracted from "Philosophical Transactions" 1809 - Part II. Pp. 345-372. Clean and fine. First printing this importent paper in which Ivory introduces his well-known theorem which bears his name. It states that the attraction of an ellipsoid upon a point exterior to it is dependent upon the attraction of another ellipsoid upon a point interior to it."In 1809 J. Ivory proved the three-dimensional version of this theorem by straightforward calculation and by using an appropriate parametrization. This theorem holds in the n-dimensional Euclidean space n > 1. It has been shown that it is also true in the pseudo-Euclidean plane Minkowski" H. Stachel."Ivory's scientific reputation for which he was awarded many honours during his lifetime including knighthood of the Order of the Guelphs Civil Division 1831 was founded on the ability to understand and comment the work of the French analysts rather than any great originality of his own.Ivory's work conducted with great industry over a long period helped to foster in England a new interest in the application of analysis to physical problems." DSB VII. p. 37. unknown