‎[EISENSTEIN] SETON (Marie).‎
‎Eisenstein.‎

‎Nachtrag zum cubischen Reciprocitätssatze für die aus dritten Wurzeln der Einheit zusammengesetzten complexen Zahlen. Criterien des cubischen Characters der Zahl 3 und ihrer Theiler (+) Transformations remarquables de quelques séries (+) La loi de réc... - [""THERE HAVE BEEN ONLY THREE EPOCH-MAKING MATHEMATICIANS: ARCHIMEDES, NEWTON, AND EISENSTEIN""]‎

‎Berlin, G. Reimer, 1844. 4to. In ""Journal für die reine und angewandte Mathematik, 28 Band, 1 Heft, 1844"". In the original printed wrappers, without backstrip. Fine and clean. [Eisenstein:] Pp. 28-35" Pp. 36-43 Pp. 44-48 Pp. 49-52" Pp. 53-67. [Entire issue: IV, 96, (2) pp. + 2 folded plates.].‎

‎First printing of six exceedingly influential papers by the German mathematics prodigy Eisenstein. Even though he died prematurely at the age of 29, he managed to prove biquadratic reciprocity, Quartic reciprocity (Presented in the present: ""Lois de réciprocité""), Cubic reciprocity (Presented in the present: ""Nachtrag zum cubischen Reciprocitätssatze...""), to be imprisoned by the Prussian army for revolutionary activities in Berlin and making Gauss state that: ""There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein"". Alexander von Humboldt, then 83, accompanied Eisenstein's remains to the cemetery. The papers presented in the present issue is among his most prominent and made him famous throughout the mathematical world. (James, Driven to innovate, P. 88). ""The twenty-seventh and twenty-eighth volumes of Crelle's Journal, published in 1844, contained twenty-five contributions by Eisenstein. These testimonials to his almost unbelievable, explosively dynamic productivity rocketed him to fame throughout the mathematical world. They dealt primarily with quadratic and cubic forms, the reciprocity theorem for cubic residues, fundamental theorems for quadratic and biquadratic residues, cyclotomy and forms of the third degree, plus some notes on elliptic and Abelian transcendentals. Gauss, to whom he had sent some of his writings, praised them very highly and looked forward with pleasure to an announced visit. In June 1844, carrying a glowing letter of recommendation from Humboldt, Eisenstein went off to see Gauss. He stayed in Göttingen fourteen days. In the course of the visit he won the high respect of the ""prince of mathematicians,"" whom he had revered all his life. The sojourn in Göttingen was important to Eisenstein for another reason: he became friends with Moritz A. Stern-the only lasting friendship he ever made. While the two were in continual correspondence on scientific matters, even Stern proved unable to dispel the melancholy that increasingly held Eisenstein in its grip. Even the sensational recognition that came to him while he was still only a third-semester student failed to brighten Eisenstein's spirits more than fleetingly. In February 1845, at the instance of Ernst E. Kummer, who was acting on a suggestion from Jacobi (possibly inspired by Humboldt), Eisenstein was awarded an honorary doctorate in philosophy by the School of Philosophy of the University of Breslau.Eisenstein soon became the subject of legend, and the early literature about him is full of errors. His treatises were written at a time when only Gauss, Cauchy, and Dirichlet had any conception of what a completely rigorous mathematical proof was. Even a man like Jacobi often admitted that his own work sometimes lacked the necessary rigor and self-evidence of methods and proofs."" (DSB)‎

‎Théorèmes sur les Formes cubiques et Solution d'une Equation du quatrième Degré à quatre indéterminées (+) Über die Anzahl der quadratischen Formen, welche in der Theorie der complexen Zahlen zu einer reellen Determinante gehören (+) Allgemeine Auflös... - [""THERE HAVE BEEN ONLY THREE EPOCH-MAKING MATHEMATICIANS: ARCHIMEDES, NEWTON, AND EISENSTEIN""]‎

‎Berlin, G. Reimer, 1844. 4to. In contemporary half cloth. In ""Journal für die reine und angewandte Mathematik"", 27. band, Heft 1-4, 1844. Entire volume 27 offered. A small library stamp to lower part of p. 1 and a white label pasted on to upper part of spine. Light occassional brownspotting, otherwise fine and clean.‎

‎First printing of these influential papers by the German mathematics prodigy Eisenstein. Even though he died prematurely at the age of 29, he managed to prove Cubic reciprocity (presented in the present papers) biquadratic reciprocity, Quartic reciprocity, to be imprisoned by the Prussian army for revolutionary activities in Berlin and making Gauss state that: ""There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein"". Alexander von Humboldt, then 83, accompanied Eisenstein's remains to the cemetery. The papers presented in the present issue is among his most prominent and made him famous throughout the mathematical world. (James, Driven to innovate, P. 88). ""The twenty-seventh (the present and most extensive) and twenty-eighth volumes of Crelle's Journal, published in 1844, contained twenty-five contributions by Eisenstein. These testimonials to his almost unbelievable, explosively dynamic productivity rocketed him to fame throughout the mathematical world. They dealt primarily with quadratic and cubic forms, the reciprocity theorem for cubic residues, fundamental theorems for quadratic and biquadratic residues, cyclotomy and forms of the third degree, plus some notes on elliptic and Abelian transcendentals. Gauss, to whom he had sent some of his writings, praised them very highly and looked forward with pleasure to an announced visit. In June 1844, carrying a glowing letter of recommendation from Humboldt, Eisenstein went off to see Gauss. He stayed in Göttingen fourteen days. In the course of the visit he won the high respect of the ""prince of mathematicians,"" whom he had revered all his life. The sojourn in Göttingen was important to Eisenstein for another reason: he became friends with Moritz A. Stern-the only lasting friendship he ever made. While the two were in continual correspondence on scientific matters, even Stern proved unable to dispel the melancholy that increasingly held Eisenstein in its grip. Even the sensational recognition that came to him while he was still only a third-semester student failed to brighten Eisenstein's spirits more than fleetingly. In February 1845, at the instance of Ernst E. Kummer, who was acting on a suggestion from Jacobi (possibly inspired by Humboldt), Eisenstein was awarded an honorary doctorate in philosophy by the School of Philosophy of the University of Breslau.Eisenstein soon became the subject of legend, and the early literature about him is full of errors. His treatises were written at a time when only Gauss, Cauchy, and Dirichlet had any conception of what a completely rigorous mathematical proof was. Even a man like Jacobi often admitted that his own work sometimes lacked the necessary rigor and self-evidence of methods and proofs."" (DSB).‎

‎"Dessins Eisenstein"‎

‎"1961. Moscou Éditions Iskustvo 1961 - Cartonné toilé 23 cm x 29 cm 227 pages - Textes en russe français anglais et allemand de Sergei Eisenstein Y. Pimenov M. Myasnikov Olga Asienstat - Nombreuses ills couleurs et N&B in et hors-texte de Sergei Eisenstein - Très bon état" ‎

‎Ciné-Club S. M. Eisenstein 1898-1948. Sur le style d'Eisenetein (Jean Mitry) / Une force prodigieusement vivante (Alexandre Arnoux) / Permanence d'un style (Léon Barsacq) / S. M. Eisenstein, Le patriotisme est mon thème / Le contre-point "son-image" (Armand Panigel) / Notes au sujet d'Alexandre Nevsky (Henri Fescourt) / L'oeuvre d'Eisenstein (G. Sadoul) / La révélation du Potemkine (Georges Altman) - ...‎

‎ N° 5 - mars 1948 - Redaction, Administration : 2, rue de l'Elysée. Paris-8e - Journal illustré ‎

‎bon état ‎

‎Über die Irreductibilität und einige andere Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt (+) Über eine allgemeine Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt, nebst Anwendu... - [Eisenstein's Criterion]‎

‎Berlin, G. Reimer, 1850. 4to. Bound in later marbled wrappers, as extracted from ""Journal für die reine und angewandte Mathematik, 28 Band, 4. Heft, 1844"". Very fine and clean. Pp. 160-179" Pp. 224-274 Pp. 275-287 [Entire issue: 289-380 + 2 folded plates].‎

‎First publication of lemniscate function and Eisenstein's Criterion, one of the best known irreducibility criteria of polynomials. It is often seen referred to as the Schönemann-Eisenstein. Euler had introduced and studied the arc length of the lemniscate in the 18th century, this work laying the ground work for the later development of elliptic functions. The lemniscate function expresses the parameter of the lemnicate in terms of its arc-length. It can be extended to complex values of the parameter, and it then makes sense to ask for the points which divide the lemniscate into m equal parts, where m is a Gaussian integer (a complex number). Abel had shown that the determination of these points reduced to finding the roots of a certain polynomial equation. A crucial point in Eisenstein's extension of Abel's work described in the present papers was to prove that this polynomial is irreducible. Eisenstein developed his eponymous criterion to establish this (although today it is most familiar when applied to the more elementary case of a polynomial with ordinary integer coefficients).‎