Was sind und was sollen zahlen
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- Braunschweig: Vieweg, 1888
Braunschweig: Vieweg, 1888. WITH: O. Fischer, Matyas Lerch, E. Phragmen, C. Neumann, C. Meray. 1. DEDEKIND, Richard
Was sind und was sollen die Zahlen. Braunschweig: Vieweg and Son, 1888.
8vo. xviii, 58 pp., including half-title.
First edition, rare, of Dedekind’s important work on set theory. His epochal 1872 publication, Stetigkeit und irrationale zahlen, gave the first rigorous definition of the system of real numbers, laying the foundation for much of modern day real analysis and point-set topology. This, his follow-up work, elaborates on his attempts “to derive a purely logical foundation for arithmetic, and devised a number of axioms that formally and exactly represented the logical concept of whole numbers” (DSB). Dedekind (1831-1916), a German mathematician, friend and colleague of Georg Cantor, claimed all of mathematics to be a branch of logic. In this work (The nature and meaning of numbers), he “presents a theory of the integers using set-theoretic concepts and outlines a possible approach to placing the rationals on a logistically well-founded axiomatic basis” (Parkinson, p. 415).
2. FISCHER, Otto
Konforme abbildung sphärischer dreiecke auf einander mittelst algebraischer funktionen. Leipzig: von Metzger & Wittig, 1885.
8vo. 76 pp. Complete with half-title and 2 large folding plates on heavier stock.
First edition of the author’s thesis on conforming images of spherical triangles by means of algebraic functions. Fischer (1861-1916) was a German physiologist and mathematician, earning a doctorate degree from the Franke Foundation in Halle an der Saale in 1885 under Felix Klein. His main interest was the mechanics of the muscles and joints of the human musculoskeletal system. He was a professor at the University of Leipzig, where he taught both medicine and mathematics.
3. PHRAGMÉN, [Lars] E[dvard]
Über die Berechnung der einzelnen Glieder der Riemann’schen primzahlformel. Stockholm: Kongliga vetenskaps-Akademiens Förhandlingar, 1891.
8vo. pp. 721-744.
First edition of this famous work on the calculation of the individual members of the Riemann prime number formula.
The son of mathematics teachers, Phragmén (1863-1937) also taught mathematics before obtaining his degree at the University of Uppsala. He was an editor at the Acta Mathematica, where he corresponded with Poincare to correct a book in which he found a number of errors. He was also president of the Swedish Society of Actuaries. He is best known, however, for the Phragmén-Lindelöf principle, an extension of the maximum modulus principle of complex analysis to unbounded domains.
4. NEUMANN, Carl
Ueber den Satz der virtuellen verrückungen; Ueber das princip der virtuellen oder facultativen verrückungen. [Leipzig: von Breitkopf und Härtel, 1869].
Two separate papers. 8vo. pp. [257]-280; [53]-64. In Konigl. Sachs. Gesellschaft der Wissenchaften. With annotations on the first couple of pages. At the end of the second paper, a thank you by C.F. Gauss.
Two works on virtual displacements. Neumann created the second-type boundary, which, when imposed on an ordinary or partial differential equation, if specifies the value that the derivative of a solution is to take on the boundary of the domain.
Neumann (1832-1925) was professor of mathematics at both the Universities of Tübingen and Leipzig. His main interests were in applied mathematics, and he wrote on mathematical physics, potential and electrodynamics. He was also editor of Mathematische Annalen.
5. LERCH, M[atyáš]
Contributions à la théorie des fonctions; Addition au mémorie présenté dans la séance du 15 Octobre [Prag, 1886].
Two separate papers. 8vo. pp. 571-582; pp.423-432. With a 4 page letter containing mathematical
symbols handwritten by Lerch to Karl Weierstrass (1815-1897) tipped in between the two papers. The letter is signed by Lerch and dated October 1890. A small section of page 582 is crossed out in the same hand.
First printings of Lerch’s contributions to general mathematical functions. These papers are the first in a series dealing with the general theory of functions, the most significant of which constitutes construction of continuous functions having no derivative. These works were written quite early. Lerch (1860-1922) showed exceptional abilities while still studying at the Czech Technical University at Prague. Before 1896 he published more than 110 scientific papers in domestic as well as prominent foreign journals. Much of his work concerned mathematical analysis, including theories of infinite series, of the gamma function, of elliptic functions, and the integral calculus.
Weierstrass is generally referred to as the father of modern analysis. He made significant contributions and advancements in the field of calculus of variations. Numerous theories and functions bear his name.
6. MÉRAY, [Hugues Ch[arles Robert]
Théorie des radicaux fondée exclusivement sur les propriétés générales des séries entières. Dijon, Darantiere, [1885].
8vo. 75, [1] pp. Title page in manuscript signed by Méray and dated Dijon, 1891. With annotations throughout probably by the author for another edition.
First edition of Méray’s famous work, Radical theory based exclusively on the general properties of power series.
Méray (1835-1911) is remembered for having anticipated, clearly and with only minor differences of style, Cantor’s theory of irrational numbers, one of the main steps in the arithmetization of analysis. Of interest, an earlier “arithmetical” theory of irrational numbers was propounded by Weierstraass in his lectures when he introduced the real numbers as sums of sequences of rational numbers. Dedekind also seems to have developed his theory of irrationals at an earlier date.
No copies of Phragmén, Lerch or Méray are located by OCLC.
Was sind und was sollen die Zahlen. Braunschweig: Vieweg and Son, 1888.
8vo. xviii, 58 pp., including half-title.
First edition, rare, of Dedekind’s important work on set theory. His epochal 1872 publication, Stetigkeit und irrationale zahlen, gave the first rigorous definition of the system of real numbers, laying the foundation for much of modern day real analysis and point-set topology. This, his follow-up work, elaborates on his attempts “to derive a purely logical foundation for arithmetic, and devised a number of axioms that formally and exactly represented the logical concept of whole numbers” (DSB). Dedekind (1831-1916), a German mathematician, friend and colleague of Georg Cantor, claimed all of mathematics to be a branch of logic. In this work (The nature and meaning of numbers), he “presents a theory of the integers using set-theoretic concepts and outlines a possible approach to placing the rationals on a logistically well-founded axiomatic basis” (Parkinson, p. 415).
2. FISCHER, Otto
Konforme abbildung sphärischer dreiecke auf einander mittelst algebraischer funktionen. Leipzig: von Metzger & Wittig, 1885.
8vo. 76 pp. Complete with half-title and 2 large folding plates on heavier stock.
First edition of the author’s thesis on conforming images of spherical triangles by means of algebraic functions. Fischer (1861-1916) was a German physiologist and mathematician, earning a doctorate degree from the Franke Foundation in Halle an der Saale in 1885 under Felix Klein. His main interest was the mechanics of the muscles and joints of the human musculoskeletal system. He was a professor at the University of Leipzig, where he taught both medicine and mathematics.
3. PHRAGMÉN, [Lars] E[dvard]
Über die Berechnung der einzelnen Glieder der Riemann’schen primzahlformel. Stockholm: Kongliga vetenskaps-Akademiens Förhandlingar, 1891.
8vo. pp. 721-744.
First edition of this famous work on the calculation of the individual members of the Riemann prime number formula.
The son of mathematics teachers, Phragmén (1863-1937) also taught mathematics before obtaining his degree at the University of Uppsala. He was an editor at the Acta Mathematica, where he corresponded with Poincare to correct a book in which he found a number of errors. He was also president of the Swedish Society of Actuaries. He is best known, however, for the Phragmén-Lindelöf principle, an extension of the maximum modulus principle of complex analysis to unbounded domains.
4. NEUMANN, Carl
Ueber den Satz der virtuellen verrückungen; Ueber das princip der virtuellen oder facultativen verrückungen. [Leipzig: von Breitkopf und Härtel, 1869].
Two separate papers. 8vo. pp. [257]-280; [53]-64. In Konigl. Sachs. Gesellschaft der Wissenchaften. With annotations on the first couple of pages. At the end of the second paper, a thank you by C.F. Gauss.
Two works on virtual displacements. Neumann created the second-type boundary, which, when imposed on an ordinary or partial differential equation, if specifies the value that the derivative of a solution is to take on the boundary of the domain.
Neumann (1832-1925) was professor of mathematics at both the Universities of Tübingen and Leipzig. His main interests were in applied mathematics, and he wrote on mathematical physics, potential and electrodynamics. He was also editor of Mathematische Annalen.
5. LERCH, M[atyáš]
Contributions à la théorie des fonctions; Addition au mémorie présenté dans la séance du 15 Octobre [Prag, 1886].
Two separate papers. 8vo. pp. 571-582; pp.423-432. With a 4 page letter containing mathematical
symbols handwritten by Lerch to Karl Weierstrass (1815-1897) tipped in between the two papers. The letter is signed by Lerch and dated October 1890. A small section of page 582 is crossed out in the same hand.
First printings of Lerch’s contributions to general mathematical functions. These papers are the first in a series dealing with the general theory of functions, the most significant of which constitutes construction of continuous functions having no derivative. These works were written quite early. Lerch (1860-1922) showed exceptional abilities while still studying at the Czech Technical University at Prague. Before 1896 he published more than 110 scientific papers in domestic as well as prominent foreign journals. Much of his work concerned mathematical analysis, including theories of infinite series, of the gamma function, of elliptic functions, and the integral calculus.
Weierstrass is generally referred to as the father of modern analysis. He made significant contributions and advancements in the field of calculus of variations. Numerous theories and functions bear his name.
6. MÉRAY, [Hugues Ch[arles Robert]
Théorie des radicaux fondée exclusivement sur les propriétés générales des séries entières. Dijon, Darantiere, [1885].
8vo. 75, [1] pp. Title page in manuscript signed by Méray and dated Dijon, 1891. With annotations throughout probably by the author for another edition.
First edition of Méray’s famous work, Radical theory based exclusively on the general properties of power series.
Méray (1835-1911) is remembered for having anticipated, clearly and with only minor differences of style, Cantor’s theory of irrational numbers, one of the main steps in the arithmetization of analysis. Of interest, an earlier “arithmetical” theory of irrational numbers was propounded by Weierstraass in his lectures when he introduced the real numbers as sums of sequences of rational numbers. Dedekind also seems to have developed his theory of irrationals at an earlier date.
No copies of Phragmén, Lerch or Méray are located by OCLC.
Details
Title
Was sind und was sollen zahlen
Author
[MATHEMATICS SAMMELBAND]. DEDEKIND, R.
Condition
Unknown
Publisher
Vieweg: Braunschweig
Date
1888