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181542184London W. Bulmer and Co. 1815 and 1816. 4to. No wrappers as extracted from "Philosophical Transactions" 1815 - Part I. and 1816 - Part II. Having both titlepages to the parts. Pp. 2389-446 and 2179-256. First titlepage with a stamp on verso. Otherwise fine and clean. <br/><br/><em>First printings of Babbage's main mathematical contributions."Babbage's major Contribution to mathematics was his calculus of functions which he became interested in as early as 1809 and continued to develop during his years at Cambridge. Babbage presents his major ideas on the subject in the above two papers published in the "Philosophical Transactions" in 1815 and 1816. "It can be said with some assurance that no mathematician prior to Babbage had treated the calculus of functions in such systematic way.Babbage must be given full credit as the inventor of a distinct and importent branch of mathematics" Dubbey 1978 90. Elsewhere Dubby states that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation and it is possible to see here a hint of the inspiration for his concept of THE ANALYTICAL ENGINE. While the work on the engines and his other scientific social and political activities caused him virtually to abandon mathematical research at the age of thirty the calculus of functions was the area he often yearned to continue. In fact the calculus of functions was not taken up by other workers and it is the aspect of Babbage's mathematical work that modern mathematicians find most fascinating Dubbey 1989 18-19." Hook a. Norman No. 19.Charles Babbage William Herschel and George Peacock founded in 1810 in Cambridge the "Analytical Society" at Trinity College in order to reform the notation and the teaching of mathematics in England introducing Leibniz' differential notation instead of Newton's fluxions. The continental texts and papers then became accessible to English students. </em> unknown
188814319Braunschweig: Vieweg 1888. WITH: O. Fischer Matyas Lerch E. Phragmen C. Neumann C. Meray. 1. DEDEKIND Richard <br /> <br /> Was sind und was sollen die Zahlen. Braunschweig: Vieweg and Son 1888.<br /> <br /> 8vo. xviii 58 pp. including half-title.<br /> <br /> 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.<br /> <br /> <br /> 2. FISCHER Otto<br /> <br /> Konforme abbildung sphärischer dreiecke auf einander mittelst algebraischer funktionen. Leipzig: von Metzger & Wittig 1885.<br /> <br /> 8vo. 76 pp. Complete with half-title and 2 large folding plates on heavier stock.<br /> <br /> 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.<br /> <br /> <br /> <br /> <br /> <br /> 3. PHRAGMÉN Lars Edvard<br /> <br /> Über die Berechnung der einzelnen Glieder der Riemann’schen primzahlformel. Stockholm: Kongliga vetenskaps-Akademiens Förhandlingar 1891.<br /> <br /> 8vo. pp. 721-744.<br /> <br /> First edition of this famous work on the calculation of the individual members of the Riemann prime number formula.<br /> <br /> 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. <br /> <br /> 4. NEUMANN Carl<br /> <br /> Ueber den Satz der virtuellen verrückungen; Ueber das princip der virtuellen oder facultativen verrückungen. Leipzig: von Breitkopf und Härtel 1869.<br /> <br /> 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.<br /> <br /> 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. <br /> <br /> 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.<br /> <br /> 5. LERCH Matyáš<br /> <br /> Contributions à la théorie des fonctions; Addition au mémorie présenté dans la séance du 15 Octobre Prag 1886.<br /> <br /> Two separate papers. 8vo. pp. 571-582; pp.423-432. With a 4 page letter containing mathematical <br /> <br /> <br /> 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.<br /> <br /> 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.<br /> <br /> 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.<br /> <br /> 6. MÉRAY Hugues Charles Robert<br /> <br /> Théorie des radicaux fondée exclusivement sur les propriétés générales des séries entières. Dijon Darantiere 1885.<br /> <br /> 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.<br /> First edition of Méray’s famous work Radical theory based exclusively on the general properties of power series. <br /> <br /> 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.<br /> <br /> No copies of Phragmén Lerch or Méray are located by OCLC. Vieweg unknown