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ABEL, N.H. [B.HOLMBOE ed.] - Oeuvres complètes de N.H. Abel, mathématicien, avec des notes ét développements, rédigées par ordre du Roi, par B. Holmboe, professeur de mathématiques à l'université de Christiania, membre de la société physiographique à Christiania et de l'Académie Royale des Sciences de Guerre à Stockholm. Tome Premier. ... Tome Second contenant les oeuvres de l'auteur qui nónt pas été publiées auparavant. B.u.w. 2) C. [Fr.] STURM, On the solution of numerical equations. Transl. from the 'Mémoires présentés par divers Savans à l'Académie Royale des Sciences ... by W.H.Spiller.

Christiania; London & Paris, Chez Chr. Gröndahl, Imprimeur-Librarire; John Souter, 73, St. Paul's Church-Yard; Chez Bachelier, 1839. - 1835. 4to. 3 vols. in 1. A mod. half clf. spine, original marbled endp. preserved. The original marbled brds. preserved. (edges of covers rubb.; (Original) corners bumped and dam.). [1 in 4s, 2 in 4s; 1-60 in 4s; n4, 1-37 in 4s; n2, B-G4, H2]. (XVI, 479, I (errata) pp; II (blank), VI (pr. title, preface etc), 294, II (errata) pp.; IV, 51, I (blank) pp.). (Second vol. of the Abel pp. 284 to end some browning and foxed spots;). (The Sturm 2 quires light even browning.). ad 1) First collected edition. Good copy, good quality. Firm in a sympathetic modern half clf. binding, author and title giltlettered on spine. DSB vol. I (Abel), pp. 12 - 17 Niels Henrik Abel, 1802 - 1829, mathematics. Holmboe, assistant of Hansteen, took Abel under his wings and 'It didn't take [him] long to discover young Abel's extraordinary ability in mathematics. He began by giving him special problems ... The two then started to study together the calculus texts of Euler, ... later the works of .. LaGrange and Laplace. ... [on the suggestion of the Danish mathematician Degen Abel turned to elliptic integrals] ... within a cpouple of years he had in the main completed his theory of elliptic functions. ... [his] "Recherches sur les fonctions elliptiques", his most extensive publication (125 pp. in the 'Oeuvres complètes') ... radically transformed the theory of elliptic integrals to the theory of elliptic functions... The first part of the "Recherches" was published in 'Crelle's Journa;' in September 1827, and Abel completed the second part during the winter. He lived in isolation in Oslo ... and he had no inkling of the interest his memoir had created among European mathematicians. Nor did he know that a competitor had appeared in the field of elliptic functions, until early 1828, ... K.G.J.Jacobi, ... [Abel] then wrote, in rapid succession, a series of papers on elliptic functions, ... Jacobi, on the other hand, wrote only brief notices which did not reveal his methods; these were reserved for his book "Fundamenta Nova theoriae functionum ellepticarum (1829). ... On 28 June 1830, The French Academy of Sciences awarded its Grand Prix to Abel and Jacobi for their outstanding mathematical discoveries..': Idem, vol. VI, p. 474 (Holmboe) 'He was appointed teacher at the Cathedral School in 1818; here he made his greatest contribution to mathematics by discovering and nurturing the genius of his pupil Niels Henrik Abel. Together they explored the whole mathematical literature in a quest in which the pupil soon became the leader. ... After Abel's death Holmboe edited his works at the request of the Government; ... ': Poggendorff vol. I, pp. 2 - 3: Darmstaedter p. 362: Volume 2 contains works that are published here for the first time.: Ad 2) DSB Vol. XIII, pp. 126 - 132: First English edition of the 'Complete text of the work containing the statement and demonstration of Sturm's theorem'. It was originally publ. in the 'Mémoires ...', for 1835, vol. 6, pp. 271 - 318, as 'Mémoire sur la résolution des équations numériques'. Charles François Sturm, 1803 - 1855, mathematics, physics. 'Sturm's Theorem. Although the problem of finding the number of real roots of the equation f(x)=0 had already been encountered by Descartes and by Rolle, it was not investigated systematically until the mid 18th century. Gua de Malves .. Fourier... Cauchy [who offered the first solution, but too elaborate]... Sturm's discovery elicited great excitement, and he became famous as the mathematician who had filled a lacuna in algebra. ... Charles Hermite made the following assessment: "Sturm's Theorem had the good fortune of immediately becoming classic and of finding a place in teaching that it will hold forever. His demonstration, which utilizes only the most elementary considerations, is a rare example of simplicity and elegance."':
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