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‎"BEZOUT, ÉTIENNE.‎ ‎Mémoire sur plusieurs Classes d'Équations de tous les Degrés, Qui admettent une Solution algébrique.‎ ‎(Paris, L'Imprimerie Royale, 1764.) 4to. Without wrappers. In ""Histoire de L'Academie Royale des Sciences. Année MDCCLXII. Avec les Memoires de Mathematiques & de Physique, pour la même Année."" Pp. 17-52. Clean and fine.‎ ‎First printing of a main work on algebraic elimination theory, being Bezout's first paper in this field. This paper provides the method of solution for certain nth-degree equations.‎ Bookseller reference : 53466	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎FELICI, RICCARDO.‎ ‎Ueber die mathematische Theorie der elektrodynamischen Induction. uebersetzt von B. Dessau. herausgegeben von E. Wiedemann.‎ ‎Leipzig, Engelmann, 1899. Orig. printed stiff boards. 121 pp.‎ ‎Ostwald's Klassiker der Exakten Wissenschaften Nr. 109.‎ Bookseller reference : 53474	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €33.57 Buy
‎SKOLEM, TH.‎ ‎Untersuchungen über die moglichen Verteilungen ganzzahliger Losungen gewisser Gleichungen.‎ ‎Kristiania, 1921. Royal8vo. Unopened, uncut in the original printed wrappers. Very fine and clean. 57 pp.‎ ‎First edition.‎ Bookseller reference : 53578	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €47.00 Buy
‎LAPLACE, P.S. (PIERRE-SIMON).‎ ‎Mechanik des Himmels. Aus dem Französischen übersetzt und mit erläuternden Anmerkungen versehen von J.C. Burckhardt. 1.-2. Theil. 2 Bde.‎ ‎Berlin, La Garde, 1800-02. 4to. 2 contemp. hcalf. Title-and tome labels. A paperlabel pasted on lower part of spine. Stamp on foot of title-page. (2),VIII,482"(2),458 pp. + (4) pp. of Publisher's announcement. Light browning to the first few leaves, otherwise fine and clean.‎ ‎First German edition of the general section of the famous ""Traité de Méchanique Céleste"" comprising the translation of its 2 first volumes, being all translated into German.PMM, 252 (the French ed.).‎ Bookseller reference : 53593	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €872.95 Buy
‎"TURING, A.M.‎ ‎A Method for the Calculation of the Zeta-Function. [Received 7 March, 1939. - Read 16 March, 1939]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 48]. - [TURING'S FIRST WORK ON THE ZETA-FUNCTION]‎ ‎London, Hodgson & Son, 1945. Royal8vo. In a recent nice green full cloth binding with gilt lettering to spine. Entire volumes 48 of ""Proceedings of the London Mathematical Society. Second Series"". A very nice and clean copy without any institutional stamps. Pp. 180-197. [Entire volume: (4),477 pp.]‎ ‎First printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous ""Zeta-function Machine"", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. ""Turing had ideas for the design of an ""analogue"" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides."" (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking ""A Method for the Calculation of the Zeta-Function"", which constitutes his first printed contribution to the subject.""After the publication of his paper ""On computable Numbers,"" Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers... Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]..."" (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).‎ Bookseller reference : 54013	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €2,350.25 Buy
‎"BABBAGE, CHARLES‎ ‎Observations on the Notation employed in the Calculus of Functions. (Read May 1. 1820).‎ ‎London, Cambridge University Press, 1822. 4to. In recent paper wrappers. Extracted from the ""Transactions of the Cambridge Philosophical Society"", Volume 1, bound with the title-page of the volume. Fine and clean. (2), (63)-76‎ ‎First appearance of Babbage paper on the notation employed in the Calculus of Functions.""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).‎ Bookseller reference : 54404	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €470.05 Buy
‎"MAXWELL, JAMES CLARK.‎ ‎On Boltzmann's Theorem on the Average Distribution of Energy in a System of material points.‎ ‎London, Taylor and Francis, 1879. 4to. Extracted and rebound in recent green plain wrappers. In ""Transactions of the Cambridge Philosophical Society, vol. 12"" Title-page of vol. 12 withbound. A fine copy. Pp. (2), 547-570.‎ ‎First appearance of Maxwell's paper on Boltzmann's theorem on the average distribution of motion, in which he showed that when a material system has arrived at that steady distribution of motion among its parts which corresponds in real bodies to thermal equilibrium, the energy of the internal motion for any portion of the system is proportional to the number of degrees of freedom of that portion.‎ Bookseller reference : 54406	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €376.04 Buy
‎"TURING, A.M.‎ ‎Systems of Logic based on Ordinals. [Received 31 May, 1938. - Read 16 June, 1938.]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 45]. - [TURING'S PH.D.-THESIS]‎ ‎London, Hodgson & Son, 1939. Royal8vo. In a recent nice red full cloth binding with gilt lettering to spine. Entire volume 45 of ""Proceedings of the London Mathematical Society. Second Series"". Small white square paper label pasted on to lower part of spine, covering year of publication stating: ""A Gift / From /Anna Wheeler"". A very nice and clean copy without any institutional stamps. Pp. 161-240. [Entire volume: (4), 475 pp.].‎ ‎The rare first printing of Turing's Ph.D.-thesis, which ""opened new fields of investigation in mathematical logic"". This seminal work constitutes the first systematic attempt to deal with the Gödelian incompleteness theorem as well as the introduction to the notion of relative computing. After having studied at King's College at Cambridge from 1931 to 1934 and having been elected a fellow here in 1935, Turing, in 1936 wrote a work that was to change the future of mathematics, namely his seminal ""On Computable Numbers"", in which he answered the famous ""Entscheidungsproblem"", came up with his ""Universal Machine"" and inaugurated mechanical and electronic methods in computing. This most famous theoretical paper in the history of computing caught the attention of Church, who was teaching at Princeton, and in fact he gave to the famous ""Turing Machine"" its name. It was during Church's work with Turing's paper that the ""Church-Turing Thesis"" was born. After this breakthrough work, Newman, under whom Turing had studied at Cambridge, urged him to spend a year studying with Church, and in September 1936 he went to Princeton. It is here at Princeton, under the guidance of Church, that Turing in 1938 finishes his thesis [the present paper] and later the same year is granted the Ph.D. on the basis of it. The thesis was published in ""Proceedings of the London Mathematical Society"" in 1939, and after the publication of it, Turing did no more on the topic, leaving the actual breakthroughs to other generations. In his extraordinary Ph.D.-thesis Turing provides an ingenious method of proof, in which a union of systems prove their own consistency, disproving, albeit shifting the problem to even more complicated matters, Gödel's incompleteness theorem. It would be many years before the ingenious arguments and striking partial completeness result that Turing obtained in the present paper would be thoroughly investigated and his line of research continued. The present thesis also presents other highly important proofs and hypotheses that came to influence several branches of mathematics. Most noteworthy of these is the idea that was later to change the face of the general theory of computation, namely the attempt to produce an arithmetical problem that is not number-theoretical (in his sense). Turing's result is his seminal ""o-machines"""" he here introduces the notion of relative computing and augments the ""Turing Machines"" with so-called oracles (""o""), which allowed for the study of problems that could not be solved by the Turing machine. Turing, however, made no further use of his seminal o-machine, but it is that which Emil Post used as the basis for his theory of ""Degrees of Unsolvability"", crediting Turing with the result that for any set of natural numbers there is another of higher degree of unsolvability. This transformed the notion of computability from an absolute notion into a relative one, which led to entirely new developments and in turn to vastly generalized forms of recursion theory. ""In 1939 Turing published ""Systems of Logic Based on Ordinals,""... This paper had a far-reaching influence"" in 1942 E.L. Post drew upon it for one of his theories for classifying unsolvable problems, while in 1958 G. Kreisel suggested the use of ordinal logics in characterizing informal methods of proof. In the latter year S. Feferman also adapted Turing's ideas to use ordinal logics in predicative mathematics."" (D.S.B. XIII:498). A part from these groundbreaking points, which Turing never returned to himself, he here also considers intuition versus technical ingenuity in mathematical reasoning, does so in an interesting and provocative manner and comes to present himself as one of the most important thinkers of modern mathematical as well as philosophical logic.""Turing turned to the exploration of the uncomputable for his Princeton Ph.D. thesis (1938), which then appeared as ""Systems of Logic based on Ordinals"" (Turing 1939). It is generally the view, as expressed by Feferman (1988), that this work was a diversion from the main thrust of his work. But from another angle, as expressed in (Hodges 1997), one can see Turing's development as turning naturally from considering the mind when following a rule, to the action of the mind when not following a rule. In particular this 1938 work considered the mind when seeing the truth of one of Gödel's true but formally unprovable propositions, and hence going beyond rules based on the axioms of the system. As Turing expressed it (Turing 1939, p. 198), there are 'formulae, seen intuitively to be correct, but which the Gödel theorem shows are unprovable in the original system.' Turing's theory of 'ordinal logics' was an attempt to 'avoid as far as possible the effects of Gödel's theorem' by studying the effect of adding Gödel sentences as new axioms to create stronger and stronger logics. It did not reach a definitive conclusion.In his investigation, Turing introduced the idea of an 'oracle' capable of performing, as if by magic, an uncomputable operation. Turing's oracle cannot be considered as some 'black box' component of a new class of machines, to be put on a par with the primitive operations of reading single symbols, as has been suggested by (Copeland 1998). An oracle is infinitely more powerful than anything a modern computer can do, and nothing like an elementary component of a computer. Turing defined 'oracle-machines' as Turing machines with an additional configuration in which they 'call the oracle' so as to take an uncomputable step. But these oracle-machines are not purely mechanical. They are only partially mechanical, like Turing's choice-machines. Indeed the whole point of the oracle-machine is to explore the realm of what cannot be done by purely mechanical processes...Turing's oracle can be seen simply as a mathematical tool, useful for exploring the mathematics of the uncomputable. The idea of an oracle allows the formulation of questions of relative rather than absolute computability. Thus Turing opened new fields of investigation in mathematical logic. However, there is also a possible interpretation in terms of human cognitive capacity."" (SEP).Following an oral examination in May, in which his performance was noted as ""Excellent,"" Turing was granted his PhD in June 1938.‎ Bookseller reference : 54748	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €6,043.50 Buy
‎"MAXWELL, JAMES CLARK.‎ ‎On Boltzmann's Theorem on the Average Distribution of Energy in a System of material points.‎ ‎London, Taylor and Francis, 1879. 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society, vol. 12. Fine and clean. Pp. 547-570.‎ ‎First appearance of Maxwell's paper on Boltzmann's theorem on the average distribution of motion, in which he showed that when a material system has arrived at that steady distribution of motion among its parts which corresponds in real bodies to thermal equilibrium, the energy of the internal motion for any portion of the system is proportional to the number of degrees of freedom of that portion.‎ Bookseller reference : 54753	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €376.04 Buy
‎"BABBAGE, CHARLES‎ ‎Observations on the Notation employed in the Calculus of Functions. (Read May 1. 1820).‎ ‎London, Cambridge University Press, 1822. 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society"", Volume 1. Fine and clean. Pp. (63)-76‎ ‎First appearance of Babbage paper on the notation employed in the Calculus of Functions.""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).Erwin Tomash B47‎ Bookseller reference : 54754	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €470.05 Buy
‎"BABBAGE, CHARLES.‎ ‎On the Determination of the General Term of a New Class of Infinite Series. [Read May 3, 1824].‎ ‎London, Taylor and Francis, 1826 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society"", Volume 2, part 1. . Fine and clean. Pp. (217)-225 + the pasted on title-page.‎ ‎First printing of the early mathematical paper. Erwin Tomash B14.‎ Bookseller reference : 54757	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎"BOOLE, GEORGE.‎ ‎Of Propositions Numerically Definite. [Read March 16th], 1868].‎ ‎London, Taylor and Francis, 1869. 4to. In plain white paper-wrappers with title-page of journal volume pasted on to front wrapper. In ""Transactions of the Cambridge Philosophical Society"", Volume 11. Fine and clean. Pp. 395-411, (1) + the pasted on title-page.‎ ‎First appearance.‎ Bookseller reference : 54758	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €134.30 Buy
‎"HERSCHEL, J. F. W.‎ ‎Description of a Machine for resolving by Inspection certain important Forms of Transcendental Equations. [Read May 7, 1832].‎ ‎London, Taylor and Francis, 1833. 4to. As extracted, in ""Transactions of the Cambridge Philosophical Society"", volume 4. Fine and clean. Pp. (425)-440 + 1 plates.‎ ‎First appearance of Herschel's paper on transcendental equations.‎ Bookseller reference : 54760	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎ARNOLD, JOH. N. (JOHANN NIKOLAUS).‎ ‎Praktischer Ingenieur worinnen die Rechenkunst, Geometrie theoretisch und praktisch bewiesen, vom Proportionalzirkel, von der Bauberechnung, Wasserwage, von Festungswerker, Belagerung und Vertheidigung der Städten, von den Sinustafeln und trigonometri...‎ ‎Köln am Rhein, Kosten des Verfassers, (17939. 4to. Contemp. hcalf. Gilt spine. Title-label with gilt lettering. A paperlabel pasted on lower part of spine. Stamps on title-page. Stamped monogram of the Danish King Frederik VI on inside frontcover. (10),140,168,56,76 pp., 1 folded table and 20 folded engraved plates. Some scattered brownspots, mainly on the first leaves.‎ ‎First edition. - Klaus Jordan, 104.‎ Bookseller reference : 54799	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €1,007.25 Buy
‎"URSIN, GEORG FREDERIK.‎ ‎Øvelses=Exempler af Decimal=regning, Kjædebrøk, Bogstavregning, Ligninger, Logarithme=regning samt Opgaver af Plangeometrien.‎ ‎Kjöbenhavn, Schultz, 1835. Lille 8vo. Samtidigt beskedent hldrbd. stempel på titelblad. 60 pp., tekstfigurer. Med dedikation på fribladet, underskrevet ""Forfatteren""‎ Bookseller reference : 54851	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €60.43 Buy
‎VENTURINI, G.‎ ‎Mathematisches System der reinen taktik zur uebersicht und zum gebrauch für officiere und für Lehrer dieser Wissenschaft in Militairschulen.‎ ‎Braunschweig, Vieweg, 1802. Cont. hcalf. Titlelabel with gilt lettering. Upper compartment on spine, rubbed. Stamp on title. VI,132 pp.‎ Bookseller reference : 54940	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €134.30 Buy
‎EUCLID (EUKLID) OF ALEXANDRIA.‎ ‎Euclides Elemente, für den gegenwärtigen Zustand der Mathematik bearbeitet, erweiter und fortgesetzt. Erste Abtheilung (alles ersch. -Book 1-6).‎ ‎Berlin, Matzdorff, 1791. Small 8vo. Contemp. hcalf. Gilt spine. Titlelabel with gilt lettering. Stamps on title-page. 402 pp., 3 folded engraved plates.‎ ‎Contains extensive commentaries to the first 6 Books.‎ Bookseller reference : 55348	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €134.30 Buy
‎MEINERT, FRIEDRICH.‎ ‎Anweisung zum Nivelliren und Profiliren. Mit 5 Kupfertafeln.‎ ‎Halle, Rengerschen Buchhandlung, 1801. Contemp. hcalf. Richly gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on upper part of spine. Stamps on title-page. (4),VIII,340 pp., 5 folded engraved plates. Light scattered browning and 1 leaf strenghtened in right margin.‎ ‎First edition.‎ Bookseller reference : 55399	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €268.60 Buy
‎PENTHER, JOH. FRIEDRICH.‎ ‎Praxis Geometriæ, worinnen nicht nur alle bey dem Feld=Messen vorkommende Fälle, mit Stäben, dem Astrolabio, der Bussole, und der Mensul, in Ausmessung eintzeler Linien, Flächen und gantzer Revier, welche, wenn deren etliche angräntzende zusammen geno...‎ ‎Augsburg, Probst, 1768 u. 1776. Folio. Recent full fabrikoid. Gilt lettering on spine. (10),97,(5) - 55 pp. (Zugabe, with its own titlepage dated 1776) and 39 foldede engraved plates and 2 engraved vignettes. Lower third of all leaves and all plates heavely soiled and foxed.‎ Bookseller reference : 55597	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎TEGNER, P.W.‎ ‎Analytisk retlinet og sphærisk Trigonometrie, til Brug ved det kongelige S'cadet0Academie.‎ ‎Kjøbenhavn, Qvist, 1834. Samtidigt hldrbd., permer moirepræget med guldbordure. Forgyldt rygtitel. Øverste del af ryg med lidt tab. 63,(1) pp., 3 foldetabeller, 1 foldet kobberstukket planche. I udstyr som et gaveeksemplar. Trykt på velin. Aldeles frisk.‎ Bookseller reference : 55898	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €67.15 Buy
‎MATTHISEN, SØREN.‎ ‎En let Arithmetica eller Regne=Kunst, hvorudi findes alle Slags Udregninger udi Kiob og Sal.... Paa nye med Fliid igiennemseet og forbedret.‎ ‎Kiøbenhavn, Brødrene Berling, 1785. 12mo. Samtidigt helldrbd. over træ. Blindtrykte stregdekorationer på ryg. Rester af messinglukke. (8),(216) pp. lettere brugsspor.‎ Bookseller reference : 56123	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €167.87 Buy
‎LE BLOND, G.‎ ‎Élémens D'Algebre, ou du Calcul Littéral. Avec un Précis de la Methode analytique appliquée à la résolution des Équations du premier & du second dégré.‎ ‎Paris, Jombert, 1768. Contemp. hcalf. Gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on spine. Stamps on title-page. XXXII,430,(8) pp., 2 folded plates. Large engraved vignette on dedication-leaf. Internally clean, printed on good paper.‎ ‎Poggendorff I, 1398.‎ Bookseller reference : 56167	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €248.45 Buy
‎GRAY, JOHN.‎ ‎A Treatise of Gunnery.‎ ‎London, William Innys, 1731. Contemp. full calf. 5 raised bands. Richly gilt compartments. Titlelabel with lettering. Gilt borders on covers with gilt cornerpieces. Edges of covers gilt. Wear to upper joint, joint starting. Small stamp on title-page. (4),XLIII,94 pp., 2 pp. of publisher's announcement. Textdiagrams, 1 folded engraved plate. Internally clean and fine, printed on good, thick paper.‎ ‎Scarce first edition. Importent mathematical treatise on ballistics, treating the subject in an axiomatic way and with a long historical preface.Riling, 223.‎ Bookseller reference : 56169	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €1,275.85 Buy
‎SAVERIEN, (ALEXANDRE).‎ ‎Dictionnaire universel de Mathematique et de Physique, ou l'on traite de L'origine, du progrès de ce deuz Sciences & des Arts qui en dépendent, & des diverses révolutions qui leur sont arrivées jusqu'à notre tems avec l'exposition de leurs Princ...‎ ‎Paris, Rollin, Jombert, 1753. Large 4to. 2 contemp. full mottled calf. Raised bands. Tome- and titlelabels with gilt lettering. Richly gilt spines. Corners a bit bumped. With the royal crowned monogram of King Christian VII in gold on red background on upper boards. Stamp on foot of title-pages. (4),XXVIII,483(4),486,(2) pp., 101 large folded engraved plates with numerous figs. (mathematics, physics, applied and pure...). A few scattered brownspots.‎ ‎Scarce first edition of this encyclopedia of the mathematical sciences, pure and applied.Poggendorff II,761.‎ Bookseller reference : 56399	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €1,141.55 Buy
‎BELIDOR, B.F. de.‎ ‎Dictionnaire Portatif de L'Ingenieur, Ou l'on explique les principaux Termes des Sciences les plus nécessaires à un Ingénieur, scavoir: L'Arithmetique, L'Algebre, La Geometrie, L'Architecture.... La Pyrotechnique.‎ ‎Paris, Charles-Antoine Jombert, 1755. Contemp. full mottled calf. Raised bands. Richly gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on spine. Small crack in leather at lower compartment. Stamp on title-page. IX,(3),339 pp. Internally clean.‎ Bookseller reference : 56576	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €241.74 Buy
‎MATTHISEN, SØREN.‎ ‎Compendium Arithmeticum, eller Veyviiser, hvorved man paa korteste og netteste Maade kan ledsages til Regne=Konstens rette Brug. Første formeerede og forbedrede Edition. (+ Sammes:) En kort Formular, til Adskillige Breve udi Husslige, Handels, Vexlers...‎ ‎Kjøbenhavn, Berling, 1747. Lille8vo. Samtidigt hldrbd. Ophøjede bind på ryggen. Blindtrykte stempler i rygfelter. En papirsetiket påsat nederste rygfelt. Revner i skindet ved forreste kapitæl, men permen ikke løs. Stempel på titelbladet. (12),260 pp., 1 blad Mangler (pp.153/54), tekstfigurer. + (4),140 pp. Lettere brugsspor.‎ Bookseller reference : 56607	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎FRANCAIS, J.F.‎ ‎Cours de Géodèsie, á l'usage des Eléves de L'Ecole Royale de l'Artillerie et du Génie. 2.me Edition.‎ ‎Metz, Lithographie de l'Ecole Royale de l'Art.rie et du Genie, 1828. Folio. Original blank blue wrappers. Upper right corner on upper wrapper torn/gone. Original printed titlelabel on spine. Stamp on title-page. (2),85 pp., 4 large folded lithographed plates. Throughout authographed in lithography. Internally clean.‎ ‎Scarce. Published in only a very limited number.‎ Bookseller reference : 56614	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €537.20 Buy
‎NIEUPORT, CHARLES FRANCOIS LE PROUDHOMME D'HAILLY.‎ ‎Mélanges Mathematiques, ou Mémoires sur différens sujets de Mathématiques tant pures qu'appliquées. Premier (- Second) Recueil. 2 Vols. (+ Suite) Mémoire sur l'intégrabilité médiate des équations différentielles, d'un ordre quelconque, et entre un ...‎ ‎Bruxelles, Lemaire, 1794-99. 4to. Bound in one, a bit later, hcalf. Gilt spine. Tome- and titlelabels with gilt lettering. Neath repairs to spine. XXIII,282,(6)XXVI,242,(6) pp., 3 folded engraved plates. + (4),54 pp. Internally clean and fine.‎ ‎Poggendorff II,288.‎ Bookseller reference : 56685	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €517.05 Buy
‎NIEWENGLOWSKI, B.‎ ‎Cours de Géometrie Analytique. Troisieme - Deuxieme Edition. 3 Vols. (1. Sections Coniques. 2. Construction des Courbes Planes - Complements relatifs aux coniques. - Courbes definies par des équations différentielles. 2 vols [out of 3].‎ ‎Paris, Gauthier-Villars, (1894-) 1926. Royal8vo. 2 volumes, both in the original blank wrappers. VI,496 328 pp.‎ Bookseller reference : 56930	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €100.72 Buy
‎"BABBAGE, CHARLES‎ ‎An examination of some questions connected with games of chance (+) On the Application of Analysis to the Discovery of Local Theorems and Porisms. - [BABBAGE'S ONLY PAPER ON PROBABILITY]‎ ‎Edinburgh, William & Charles Tait / London, Longman, etc, 1823. 4to. In recent marbled paper wrappers. Extracted from ""Trans. Roy. Soc. Edinburgh"" 9, pt. 1 (1821). Leaves reinforced in margin. Pp. (6), 153-177, 337-352.‎ ‎First Edition of Babbage's only paper on probability. ""In this paper [Babbage's] concern was primarily mathematical, and we will find considerable skill in the manipulation of functions and polynomials. [...] The major interest in this particular paper [is] the ingenious use of algebra to solve probability problems, especially the devices using the coefficients of polynomials and the roots of unity"" (Dubbey, The Mathematical Work of Charles Babbage, pp. 141-42).Erwin Tomash B22‎ Bookseller reference : 56997	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €1,007.25 Buy
‎HOËNÉ-WRONSKI (HOEHNE), (JÓZEF MARIA).‎ ‎Véritable Science Nautique des Marées spécialement sur les Côtes maritimes et Réforme des Mathematiques par leur Réduction a trois Lois fondamentales.‎ ‎Paris, Amyot, 1853. 4to. Contemp. hcloth. Stamp on title-page. (4),47,(3) pp.‎ ‎First edition of a controversial mathematical paper on the tides.‎ Bookseller reference : 57170	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎MÜLLER, JOHANN WOLFGANG.‎ ‎Auserlesene mathematische Bibliothek oder alphabetisches und wissenschaftliches verzeichnis der besten arithmetischen, algebraischen, geometrischen etc. etc.‎ ‎Nürnberg, Lehnerischen Buchhandlung, 1820. Contemp. hcalf. Gilt spine. Titlelabel with gilt lettering. Stamps on title-page. 22,266 pp. Scattered brownspots.‎ Bookseller reference : 57301	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €134.30 Buy
‎(SCHEIBEL, JOHANN EPHRAIM).‎ ‎Einleitung zur mathematischen Bücherkentnis. 1.-16. Stück (1. Stück in neue Auflage 1772).‎ ‎Breslau, Meyer, 1772-86. Part 1-8 bound in 2 contemp. hcalf. Titlelabels with gilt lettering. Stamp on title-pages. Part 9 -16 uncut in original stiff papercovers. In all ca. 2000 pp.‎ Bookseller reference : 57603	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €470.05 Buy
‎BÜSCH, JOHANN GEORG.‎ ‎Encyclopedie, angaaende de historiske, philosophiske og mathematiske Videnskaber. Fordansket. (Første-) Anden Deel.‎ ‎Kiøbenhavn, Simmelkiær, 1783. Samtidigt hldrbd. Rygforgyldning. Forgyldt skindtitel. 2 etiketter påsat ryggen. Stempel på titelblad. 88),432,300 pp., 1 kobberstukket foldeplanche.‎ ‎Første danske udgave.‎ Bookseller reference : 57623	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €161.16 Buy
‎BION, NICOLAI (und) JOHANN GABRIEL DOPPELMAYR.‎ ‎Neueröffnete mathematische Werckschule, oder gründliche Anweisung, wie die mathematische Instrumenten nicht allein schicklich und recht zu gebrauchen, sondern auch auf die beste und accurateste Art zu verfertigen, zu probiren, und allezeit in guten St...‎ ‎Nürnberg, Monath, 1765. 4to. Cont. hvellum. Titlelabel with gilt lettering. Stamps on first title-page. Engraved frontispiece, 3 title-pages. (14),432(8),48(12),176 pp. and 62 large folded engraved plates (30+20+12). Clean and fine.‎ ‎The last edition of this esteemed work on instruments. - Poggendorff I:194.‎ Bookseller reference : 57634	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €1,141.55 Buy
‎"THE MAGNETRON ISSUE - FISK, J. B. (+) H. D. HAGSTRUM (+) P. L. HARTMAN.‎ ‎The Magnetron as a Generator of Centimeter Waves. Developments at the Bell Telephone Laboratories, 1940-1945.‎ ‎New York, American Telephone and Telegraph Company, 1946. 8vo. In the original printed blue wrappers. In ""The Bell System Technical Journal"", Volume XXV, Number 2, April 1946. Light miscolouring to spine and previous owner's name to front wrapper. Other wise a fine and clean copy. Pp. (4), 167-349.‎ ‎First printing of Bell Labs Magnetron issue. The Magnetron is a high-powered vacuum tube that through a stream of electrons in a magnetic field generates microwaves. This reduced the size of radar sets which made it possible to install them in anti-submarine aircrafts and escort ships. This had a profound influence on the warfare during WWII. Today magnetrons are commonly used in microwave ovens and in various radar applications.""The studies of Fisk, H. D. Hagstrum, and P. L. Hartman [the present paper] increased the understanding of the role that the various possible modes of oscillation played in magnetron operation and the effect of the wire straps - which later evolved into two pair of concentric copper rings."" (Millman, S. A History of Engineering & Science in the Bell System, 1984, p. 173).‎ Bookseller reference : 57762	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €268.60 Buy
‎"[CALANDRI, FILIPPO].‎ ‎Aritmetica. - [THE FIRST ILLUSTRATED ITALIAN BOOK ON ARITHMETIC]‎ ‎Firenze, Lorenzo de Morgiani and Giovanni Thedesco da Maganza, 1491. 8vo. Leaves loosely inserted in a later full vellum binding with four raised bands, preserved in cloth clamshell box. Several loose leaves. Several leaves closely shaved, some with minor loss of text, all with loss of signatures. 83 ff. (out of 104 ff).‎ ‎Rare first edition of the first illustrated Italian book on arithmetic, also constituting one of the first inexpensive illustrated textbooks making it available to many more students than earlier teaching materials. The woodcuts, which range from ornamental classicizing borders framing multiplication tables to lively depictions of people and animals that illustrate word problems, are exquisite examples of the flowering of Florentine woodcut illustration in the 1490s.Two variant issues were published simultaneously: One by Lorenzo Morgiani and Giovanni Petri, 1 january 1491/92 and the present by Lorenzo de Morgiani and Giovanni Thedesco da Maganza, 1491. Priority of issue has not been established (Hain, Smith, BM-Ital., De Morgan and Tomash & William quote this variant as the first), but there can be no doubt this present variant by far is the rarest. Calandri here gives the leading rules for integers and for lire, soldi and denari, and likewise puts division down in examples. Calandri is the first to give long divisons in the modern form, known to the Italian writers by the name ""a danda"". ""Indeed Calandri gives only the 'a danda' method, omitting the galley forms, and is therefore fully a century ahead of his time."" (David E. Smith). - In Augustus de Morgan's bibliography: Arithmetical Books from the Invention of Printing to the Present Time, 1847, Calandri's Arithmetic is listed as the first. GW 5884" BMC VI68I BM-Ital 136 Oates 2423 Klebs 236.1 Stillwell 154 Goff C-34 Smith, Rara. Pp. 47-49 Tomash & William C9 Hain 4234. De Morgan p. 1.‎ Bookseller reference : 57782	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €6,043.50 Buy
‎VEGAS, GEORG.‎ ‎Forelæsninger over Mathematiken. Første deel, indeholdende regnekunsten og Algebra. Fordansket, forkortet og for endeel omarbeidet af F.G.H. Mourier.‎ ‎Kjøbenhavn, Christensen, 1813. Samtidigt hldrbd. Forgyldt rygtitel. Ryg lidt slidt. Stempel på titelblad. Gl. ejernavn på titel og friblad: M. Moltke. VIII,388,(4) pp. Spredte brunpletter.‎ Bookseller reference : 57981	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €60.43 Buy
‎"SONIN, N. (NIKOLAY YAKOVLEVICH).‎ ‎(Sur la fonction discontinue (x) et ses applications par N. Sonin). In Russian, but transcribed by the author in his own hand on the title-page.‎ ‎Varsovie, 1889. Orig. printed wrappers. (2),78 pp. Inscribed to the Danish mathematician Niels E. Nørlund: ""A Monsieur N. Nörlund/ hommage de l'auteur"" together with the title translated into French by Sonin.‎ ‎First edition. ""Sonin made a substantial contribution to the theory of special functions" the unifying idea of his researches was to establish a few convenient definitions of initial notions and operations leading to broad and fruitful generalizations of these functions.... From 1901 to 1915 president of the Scientific Committee of the Ministry of National Education. With A. A. Markov, Sonin prepared a two-volume edition of the works of Chebyshev in Russian and French. (DSB).‎ Bookseller reference : 58149	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €161.16 Buy
‎ELM, P. H. (H. P. SELMER).‎ ‎Forsøg til at angive et nasjonalt kunstsprog i den lavere matematik.‎ ‎Kjöbenhavn, Popp, 1828. 8vo. I det originale hollanderede bind med håndskrevet titeletiket på forpermen. Nyere shirtingsryg. Lidt spredte brunpletter. 38pp.‎ ‎Originaltrykket af Selmers første afhandling. Eksemplaret har tilhørt Rasmus Rasks halvbroder H. K. Rask og bærer hans navnetræk på titelbladet.Bibl. Dan. II, 6.‎ Bookseller reference : 58234	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €100.72 Buy
‎"WESSEL, CASPAR. - THE FIRST SYSTEMATICAL THREATMENT OF COMPLEX NUMBERS.‎ ‎Om Directionens analytiske Betegning, et forsøg, anvendt fornemmelig til plane og sphæriske Polygoners Opløsning. (Essai sur la représentation analytique de la direction, avec des applications, en particular à la détermination des polygones plans et d...‎ ‎Kiøbenhavn, Johan Rudolph Thiele, (1797) 1799. 4to. Uncut and unopened in original blue boards. Published in: ""Nye Samling af det Kongelige Danske Videnskabernes Selskabs Skrifter."" Vol. V. Wessel's paper: pp.469-518 and 3 folded engraved plates (the last plate inserted at p. 463). The whole volume V offered in its original binding. Engraved titlevignette. XII,670 pp., 15 engraved plates. 4 leaves with upper right corners gone, not affecting Wessel's paper.‎ ‎First edition of this important first systematical treatment of the theory of complex numbers and at the same time, the first work to add vectors in three-dimensional space.""Wessel’s fame as a mathematician is based entirely on one paper, written in Danish and published in the Mémoires of the Royal Danish Academy, that established his priority in publication of the geometric representation of complex numbers. John Wallis had given a geometric representation of the complex roots of quadratic equations in 1685"" Gauss had had the idea as early as 1799 but did not explicitly publish it until 1831. Robert Argand’s independent publication in 1806 must be credited as the source of this concept in modern mathematics because Wessel’s work remained essentially unknown until 1895, when its significance was pointed out by Christian Juel. The title of Wessel’s treatise calls it an ""attempt"" to give an analytic representation of both distance and direction that could be used to solve plane and spherical polygons. The connection of this goal with Wessel’s work as a surveyor and cartographer is obvious. The statement of the problem also suggests that Wessel should be credited with an early formulation of vector addition. In fact, Michael J. Crowe, in A History of Vector Analysis (University of Notre Dame Press, 1967), defines the first period in that history as that of a search for hypercomplex numbers to be used in space analysis and dates it from the time of Wessel, whom he calls the first to add vectors in three-dimensional space."" (DSB).‎ Bookseller reference : 58364	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €3,357.50 Buy
‎ANONYMOUS.‎ ‎Kurze und deutliche Anweisung zum Feldmessen für einem forstgerechten Förster wornach derselbe sein anvertrautes Forst=Revier vermessen, dasselbe nach Hannoverschen Qvadrat=Ruthen und Morgenzahl und mittelst eines verjüngten Massstabes in einen Riss b...‎ ‎Göttingen und Gotha, Dieterich, 1773. Small 8vo. Contemp. hcalf. Gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on spine. Stamp on title-page. 108 pp., 18 folded engraved plates. A few faint scattered brownspots.‎ Bookseller reference : 58388	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €268.60 Buy
‎TEMPELHOF, (GEORG FRIEDRICH von).‎ ‎Le Bombardier Prussien ou du Mouvement des Projectiles en supposant la résistance de l'air proportionelle au quarré des vitesses.‎ ‎Berlin, de l'Auteur - Spener, 1781. Uncut in original blank, green stiff wrappers. Handwritten titlelabel on spine. A paperlabel pasted on lower part of spine. XXVI,(6),128 pp., 1 folded engraved plate. The first 5 leaves with a dampstain in upper margins.‎ ‎Scarce first edition. - Poggendorff II,1078.‎ Bookseller reference : 58400	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €470.05 Buy
‎DECKER, AUGUST.‎ ‎Lehrbuch der höheren Geodäsie. Mit drei Figurentafeln.‎ ‎Mannheim, Hoff, 1836. Contemp. hcalf. Gilt spine, gilt lettering. Stamp on title-page. VI,304 pp., 3 folded lithographed plates. Clean and fine.‎ Bookseller reference : 58417	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €134.30 Buy
‎"KÄSTNER, ABRAHAM GOTTHELF.‎ ‎Begyndelsesgrunde af Arithmetik, Geometrie og plane og sphæriske Trigonometrie. Oversat efter fjerde forøgede Oplag af Jacob Wolf. Mathem. Begyndelsesgr. 1 Deels 1ste Afdeling.‎ ‎Kiøbenhavn, Gyldendals Forlag, 1788. 8vo. Indbundet i et samtidigt lidt slidt hellæderbind. Enkel stregforgyldning og fem ophøjede bind på ryggen. Forgyldt rygtitelfelt delvist slidt væk. Enkel blindtrykt ramme på permerne. Forgyldte initialer ""F. S. S."" på forpermen. Brugsspor ved kapitæler og false. Hjørner stødte. Enkelte spredte brunpletter og noter. (24),542,(1) pp.‎ ‎Den første danske oversættelse af Abraham Gotthelf Kästners ""Anfangsgründe der Arithmetik Geometrie ebenen und sphärischen Trigonometrie, und Perspectiv.""Bibl. Dan. II: 8.‎ Bookseller reference : 58800	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €201.45 Buy
‎"WEIERSTRASS, KARL.‎ ‎Über eine besondere Gattung von Minimalflächen.‎ ‎Berlin, Harrwitz und Gossmann, 1867. 8vo. Uncut opened in the original printed wrappers. In ""Monatsbericht der Königlich Preussischen Akademie der Wissenschaften zu Berlin"", August 1867. Pp. 511-518. [Entire heft: Pp. 511-488].‎ ‎First edition.‎ Bookseller reference : 58878	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €100.72 Buy
‎MATTHISEN, SØREN.‎ ‎En let Arithmetica eller Regne=Kunst, hvorudi findes alle Slags Udregninger udi Kiob og Sal. Forøget og forbedret.‎ ‎Kiøbenhavn, Brødrene Berling, 1772. 12mo. Samtidigt helldrbd. med klap, blindtrykte dekorationer på ryg og permer. (200) pp.‎ Bookseller reference : 5891	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €167.87 Buy
‎"MAUPERTUIS, (PIERRE LOUIS MOREAU DE).‎ ‎Sur une Question de Maximis et Minimis. - [MAUPERTUIS'S FIRST PAPER]‎ ‎Paris, De l'Imprimerie Royale, 1728.. 4to. In a nice contemporary full mottled calf binding with five rasied bands and rchly gilt spines. Gilt borders on covers. In ""Histoire de L'Academie Royale des Sciences. Année M. DCCXXVI"", entire volume offered. Small tear to upper part of spine and ex-libris pasted on to pasted down front end-paper. A fine copy. Pp. 84-94. [entire volume: (8), 84, 341, (2) pp + 16 folded plates.‎ ‎First appearance of Maupertuis's first mathematical paper, a solution to the problem maxima and minima.""His early paper represent the the possibilities opened up by the calculus. [The present paper] is as much an exploration of the power of the method to discover unexpected results as it is the solution to a specific problem. The problem is a simple one from plane geometry: to fine trapezoids of greatest and least area, given certain conditions for the length of the sides."" (Terrall, The Man Who Flattened the Earth: Maupertuis).‎ Bookseller reference : 58915	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €402.90 Buy
‎"GAUSS, CARL FRIEDRICH.‎ ‎Demonstratio Nova Theorematis Omnem Functionem Algebraicam Rationalem Integram unius Variabilis in Factores Reales Primi vel Secundi Gradus resolvi posse (i.e. English: ""A new proof of the theorem that every integral rational algebraic function of one... - [GAUSS'S DOCTORAL THESIS - HIS FIRST GREAT WORK]‎ ‎Helmstadt, C. G. Fleckeisen, 1799. 4to. Bound uncut in a very nice recent pastiche-binding in brown half calf with elaborately gilt spine and marbled paper covered boards. With repair to title-page, not affecting text. Small restorations to upper margin of leaf A2 and A3. Brownspotted throughout. 39, (1) pp. + engraved plate.‎ ‎Rare first edition of Gauss's first book in which he proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Gauss received his doctorate degree for this work, which is considered his first great work. It marks the beginning of an extraordinary ten years often referred to as his 'Triumphal Decade' with landmark achievements such as the publication of 'Disquisitiones Arithmeticae' and the calculation of the orbit of the newly discovered planet Ceres. On june 16, 1799, even before the thesis was published, Gauss was awarded the title Doctor Philosophiae after the usual requirements of an oral examination, particularly tedious to Gauss, was dropped. In a letter to Bolyai, Gauss's close friend, Gauss described his thesis: ""The title describes the main objective of the paper quite well though I devote to it only about a third of the space. The rest mainly contains history and criticisms of the works of other mathematicians (name d'Alembert, Bougainville, Euler, de Foncenex, Lagrange, and the authors of compendia - the latter will presumably not be too happy) about the subject, together with diverse remarks about the shallowness of contemporary mathematics"" ""Professor Pfaff, Gauss's formal research supervisor, shared with Gauss an interest in the foundations of geometry, but it is mere speculation that the two discussed this topic. Gauss's dissertation is about the fundamental theorem of algebra. The proof and discussion avoid the use of imaginary quantities through the work is analytic and geometric in nature"" its underlying ideas are most suitably expressed in the complex domain. Like the law of quadratic reciprocity, the fundamental theorem of algebra was a recurring topic in Gauss's mathematical work - in fact, his last mathematical paper returned to it, this time explicitly using complex numbers."" (Gauss, A Biographical Study, p. 41). ""There is only one thing wrong with this landmark in Algebra. The first two words in the title would imply that Gauss had merely added a 'new' proof to others already known. He should have omitted ""nova"". His was the first proof . Some before him had published what they supposed were proofs of this theorem - usually called the fundamental theorem of algebra - but logical and mathematical rigor Gauss insisted upon a proof, and gave the first"" (Bell, Men of Mathematics, p. 32) ""Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics."" (Printing & the Mind of Man). Dibner 114‎ Bookseller reference : 59012	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €22,159.50 Buy
‎"HINDENBURG, CARL FRIEDRICH.‎ ‎Novi systematis permutationum combinationum ac variationum primae lineae et logisticae serierum formulis analytico-combinatoriis per tabulas exhibendae conspectus et specimina. - [""FOUNDER OF THE COMBINATORIAL SCHOOL IN GERMANY""]‎ ‎Leipzig, S. L. Crusium, 1781. 4to. Bound uncut in a nice recent cardboard-binding with red leather title-label to spine with gilt lettering. Title-page partly detached. Occassional brownspotting throughout. XII, LXXXIII, (1) pp.‎ ‎Rare first edition of Hindenburg's paper on combinatorics, which partly earned him the title as ""founder of the combinatorial school"" (DSB) in Germany. Combinational mathematics was not new at that time: Pascal, Leibniz, Wallis, the Bernoullis, De Moivre, and Euler, among others, had contributed to it. Hindenburg and his school attempted, through systematic development of combinatorials, to give it a key position within the various mathematical disciplines. ""Combinatorial consideration, especially appropriate symbols, were useful in the calculations of probabilities, in the development of series, in the inversion series, and in the development of formulas for higher differentials. The utility led Hindenburg and his school to entertain great expectations: they wanted combinatorial operations to have the same importance as those of arithmetic, algebra, and analysis. They developed a complicated system of symbols for fundamental combinatorial concepts, such as permutations, variations, and combinations."" (DSB)‎ Bookseller reference : 59015	Livre Rare Book Herman H. J. Lynge & Son Copenhagen Denmark Dinamarca Dinamarca Danemark [Books from Herman H. J. Lynge & Son] €1,611.60 Buy