‎Matemáticas‎

‎"[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.‎

Referencia librero : 57782

‎"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).‎

Referencia librero : 58149

‎"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).‎

Referencia librero : 58364

‎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.‎

Referencia librero : 58400

‎"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.‎

Referencia librero : 58800

‎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.‎

Referencia librero : 5891

‎"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

Referencia librero : 59012

‎"HILBERT, DAVID.‎

‎The Foundations of Geometry. Authorized translation by E.J. Townsend.‎

‎Chicago, Open Court, 1902. Small 8vo. Orig. full red cloth. Wear to topof spine. Old owners name on title-page. VII,143 pp., textfigs. Clean and fine.‎

‎First English edition of Hilbert's ""Grundlagen der Geometrie"" from 1899, one of the most influential publications in 2oth Century mathematics. Throughout the 19th century geometry was developed far beyond our intuitive conception of space" hyperbolic geometry was discovered by Gauss, Bolyai, and Lobachevsky and elliptic geometry by Riemann. However, Euclidean and non-Euclidean geometry still involved an intuitive idea about the concepts 'point', 'line', 'lies on', 'between', etc. In his 'Grundlagen' Hilbert set out to give a strictly formal formulation of geometry were points, lines, planes are nothing more than abstract symbols and concepts as 'lies on' are simply algebraic relations between these symbols. Through his method Hilbert could analyse independence and completeness of the axioms for geometry and he presented a new smaller set of axioms for Euclidean geometry. It can not be said that the 'Grundlagen' contains new and surprising discoveries, its importance lies in the great influence which Hilbert's method had on all fields of mathematics, and even other sciences as physics, chemistry, and biology. The 'Grundlagen' initiated a whole new paradigm shift and eventually evolved mathematics, throughout the 20th century, into a network of axiomatic formal systems.‎

Referencia librero : 59043

‎"ALEXANDROFF, P.‎

‎Dimensionstheorie. Ein Beitrag zur Geometrie der abgeschlossenen Mengen. [In ""Mathematische Annalen"", 106. band. 1932].‎

‎Berlin, Julius Springer, 1932. Large8vo. Uncut unopened in the original printed wrappers. In ""Mathematische Annalen"", 106. band. 1932. Entire volume offered. Wear to spine, lacking upper part of spine. Otherwise fine. Pp. 161-238. [Entire volume: IV, 795 pp.].‎

‎First appearance of Alexandroff's important paper (which he worked on in 1930) on dimension theory. ""The first half of 1930—the development of homological dimension theory, which built upon his spectral theory"" (DSB).‎

Referencia librero : 59324

‎"JESSEN, BØRGEN.‎

‎Bidrag til Integralteorien for Funktioner af uendelig mange Variable.‎

‎København, Gads Forlag, 1930. 4to. In the original printed wrappers. With author's presentation inscription to front wrapper: ""Hr Docent Dr Phil A. F. Andersen / fra deres hengivne / Børge Jessen"". Light sunning to extremities, otherwise fine and clean. 66 pp.‎

‎First edition of Jessen's doctoral thesis. He later elaborated the thesis into an article that was published in Acta Mathematica in 1934. The same year, he was appointed as a docent at The Royal Veterinary and Agricultural University in Denmark.Børge Christian Jessen (1907 – 1993) was a Danish mathematician best known for his work in analysis, specifically on the Riemann zeta function, and in geometry, specifically on Hilbert's third problem.‎

Referencia librero : 59467

‎HJELTE, C‎

‎Begyndelsesgrundene af Arithmetiken. Lærebog for Eleverne af det kongelige Lancadetacademie.‎

‎Kjøbenhavn, Schultz, 1833. Originalt hshirtbd. Stempler på titelbladet. 86 pp. Lidt spredte brunpletter.‎

Referencia librero : 59744

‎NATIONAL ACADEMY OF SCIENCES -‎

‎Proceedings of the National Academy of Sciences of the United States of America.‎

‎Washington, Office of the Academy, 1924. 8vo. In contemporary green full cloth with gilt lettering to spine. Light wear to extremities and ex-libris pasted on to pasted down front free end-paper. A few stamps to out margin in text, othewise a good copy. VII, 507 pp.‎

Referencia librero : 60055

‎"TORRES, M.L. (LEONARDO TORRES Y QUEVEDO).‎

‎Sur la constuction des machines algébriques. Extrait de la Revue de Mécanique, nos de septembre-octobre 1901. - [THE BIRTH OF COMPUTING - TORRES QUEVEDO'S CALCULATING MACHINES]‎

‎Paris, 1901. Small folio. Original printed wrappers. The fragile wrappers have been expertly restored along the edges. A stain to back wrapper, a closed horizontal tear, and spine re-enforced. A bit of soiling and discolouration. With a library-label to top of front wrapper, from the Bibliothèque des professeurs St-Stanislas, Mons, of which there is a book-plate to half-title and a stamp to title-page. Wrappers loose. Internally some brownspotting and finely restored marginal chipping, far from affecting text. 32 pp. Richly illustrated.‎

‎Exceedingly scarce original offprint of Torres y Quevedo's publication of his seminal algebraic machines, constituting a milestone in computing history. In this thoroughly illustrated publication, Torres y Quevedo explains the construction and operation of the first accurate calculating machines, following his explanation of them before the French Academy of Sciences earlier the same year. ""At the end of the nineteenth century, several analog machines had been proposed for solving algebraic equations. These machines -based not only on kinematics principles but also on dynamic or hydrostatic balances, electric or electromagnetic devices, etc.- had one important drawback: lack of accuracy. Leonardo Torres was the first to beat the challenge of designing and implementing a machine able to compute the roots of algebraic equations that, in the case of polynomials of degree eight, attained a precision down to 1/1000. The key element of Torres' machine was the endless spindle, an analog mechanical device designed to compute log(a +b) from log(a) and log(b). This short account gives a detailed description of this mechanism."" (Federico Thomas: A Short Account on Leonardo Torres' Endless Spindle). Leonardo Torres y Quevedo (1852 -1936), civil engineer and mathematician, was a one of the most important Spanish inventors of all time. Although little known outside of Spain and France in his life-time, he was an inventor of the utmost importance and would later be recognized as one of the most significant inventors of the beginning of the twentieth century. Apart from pioneering accurate automated calculation machines, he was also a pioneer in the development of the radio control, the inventor of a chess automaton (the first decision-making automaton), an innovative designer of the three-lobed non-rigid Astra-Torres airship as well as the Whirlpool Aero Car located in Niagara Falls, and with his Telekine, he created wireless remote-control operation principles.""Leonardo Torres was probably the most eminent Spanish engineer in the first half of the 20th century. He had a great influence, truncated by the Spanish Civil War, in the development of automatic control in Spain. As Randell points out in, we can only speculate on what might happened if Torres' writings had become better known to the English-speaking world. For instance, he qualifies Torres' paper Essays on Automatics as ""a fascinating work which well repays reading even today."" The paper contains what Randell believes to be the first proposal of the idea of floating-point arithmetic. It seems clear that Torres' contributions deserve much wider appreciation outside Spain"". (Federico Thomas: A Short Account on Leonardo Torres' Endless Spindle). ""Because of Torres Quevedo's work on analog machines, the Paris Academy of Sciences welcomed his ""Calculating Machines"" report in 1900. As a result, he was elected to the Academy of Sciences in Madrid in 1901, where he delivered a lecture on algebraic machines.The endless spindle was a critical component of the 8-term equation-solving computing machine. It created sums to answer the algorithm's central equation. The mechanism was the first of its sort, and it was the most intriguing and unique of Torres Quevedo's inventions.Torres Quevedo's calculating machine was both theoretically and practically groundbreaking. The endless spindle is a mechanical device that evaluates an expression's logarithm as the sum of numerous logarithms, overcoming the difficulty of reaching enough precision with an automatic set of parts."" (The History of the Computer) The algebraic machine of Torres was an analog computing device, featuring a mechanism based on cone-shaped pulley with a helical groove around it. The machine was used for the resolution of equations like: + Ax = B or + Ax = B. His publications marked the beginning of a new era in mathematical theory, and his contributions resulted in the creation of cutting-edge new machinery. ""Torres Quevedo's writings ushered in a new era in mathematical theory based on new concepts. His contributions led to the development of innovative new machines.He built a series of analog calculating machines to complement his theoretical work, all of which were mechanical."" (Torres Quevedo Museum - where another copy of the present offprint is displayed) ""Leonardo Torres (1852-1936), usually known as Leonardo Torres y Quevedo in Spanish-speaking countries, was a Spanish engineer and mathematician. He was president of the Academy of Sciences of Madrid, a member of the French Academy of Sciences, and famous-mainly in Spain and France- as a prolific and successful inventor... Some of the earliest Torres' inventions took the form of mechanical analog devices, considered of great originality, aiming at implementing what he called the Algebraic Machine. This machine had the ability of computing the values of arbitrary polynomial functions in one variable. Since it was an analogue machine, the variable could attain any value, not only a preestablished set of discrete values, contrarily to what happened, for example, with the celebrated Babbage's Difference Engine, an engine that used the method of finite differences to generate successive values of polynomial functions. In Torres' Algebraic Machine, all quantities were represented by means of angular displacements in logarithmic scale. Then, adding a counter to keep track of the number of turns, it was possible to compactly represent very large variations for all quantities. When the wheel representing the variable spun round, the final result was obtained as the angular displacement of another wheel that accumulated the addition of all involved monomials. When this result was zero, a root of the function was found. Using proper modifications, it was even possible to obtain the complex roots. The use of logarithms had two main advantages. Firstly, assuming that all absolute errors for the angular displacements were constant, all relative errors for the represented quantities were also kept constant. Secondly, the computation of monomials was greatly simplified. Actually, the logarithm of a monomial of the form aixi is an expression, ai+ilogx, that can be easily calculated using a differential transmission. Nevertheless, the use of logarithms had a number of disadvantages. It was necessary to introduce some transformations to ensure that all quantities were positive and, what was much more challenging, it was necessary to design a sophisticated mechanical device able to compute log(a +b) from log(a) and log(b) that would permit to accumulate the sum of all involved monomials. This device was the endless spindle. In 1893, Leonardo Torres presented, before the Academy of Exact, Physical and Natural Sciences, a memoir on his Algebraic Machine. In his time, this was considered an extraordinary success for Spanish scientific production. In 1895 the machine was presented at a congress in Bordeaux. Later on, in 1900, he would present his calculating machine before the Paris Academy of Sciences."" The present offprint, which richly illustrates, demonstrates, and presents his seminal calculating machines, was published after his presentation at the Academy of Sciences in Paris, and as he says in the preface to the present offprint ""the theoretical principles of these machines have very recently been exposed in a mémoire entitled ""Machines à calculer"" [See Tomash & Williams: T 47, printed 1902], presented by me at the l'Académie des Sciences, which should appear also in the ""Recueil des Savants étrangers."" (own translation from p. (5) ). This publication is of the utmost scarcity, and we can locate merely two copies of this offprint: at the Torres y Quevedo-museum in Spain, and at the Hungarian Academy of Sciences.‎

Referencia librero : 60101

‎EUCLID (+) GEORG FOURNIER (+) BAZIN.‎

‎Sex Primi Elementorum Geometricorum (+) Elementa Astronomica.‎

‎London, Edwardi Story, 1654. 12mo. In contemporary full vellum. Binding slightly twisted. Front board with large stain. Annotations in contemporary hand to pasted down front end-paper and free front end-paper. Small marks with annotations pasted in margin. Internally fine and clean. (10), 302, 72 pp. with many diagrams and illustrations in text.‎

‎Rare first edition of George Fournier's work on Euclid's Element. “Some of the benefits of the smaller format adopted by Clavius’s edition were negated by the length of the text, and the next phase of Euclidean publication during the seventeenth century saw the rapid adoption of smaller formats, culminating in a number of tiny duodecimo issues such as the 1644 Paris edition of Georges Fournier, later reprinted in Cambridge. (In note:) Issued as a duodecimo in Paris in 1644 and 1654, and in London in 1654 and 1665.” (Anja-Silvia Goeing, Early Modern Universities: Networks of Higher Learning). Georges Fournier, a French Jesuit priest, geographer and mathematician, served as a naval military chaplain on a ship of the line, and acquired a strong knowledge of technical and naval matters. In 1642, he published the treaty Hydrographie, where he attempted to provide a scientific foundation to the design of ships. He also authored a Treaty of fortifications or military architecture, drawn from the most estimated places of our times, for fortifications, whose original edition was published in Paris in 1649 by Jean Hénault at the Salle Dauphine of l'ange gardien. Another edition was published in 1668 in Mayence by Louis Bourgeat. His works on Euclidean geometry (Paris, 1644 and 1654) were translated into English, and gave rise to three successive editions.Georges Fournier taught René Descartes.Steck IV, p. 100.‎

Referencia librero : 60194

‎"LOBATSCHEVSKY (LOBACHEVSKY, LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKIJ), (NIKOLAI IVANOVITSCH).‎

‎Ueber die Convergenz der uendlichen Reihen (i.e. English: ""On the Convergence of Infinite Series"").‎

‎(Kazan, Universitäts-Buchdruckerei, 1841). 4to. In a contemporary modest half calf over marbled paper boards. Published in a supplement to ""Meteorologische Beobachtungen aus dem Lehrbezirk der Kaiserlich. Russischen Universitaet Kasan"". Heft 1, 1835–1836. 1841. Small stamp to upper outer corner of front free end-paper. A few leaves brownspotted. Book block split between pp. 4 and 5, otherwise a fine copy. 48 pp.‎

‎Exceedingly rare first appearance of this work by Lobachevsky in which he returns to convergence of infinite series, on the foundations of calculus and real analysis, which he previous had dealt with in his 1834-textbook Algerbra and his 1834-paper ‘Ob ischezanii trigonometricheskikh strok’. Here, he expands and further develops the modern definition of the idea of a function in the works of Dirichlet, Poisson, and himself, adding and supplying more proofs. Primarily famous for his non-Euclidean geometry, Lobachevsky published a few papers on such nongeometrical subjects as algebra and the theoretical aspects of infinite series. The chief thrust of his scientific endeavor was, however, geometrical, and his later work was devoted exclusively to his new non-Euclidean geometry, the present work being one of his last on algebra and infinite series.‎

Referencia librero : 60236

‎"COTES, ROGER.‎

‎Harmonia Mensurarum, sive Analysis & Sythensis per rationum & angulorum mensuras promotae: accedunt alia Opuscula Mathematica. - [""EARLIEST ATTEMPT TO FRAME A THEORY OF ERRORS""]‎

‎Cambridge, 1722. 4to. In contemporary full calf with five raised bands with red leather title-label with gilt lettering to spine. Boards with a few scratches, missing small parts of the leather. corners bumped. Upper endbands showing. Upper outer corner with dampstain, primarily affecting first leaves, otherwise a good copy. Printed on good paper. (20), 249, (3), 125, (1) pp. + 1 folded plate.‎

‎First edition of Cotes’ important posthumously published work. Roger Cotes (1682-1716) published only one scientific paper in his lifetime, and the present work thus constitutes the earliest and main record of his mathematical achievements. According to Augustus de Morgan, this is 'the earliest work in which decisiveness progress was made in the application of logarithms and of the properties of the circle of the calculus of fluents'"" it includes the first version of the Newton-Cotes formulas, the first introduction of Euler's formula, and the 'Cotes' theorum' of trigonometry. Furthermore, it contains the “Earliest attempt to frame a theory of errors.” (Jungnickel, Cavendish: The Experimental Life, p. 150). Roger Cotes (1682–1716), much respected in his own right, is also known for working closely with Isaac Newton by proofreading the second edition of his famous book, the Principia, before publication. He became the first Plumian Professor at Cambridge University from 1707 until his death. When Cotes died Cambridge in 1716 at the early age of 33 Isaac Newton famously remarked, ""If he had lived we would have known something."" Tomash & Williams C184 Norman 519 Wallis 246 Babson (Supplement) 29‎

Referencia librero : 60246

‎BURJA, A.‎

‎Der Selbstlernende Geometer, Oder Deutliche Anweisung Zur Messkunst. 2 vols.‎

‎Berlin, Lagarde und Friedrich, 1787. 8vo. 2 volumes bound in one modest contemporary cardboard-binding. Paper title-label to spine. Wear to extremities, some of the marbled paper worn of. Spine partly split. Internally fine and clean. XXX, 360, 416 pp. + frontispiece.‎

‎Rare first edition of Professor Burja's early textbook on geometry.‎

Referencia librero : 60387

‎"TARSKI, ALFRED (+) ALONZO CHURCH [Editor].‎

‎On The Calculus Of Relations (In: ""The Journal Of Symbolic Logic"").‎

‎(No place), The Association for Symbolic Logic, 1941. Large 8vo. Bound in blue half cloth with silver lettering to spine. In ""Journal of Symbolic Logic"", Volume 5. Small paper label to lower part of spine and upper inner margin of front board. Stamp to title-page and last leaf, otherwise internally fine. Pp. 73-89. (Entire copy: (4), 188 pp.).‎

‎First appearance of Tarski's groundbreaking work in mathematical logic. Published in 1941, it revolutionized the study of relations by introducing a formal calculus that provided a rigorous foundation for understanding and reasoning about relations.By introducing a formal calculus, Tarski provided mathematicians with a rigorous framework for reasoning about relations, leading to advancements in diverse fields of mathematics and beyond. His contributions laid the groundwork for the exploration of abstract algebra, order theory, and model theory, and found practical applications in computer science.‎

Referencia librero : 60430

‎"LOBACHEVSKY (LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKIJ), (NIKOLAI IVANOVITSCH).‎

‎Pangeometriya (i.e. Pangeometry). (In: ""Uchenye zapiski""). - [""THE MOST CONSEQUENTIAL AND REVOLUTIONARY STEP IN MATHEMATICS SINCE GREEK TIMES""]‎

‎Kazan, Kazan University Press, 1855-56. 4to (263 x 216 mm). In a nice later half calf binding with four raised bands and marbled paper covered boards. Extracted from ""Uchenye zapiski, Imperatorskago Kazanskago Universiteta"", 1855, vol. 1. Two library-stamps to p. 51 with offsetting to p. 50 and small stamp to last free end-paper. With very light creasing to outer margin, otherwise a fine and clean copy. 56 pp.‎

‎Exceedingly rare first appearance of Lobachevsky’s landmark 'Pangeometry', a seminal work that serves as a synthesis of his exploration into non-Euclidean geometry and its practical applications and is widely considered his clearest account of the subject. It is also the conclusion of his life's work and the last and final attempt he made to acquire recognition. Lobachevsky's contributions not only marked a turning point in mathematical thought, but were also a catalyst for profound shifts in physics, and philosophy as they expanded the boundaries of human understanding, challenging 2000 year old conventional wisdom"" consequently, he is often referred to as ""The Copernicus of Geometry"". Lobachevsky wrote his Pangeometry in 1855, the year before his death, at a time when he was completely blind. He dictated two versions, a first one in Russian (the present), and a second in French. Despite his revolutionary work, Lobachevsky’s received little, if any, attention from the scientific community. One reason for this was that his works were published in very small numbers in relatively obscure journals – they seem to have had minimal circulation even within Russia. The present treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. “Lobachevskii’s geometry represents the culmination of two thousand years of criticism of Euclid’s fifth, or parallel, postulate, which states that given a line and a point not on the line, there can be drawn through the point one and only one coplanar line not intersecting the given line. As this postulate had stubbornly resisted all attempts (including Lobachevskii’s) to prove it as a theorem, Lobachevskii came to the realization that it was possible to construct a logically consistent geometry in which the Euclidean postulate represented a special case of a more general system that allowed for the possibility of hyperbolically curved space. Lobachevskii’s system refuted the unique applicability of Euclidean geometry to the real world, and pointed the way to the Einsteinian concept of variably curved space” (Norman 1379.). “At the same time as Lobachevsky, other geometers were making similar discoveries. Gauss had arrived at an idea of non-Euclidean geometry in the last years of the eighteenth century and had for several decades continued to study the problems that such an idea presented. He never published his results, however, and these became known only after his death and the publication of his correspondence. Janos Bolyai, the son of Gauss’s university comrade Farkas Bolyai, hit upon Lobachevskian geometry at a slightly later date than Lobachevsky. Since Gauss did not publish his work on the subject, and since Bolyai published only at a later date, Lobachevsky clearly holds priority.” DSB. Lobachevsky's non-Euclidean geometry paved the way for further advancements in mathematics, including the development of differential geometry and the study of Riemannian manifolds. These areas of mathematics have found applications in fields as diverse as physics, engineering, and computer science. Furthermore, his work laid the groundwork for Albert Einstein's theory of general relativity, which relies on the concept of curved spacetime. It showed that there is no single ""correct"" geometry, but rather multiple valid systems. This led to a broader understanding of the nature of axiomatic systems and their relation to reality - implications that extend well beyond the realm of mathematics, shaping our understanding of space, reality, and the limits of human knowledge.‎

Referencia librero : 60473

‎"BION, NICOLAI.‎

‎Neu-eröffnete Mathematische Werck-Schule, Oder Gründliche Anweisung, Wie die Mathematische Instrumenten (+) Weitere Eröffnung der neuen Mathematischen Werck-Schule. - [""THE MOST FAMOUS BOOK DEVOTED TO INSTRUMENTS""]‎

‎Franckfurt und Leipzig, Hoffmännischen Buchladen in Nürnberg, 1712 (+) Nürnberg, Conrad Monath, 1717. 4to. In contemporary full vellum with title in contemporary hand to spine. A few dots and mark to extremities and a few annotation to pasted down front end-paper. A very nice copy. (12), 394 pp. + frontispiece and 28 plates"" (8), 48 pp. + 11 plates.‎

‎First German edition of, according to historian of science David M. Knight, ""the most famous book devoted to instruments"". The work is one of the best of that time on scientific instruments, including the compass of proportion, surveying and astronomical instruments, etc. The short work bound withbound is “written by Doppelmayr and illustrates a number of instruments, which, although claiming to be from Bion’s workshop, do not appear in any of Bion’s French editions. The most inventive are optical-binocular and reflecting telescopes”. (Erwin Tomash). The present work was translated from the French original edition, published in 1709, by J. G. Doppelmayr. Erwin Tomash B161 & B162.‎

Referencia librero : 60640

‎SYLVIUS, CHRISTIAN.‎

‎Compendium practico-geometricum mechanice udregnet, aldrig tilforn i det danske Sprog.‎

‎Kiøbenhavn, Høpffner, (1736). 4to. In a nice full calf Cambridge mirror-style binding with five raised bands. Blind-tooled ornamentation to spine and boards. Crowned monogram (Christian VI) to both front and back boards. Boards with a few holes in the leather and some scratches. Internally fine and clean, an overall vey nice copy. (12), 100 pp. + 2 plates.‎

‎Rare early Danish work on applied geometry. From library of Danish King Christian VI.OCLC only lists two copies, both in Copenhagen. Bibliotheca Danica II, p. 43.‎

Referencia librero : 60653

‎CLEMM, H.W.,‎

‎Heinrich Wilhelm Clemms mathematisches Lehrbuch oder vollständiger Auszug aller so wohl zur reinen als angewandten Mathematik gehörigen Wissenschaften nebst einem Anhang darinnen die Naturgeschichte und Experimentalphysik in einem kurzen Plan vorgetra...‎

‎Stuttgart, Johann Benedict Mezler, 1764. 8vo. In contemporary half calf with five raised bands. Wear to extremities, primarily spine. Stain in inner margin of pp. 1-36, otherwise internally nice and clean. (22), 448, 336, 64 pp. + 24 plates.‎

‎First edition of Clemm's textbook on mathematics including an appendix on natural history. The work was reprinted several times during the second half of the 18th century.‎

Referencia librero : 60761

‎STURM, JOHANN CHRISTOPH.‎

‎Mathesis enucleata, Cujus praecipua contenta sub finem praefationis, uno quasi obtutu spectanda, exhibentur.‎

‎Nuremberg, Wolfgangi Maurittii Endteri, 1689. 8vo. In contemporary full vellum with title in contemporary hand to spine. Small paper-label pasted on to top of spine. Extremities with light soiling and a few spots. Internally nice and clean. (40), 474, (4) pp. + 30 plates, mostly loosely inserted. Small contemporary geometrical illustration in contemporary hand are inserted in the text.‎

‎Rare first edition of Sturm’s textbook on mathematics and geometry. Johann Christoph Sturm(1635 – 1703) was a German mathematician, astronomer who made significant contributions to mathematics and astronomy, particularly in the areas of geometry, trigonometry, and optics. He wrote several influential textbooks on mathematics and natural philosophy that were widely used in European universities during the 17th and 18th centuries. One of Sturm's most notable contributions to mathematics is the Sturm's theorem, which he developed in collaboration with his brother, Jacob Sturm. This theorem is used to count the number of roots of a polynomial equation within a given interval‎

Referencia librero : 60898

‎"OZANAM, JACQUES.‎

‎Recreations mathematiques et physiques, qui contiennent plusieurs problemes d'aritmetique, de geometrie, de musique, d'optique, de gnomonique, de cosmographie, de mecanique, de pyrotechnie, et de physique. Nouvelle edition. 4 vols. - [FOUNDING THE GENRE ""RECREATIONAL MATHEMATICS""]‎

‎Paris, Charles Antoine Jombert, 1750 (Vol. 2: 1749). 8vo. Uniformly bound in four nice contemporary full spinkled calf binding with five raised bands and richly gilt spines. Small paper-label pasted on to top of spines. Edges of boards gilt. All edges coloured in red. Light wear to extemities, primarily affecting spine-ends. A nice and clean set. (16), 460, (20) pp. + 32 plates." (4), 462, (14) pp. + 49 plates (2), 482, (12) pp. + 31 plates. (8), 446, (6) pp. + 17 plates. (A total of 129 plates out of 136)‎

‎Beautiful later edition the first work of its kind" ""Recreational Mathematics"".Qzanam's ""contributions consisted of popular treatises and reference works on ""useful and practical mathematics,"" and an extremely popular work on mathematical recreations" the latter had by far the more lasting impact. Ozanam’s Récréations may be regarded as the forerunner of modern books on mathematical recreations. He drew heavily on the works of Bachet de Méziriac, Mydorge, Leurechon, and Daniel Schwenter" his own contributions were somewhat less significant, for he was not a particularly creative mathematician. The work was later augmented and revised by Montucla and, still later, was translated into English by Hutton (1803).""(DSB).‎

Referencia librero : 60995

‎MEGERLIN, PETER.‎

‎Theatrum divini regiminis a mundo condito usque ad nostrum seculum (...) Commentarii chronologici in tabulam mathematico-historicam.‎

‎Basel, Brandmylleri, 1683. 4to. In a contemporary Cambridge-style mirror binding with five raised bands and richlt gilt spine. Small paper-label pasted on to top of spine. Head of spine chipped, showing headbands. Small repair to spine. Lower outer corner of back board with large scratch showing the board underneath. Four-line note in contemporary hand to front free end-paper. Previous owner's name in contemporary hand to title-page. Internally fine and clean. (18), 354, 121, (1) pp. + 1 folded plate.‎

‎First (only?) edition of mathematician Megerlin's work that combines mathematics, history, and theology to create a detailed historical and chronological analysis of divine governance from the creation of the world up to the second half of the 17th century. It is structured around the cycles of significant astronomical events, specifically the conjunctions and oppositions of Saturn and Jupiter, which recur approximately every 800 years. Peter Megerlin (1623–1686) was a German scholar and professor at the University of Basel. He was a theologian and mathematician and his work often reflected an interest in the intersection of these fields, of which this present work if a fine example. Megerlin famously tought Jacob Bernoulli, who later opposed his astrological interpretations of comet appearances. The work is of the utmost scarcity and we have only been able to trace one previous copy in the trade.‎

Referencia librero : 61341