‎Matemáticas‎

‎TARKSI, ALFRED.‎

‎Cardinal Algebras.‎

‎New York, Oxford University Press, 1949. 8vo. Publishers full cloth with dust jacket fine condition. XII,326 pp.‎

‎First edition. The first exposition of cardinal arithmetic on an algebraic foundation.‎

Referencia librero : 33474

‎"CARNAP, RUDOLF.‎

‎Der Raum. Ein Beitrag zur Wissenschaftslehre. - [SPACE - CARNAP'S FIRST PUBLICATION]‎

‎Berlin, Reuther & Reichard, 1922. 8vo. Uncut in the original grey printed wrappers w. very neat professional repairs to inner hinges and to capitals. Printing on spine nearly fully intact. A very faint waterstaining to upper corner throughout, otherwise a very good, nice and clean copy of a publication, which in itself is quite fragile. 87 pp.‎

‎First edition of Carnap's first publication, his doctoral dissertation. Printed in Kant-Studien, Ergänzungshefte, Nr. 56. Issued by H. Vaihinger, M. Frischeisen-Kähler and A Liebert. Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago. In Jena he was appointed Professor of Mathematics, though his main interest at that time was in physics. By 1913 he planned to write his dissertation on thermionic emission, but this was interrupted by World War I, where he served at the front until 1917. Afterwards he studied the theory of relativity under Einstein in Berlin, and he developed the theory for a new dissertation, namely on an axiomatic system for the physical theory of space and time. He thus ended up writing the important dissertation under the direction of Bouch on the theory of space (Raum) from a philosophical point of view. The dissertation was submitted in 1921, and, due to the clear influence from Kantian philosophy, it was published the following year in this supplement to the ""Kant-Studien"". After the publication of his first work, Carnap's involvement with the Vienna Circle began to develop. He met Reichenbach in 1923 and was introduced to Moritz Schlick in Vienna, where he then moved to become assistant professor at the university. He soon became one of the leading members of the Vienna Circle, and in 1929 he, Neurath, and Hahn wrote the manifest of the Circle.As the title indicates, ""Der Raum"" deals with the philosophy of space. Partly influenced by Husserl, under whom he studied at Freiburg, Carnap poses the question whether our knowledge of space is analytic, synthetic a priori or empirical. His answer is that it depends on what is meant by ""space"", and thus differentiates between three kinds of theories of space: Formal (which is analytic [a priori]), intuitive (which is synthetic a priori), and physical (which is empirical [or synthetic aposteriori]). He compares this division of space with that of geometry into: projective, metric and topological. This, of course, anticipates much of his later philosophy, and some of his theories developed in this paper became the official position of logical empiricism on the philosophy of space. In this work he also develops a formal system for space-time topology, which became quite influential.‎

Referencia librero : 33482

‎HJELTE, C.‎

‎Lærebog i den elementære Geometrie for Eleverne af det kongelige Landcadetacademie. Anden Udgave. Anden Deel: Stereometrie.‎

‎Kjøbenhavn, Schultz, 1838. Orig. blankt blå kardusomslag. (4),95,(1) pp. samt 4 litograferede plancher med talrige figurer. Med svag skjold. Stempel på titelblad.‎

Referencia librero : 34544

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur L'Élimination des Inconnues dans les Équations.‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 303-318. Fine and clean.‎

‎First edition of this importent paper in algebraic analysis, read before the Academy October 29, 1767 and published as a Memoir 1771. He employed Cramer's method of symmetric functions but made it more rapid by use of the series development of log (1+u).‎

Referencia librero : 34680

‎"EUCLID OF ALEXANDRIA - GESTRINIUS, MARTIN ERIK.‎

‎In geormetriam Euclidis Demonstrationum Libri Sex. In quibus Geometria planorum traditur, & brevis Notis perspicue explicatur. Impensis & sumptibus Authoris. - [FIRST SWEDISH EUCLID-EDITION.]‎

‎Uppsala, Eschillus Matthiæ, 1637. Small 4to. Cont. full vellum over wood. Spine ends worn, tears to hinges, but not broken, lower edges of boards with old repairs. Some old ink annotations on boards. Inside frontcover and on title many old owner names, small wholes cut in titel without loss of letters. First ab. 20 leaves with a faint dampstain in upper margin, inkspots on last page. Internally clean. (24),350,(2) pp., numerous geometrical diagrams in the text.‎

‎Scarce first edition of the first Swedish edition of Euclid's Elements (Book I-VI) with Gestrinius' commentaries to the axioms and porpositions and with his attempt of a proof of the ""Parallel-axiom"" (The Fifth Postulate). In the preface he discusses the use of plane-geometry in the theories of Aristoteles, Eudoxus, Ptolemy and Kepler. - Gastrinius (1594-1648) became professor of mathematics in Uppsala in 1621 after studies in Greifswald.Collijn (1600-Talet) I:310. - Riccardi p. 436 (1637,2) - Poggendorff I:889. - Not in Max Steck.‎

Referencia librero : 34701

‎EUCLID OF ALEXANDRIA.‎

‎Evclide Megarense Philosopho: solo introdvtttore delle Scientie Mathematice" diligentemente Reassettato, et alla integrita ridotto per il degno Professore di tal Scientie Nicolo Tartalea, Brisciano, Secondo le due Tradottioni: e per commune commodo & ... - [FIRST ""EUCLID"" IN THE VERNACULAR BY TARTAGLIA.]‎

‎(Colophon: Venice, Venturino Rossenelli, 1543). Folio. (30,5x22 cm.). Contemporary full Italian limp vellum. Remains of ties. Old handwritten title on spine. Upper part of frontcover slightly creased. A few small nicks to hinges at cords. Vellum with brownspots. 242 leaves (2-241 numb. II-CCXXXIX). Misnumbering of leaves in sign. A (10 lvs.), due to the insertion of corrections on f A5. (Collation corresponds to that given by Thomas-Stanford No. 34). Large margins profusely illustrated with diagrams. Upper right corner of title gone with loss of of 3 letters ""NSE"" in MEGARENSE, f A2-A6 with upper right corners and a wormtract-hole in lower margin repaired. A wormtract in lower margin on the next 11 lvs. A1-A6 mounted skillfully on thin opaque parchment-paper. A rather faint dampstain in upper right corner throughout. Last 5 leaves with a small nick in right margin, no loss. Otherwise remarkable clean and printed on good strong paper. On the title a large woodcut device with arms with G.T. (Gabriele Tadino, to whom the work is dedicated). Colophon with large woodcut device with the letters .P.Z.F. and this repeated on verso of last leaf.‎

‎Scarce first edition of the first translation of Euclid in any modern language by the famous Niccolo Tartaglia. The translation and Tartaglia's commentaries, strongly accelerated the development of physics and mechanics in the 16th century, as it showed how mathematics could be applied to dynamics and mechanics as well as to architecture, construction and perspective. More than 20 years should elapse before the next language should receive the privilege of displaying Euclid among their goods, this was the French translation published by Pierre Forcadel, Paris 1564. ""When Tartaglia submits that his redaction was made ""secondo le due tradittioni"", there is no question that Campanus - who appears to be heavely favored - and Zamberti are meant. When Campanus has added propositions or premises, Tartaglia has approriately translated them and noted their absence ""nelle seconda tradittione"", while things omitted by Campanus but included by Zamberti receive the reverse treatment"" (John Murdoch in DSB).Niccolo Fontana Tartaglia of Brescia has a great name in the history of mathematics. A cut in the face from a French soldier caused him to stammer and as a consequence of this he was called 'Tartaglia' (the stammerer). He is famous for his solution of third-degree equations which occasioned a long polemic with Cardano about priority. He is also known for ""Tartaglia's Triangle"", later known as ""Pascal's Triangle"", and he is well-known for his Archimedes-edition of 1543 and 1551 with his commentaries.""The most famous source of Greek geometry is the monumental work of Euclid of Alexandria, called the ""Elements"" (around 300 B.C.). No other book of science had a comparable influence on the intellectual development of mankind. It was a treatise of geometry in thirteen books which included all the fundamental results of scientific geometry up to his time. Euclid did not claim for himself any particular discovery, he was merely a compiler. Yet, in view of the systematic arrangement of the subject matter and the exact logical procedure followed, we cannot doubt that he himself provided a large body of specific formulations and specific auxiliary theorems in his deductions. It is no longer possible to pass judgement on the authorship of much of this material"" his book was meant as a textbook of geometry which paid attention to the material, while questions of priority did not enter the discussion."" (Cornelius Lanzos in ""Space through the Ages"").Max Steck III:40 - Thomas-Stanford: 34 - Riccardi Euclideana 1543, 1 - Adams E:992. - Brunet II:1090. (Premiere edition de ce travail estimé). - Graesse II:513.‎

Referencia librero : 34704

‎VON NEUMANN, JOHN.‎

‎Über die analytischen Eigenschaften von Gruppen linearer Transformationen und ihrer Darstellungen‎

‎Berlin, Julius Springer, 1929. Offprint from 'Mathematische Zeitschrift' volume 30, pp. 3-42. 8vo. Original printed wrappers. Fine condition.‎

‎First edition offprint issue.‎

Referencia librero : 34732

‎"ACKERMANN, WILHELM.‎

‎Begründung des ""tertium non datur"" mittels der Hilbertschen Theorie der Widerspruchsfreiheit. - [ACKERMANN'S DISSERTATION]‎

‎Berlin, Julius Springer, 1925. In: 'Mathematische Annalen', volume 93, pp.1-36. Entire volume offered here (314 pp.) Bound in modern full cloth. Ex-library stamp on title page.‎

‎First edition of Ackermann's doctorial dissertation. Ackermann was a student of Hilbert and played an important role in the development of 20th century mathematical logic.‎

Referencia librero : 34751

‎CARNAP, RUDOLF.‎

‎Meaning and Necessity. A Study in Semantics and Modal Logic. - [THE DEFINITIONS OF L-TRUE AND L-FALSE]‎

‎Chicago, (1947). 8vo. Orig. green full cloth w. gilt lettering to spine. Minor bumping to extremities, otherwise a very nice, clean and fresh copy. VIII, 210 pp.‎

‎The not common first edition of Carnap's important main work on semantics, in which he, as the first logician ever, uses semantics to explain modalities. This led to a interest in the structure of scientific theories, and his main concerns here were to describe the distinction between analytic and synthetic statements and to suitably formulate the verifiability principle" -he thus wishes to find a criterion of significance that can be applied to scientific language.It is in his ""Meaning and Necessity"" that Carnap first defines the notions of L-true and L-false (Chapter II). A statement is said to be L-true if its truth depends on semantic rules, and L-false if its negation is L-true. Any statement that is either L-true or L-false is L-determined"" analytic statements are L-determined, while synthetic statements are not L-determined. As opposed to the definitions he gives in his ""The Logical Syntax of Language"", these definitions now apply to semantic in stead of syntactic concepts. It is also in this work that he gives his interesting explanation of his ""belief-sentences""Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago. In Jena he was appointed Professor of Mathematics, though his main interest at that time was in physics. By 1913 he planned to write his dissertation on thermionic emission, but this was interrupted by World War I, where he served at the front until 1917. Afterwards he studied the theory of relativity under Einstein in Berlin, and he developed the theory for a new dissertation, namely on an axiomatic system for the physical theory of space and time. He thus ended up writing the important dissertation under the direction of Bouch on the theory of space (Raum) from a philosophical point of view. After the publication of his first work, Carnap's involvement with the Vienna Circle began to develop. He met Reichenbach in 1923 and was introduced to Moritz Schlick in Vienna, where he then moved to become assistant professor at the university. He soon became one of the leading members of the Vienna Circle, and in 1929 he, Neurath, and Hahn wrote the manifest of the Circle.According to Hintikka, Carnap came extremely close to possible-worlds semantics in his ""Meaning and Necessity"", but did not succeed, because he was not able to go beyond classical model theory (see ""Carnap's heritage in logical semantics"" in ""Rudolf Carnap, Logical Empiricist"").‎

Referencia librero : 34801

‎GAUSS, CARL FRIEDRICH.‎

‎Disquisitiones generales circa superficies curvas. (General Investigations of Curved Surfaces). - [FOUNDATION OF MODERN GEOMETRY]‎

‎Göttingen, Dieterich, 1828. Small 4to. Extracted from: 'Commentationes Societatis Regiae Scientiarum Gottingensis', Volume 6, pp.99-146. 4to. Modern half morocco with gilt spine lettering. Fine and clean throughout.‎

‎First edition of the work which inspired one of the greatest breakthroughs in geometry since Euclid.Euler established the theory of surfaces in his 'Recherches sur la courbure des surfaces', 1767. But Euler's treatment of surfaces is not invariant under a natural notion of isometry with his notion of curvature, for example, the plane and cylinder have different curvatures, although one surface can be bent into the other without stretching or contracting. Such two surfaces are locally alike and one would naturally demand that geometry on these two isometric surfaces are the same. Another way of viewing this is to say that geometry on the surface depends on the geometry of the particular space, in which the surface is embedded.In this work Gauss took a fundamentally different approach to the study of surfaces" in contrast to Euler he represented the points of a surface in terms of two external parameters. Gauss then derived his own notions of the fundamental quantities of surfaces, e.g. arc length, angle between curves, and curvature. The Gauss curvature is related to the Euler curvature, but possesses a fundamentally different property, namely that it is intrinsic, e.g. isometric surfaces have the same curvature at all points. Or, in other words: Geometry (in Gauss' notion) on the surface is independent of the particular geometry of the ambient space. This remarkable result is known as Gauss' ""theorema egregium"". With this work Gauss established a whole new (and more proper) theory of surfaces. In the paper Gauss derived several important theorems about the length, area, and angles of figures on surfaces. But the ""theorema egregium"" has deep roots in the foundation of geometry and was to initiate one of the greatest breakthroughs in geometry since Euclid. To Bernhard Riemann (a student of Gauss) this result suggested that a surface could be regarded as a space in itself with its own geometry, having its own notion of distance, angles, etc. independent of the geometry of some other space containing the surface. This idea became the corner stone of Riemann's famous 'Ueber die Hypothesen, welche der Geometrie zu Grunde liegen', 1867.Norman 880.‎

Referencia librero : 34861

‎LOBATSCHEFSKIJ - ENGEL, FRIEDRICH. (LOBACHEVSKY, LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKJI)‎

‎Nikolaj Iwanowitch Lobatschefskij. Zwei geometrische Abhandlungen, aus dem Russischen übersetz, mit Anmerkungen und mit einer Biographie des Verfassers. 1. Teil: Die Uebersetzung. Mit einem Bildnisse Lobatschefskijs und 194 Fig. 2. Teil: Anmerkungen, ...‎

‎Leipzig, B.G. Tuebner, 1898-99. Royal8vo. Uncut and unopened in original printed wrappers. Wrappers with some tears. Front wrapper loose. Lithographed portrait of Lobachevsky, XVI,236,(3),237-476 pp.‎

‎First edition. Contains the first translation of Lobachevsky's seminal 1829 paper 'O Nachalakh Geometrii / On the Principles of Geometry' (see Sommerville Bibliography 1829).‎

Referencia librero : 35025

‎FRANCOEUR, L.B. (LOUIS BENJAMIN).‎

‎Géodésie, ou Traité de la Figure de la Terre et de ses Parties comprenant La Topographie, L'Arpentage, Le Nivellement, La Géomorphie terrestre et astronomique, la Construction des Cartes, La Navigation. Lecons données a la Faculté des Sciences de Par...‎

‎Paris, Bachelier, 1840. Contemporary hcalf. Gilt back. A small paperlabel at foot of back. A stamp on title and verso of. XIV,472 pp. and 10 large folded engraved plates.‎

Referencia librero : 35102

‎SZ. NAGY, BÉLA.‎

‎Spektraldarstellung linearer Transformationen des Hilbertschen Raumes.‎

‎Berlin, Springer=Verlag, 1942. Orig. printed wrappers. IV,80 pp.‎

‎First edition. (Ergebnisse der Mathematik und ihrer Grenzgebiete 5. Bd.: Heft 5)‎

Referencia librero : 35234

‎ARCHIMEDES - LURJE, S.J.‎

‎Archimedes.‎

‎Wien, 1948. Bound in solid hcloth. 204 pp., textillustr.‎

Referencia librero : 35420

‎CARNAP, RUDOLF.‎

‎Foundations of Logic and Mathematics.‎

‎(Chicago, 1965). 8vo. Orig. yellow wrappers. A bit of soiling. IV, 71 pp.‎

‎11. impression of this important work in the development of mathematical logic. Originanlly published in 1939. From the International Encycloppedia of Unified Science.‎

Referencia librero : 35497

‎"EULER, LEONHARD.‎

‎Sur quelques Proprietés des Sections Coniques, qui conviennent à une infinité d'autres Lignes Courbes. Traduit du Latin.‎

‎(Berlin, Haude et Spener, 1746). 4to. No wrappers, as issued in ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome I, pp.71-98.‎

‎First edition. In this memoir Euler deals with properties shared by Conic Sections and other curves. - Ensestrom E 83‎

Referencia librero : 35698

‎"YULE, G. UDNY.‎

‎On the Association of Attributes in Statistics: with Illustrations from the Material of the Childhood Society, &c. (Offprint from: Philosophical Transactions of the Royal Society of London. Series A, Vol. 194, pp.257-319).‎

‎London, The Royal Society, 1900. Large 4to. Original printed wrappers. Some fraying to extremeties. Back wrapper loose. Vertical folding mark.‎

‎First edition, offprint issue of this important paper. ""Yule's studies of the correlation of continuous variables led him, in 1900 [offered paper], to study measures of association for discrete variables, in particular the cross-ration c ('odds ration') in 2 x 2 contingency table and its transform Q=(1-c)/(1+c), now known as 'Yule's coefficient'. This led to an altercation with Pearson in which Pearson's capacity for acrimonious and illdirected criticism was displayed, in marked contrast to Yule's gentler mode of expression. Even Fisher, who as a young man had felt the sharpness of Pearson's pen, was later moved to remark 'Pearson' attacked Yule's work at one time much more violently than ever he did mine'."" - Heyde: Statisticians of the Centuries, p.293.‎

Referencia librero : 35749

‎"TARSKI, ALFRED.‎

‎Pojecie Prawdy w Jezykach Nauk Dedukcyjnych (Polish). [The Concept of Truth in Formalized Languages]. - [FOUNDING MODERN LOGICAL SEMANTICS]‎

‎Warszawa, 1933. Small 4to. Orig. printed wrappers, sunned at the edges, but otherwise near mint condition, also internally. An excellent copy. VII, (1), 116, (1, - errata) pp.‎

‎The exceedingly scarce first printing of Tarski's most important and influential work, ""The Concept of Truth in Formalized Languages"", which founded modern logical semantics.The work appeared in an extremely small number, in Polish, and many copies of the article have later been destroyed, thus, the work is of the utmost scarcity. In this seminal article the Polish-American logician and mathematician Alfred Tarski devotes himself to ""the definition of truth"". ""Its task is to construct -with reference to a given language- a materially adequate and formally correct definition of the term ""true sentence""."" (Introduction, English translation, 1956). With this work the face of logic was changed forever. The ""Concept of Truth"" constitutes a landmark event in 20th century analytic philosophy, and it ranks as one of the most important contributions to symbolic logic, semantics and philosophy of language. In this work Tarski develops the semantic theory of truth for formal languages and determines the fact that no language can contain its own truth predicate. Tarski thus concluded that the semantic theory could not be applied to any natural language. -This was later used by e.g. Davidson to construct his truth-conditional semantics, and the problems solved by Tarski are some of the same that Russell and Whitehead struggled to solve in their ""Principia Mathematica"".Tarski (1901-1983) has contributed seminally to the fields of mathematics and logic in a number of ways, and together with Frege, Russell and Gödel, he now ranks as one of the most important contributors to the field of modern logic. At the time of Franz Brentano (1838-1917), one of the philosophers of the greatest significance for contemporary philosophy and in many ways a forerunner of present-day empiricism, it was very unusual for a metaphysician to acknowledge that philosophical investigation must go hand in hand with an analysis of language. Linguistic analysis has thus been almost totally limited to the pure empiricists of philosophy, who reject all forms of metaphysics. Meanwhile, ontologists and metaphysicians have been satisfied with the ordinary language and asked no questions about its possible limitations, merely dismissing the logical faults and adding the odd neologisms. Today, however, especially within the English speaking tradition, linguistic analysis has reached a degree unheard of at the time of Brentano, and it is now generally accepted that certain logical and epistemological problems can be solved only by forsaking ordinary language and substituting it for artificially constructed language systems that follow certain principles. Thus, difficulties that appeared within earlier philosophical doctrines are meant to disappear if the theory can be formulated more precisely, and one of the most important examples is the ""adequacy theory of truth"". Tarski shows that the concept of truth of the adequacy theory can be introduced in a perfectly exact way within the formalized language systems that are equipped with precise rules of interpretation, and thus he rids us of the usual misgivings against the concept of truth. And thus he has developed one of the most important theories of modern logic.""Tarski's investigations are of singular philosophical significance for another reason as well. Within the framework of semantics, which he founded and which Carnap later developed further, it becomes possible for the first time to introduce the notion of an analytic judgment (or an analytic statement) in a form that is both sufficiently general and of the utmost precision. This notion also plays an exceptionally important role in Brentano's philosophy, especially in his studies in formal logic."" (Stegmüller, Main Currents... p. 56). When constructing a semantical system, a vocabulary of the desired object language must be determined as the first. Then formulation rules must be specified, before the rules of interpretation are laid down, and finally the rules of application are supplied. The most important rules here are the rules of truth, and the concept of truth is one of the most important semantical concepts at all, for without them no understanding of the sentences within the system would be ensured. And, of course, the truth definitions must satisfy a condition of adequacy. ""...This form of an adequacy condition that must be satisfied by every semantical truth concept goes back to the Polish logician, Stanislaw Lesniewski. But it was the logician Alfred Tarski who above all made use of this notion, and who first studied in detail the possibilities of introducing a formally exact and materially adequate concept of truth into the precise languages of science. Carnap's accounts of semantical systems rest largely on the prior works of Tarski."" (Stegmüller, p. 311). Tarski also pointed out that it is necessary for all semantical concepts, and especially for the concept of truth, to strictly separate object language and metalanguage. Otherwise we would put ourselves in the unlucky position of being able to prove both a statement and its negation at the same time. In the English translation from 1956 of Tarski's works, ""Logic, Semantics, Metamathematics"", the bibliographical information about this article is erroneous.‎

Referencia librero : 35832

‎"LEUPOLD, JACOB. & ERNST SCHEFFLER.‎

‎Theatrum arithmetico geometricum, das ist: Schau-Platz der Rechen- und Mess-Kunst, ... [With:] Theatri machinarum supplementum das ist: Zusatz zum Schau-Platz der Machinen und Instrumenten, ... - [THE ART OF CALCULATION AND MEASUREMENT]‎

‎Leipzig: Christoph Zunkel and Bernhard Christoph Breitkopf, 1727-1739. Folio. (372x239mm). Two parts in one volume. Contemporary vellum, two cuts in spine, modern slip case. Provenance: Book plates of Arnaud de Vitry and Andras Gedeon. Stamps to half-title and title-page, from Stadtbibliothek Augsburg - sold as duplicate. First part: (14], 200, (4) pp. and 45 plates, numbered I-XLIII (plate III with volvelle). Second part: (12), 100, (94) pp. and 40 plates on 36 sheets, numbered I-XL. All plates intact. An exceptionally fine copy.‎

‎The scarce first edition of the of the eighth and tenth volumes (each volume being a complete work in itself) of Leupold's magnificent ten-volume ""Theatrum Machinarum"" - one of the first encyclopedias of technology, being the most complete and the most extensively illustrated work on mechanical engineering published hitherto. Complete sets of Leupold's Theatrum are virtually never found and Ferguson stated in his bibliography of technology that he had never seen a complete set. Each volume is complete in itself. The eighth volume is of particular interest in the history of computers, as it deals mainly with calculating machines. This volume contains detailed descriptions of the calculating machines of Schott (1668), Grillet (1673), Leibniz (1674), Poleni (1709), and Leupold himself. The tenth volume is a supplement to the series published after Leupold's death by Ernst Scheffler. It deals with odometers, gyrometers, step counters and other devices for the measurement of distances. This volume is furthermore of importance, because it contains the 90 page general index to the entire series. Hook & Norman: Origins of Cyberspace, no. 6 (volume 8 only).Honeyman Sale, lot 1997 (volume 7 and 8).Macclesfield Sale, lot 1242 (volume 8 only).Ferguson: Bibliography of the History of Technology, pp.45-46.Wolf: A History of Science, Technology, & Philosophy in the 18th Century, pp.657-8.‎

Referencia librero : 35955

‎"EULER, LEONHARD - LOGARITHMS OF NEGATIVE NUMBERS.‎

‎De la Controverse entre Mrs. Leibnitz & Bernouilli sur les Logarithmes des Nombres Negatifs e Imaginaires. (Controversy between Mr Leibniz and Mr Bernouilli on the logarithms of negative and imaginary numbers).‎

‎(Berlin, Haude et Spener, 1751). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome V, pp. 139-179.‎

‎First edition of this importent paper on the logarithms of complex numbers, where Euler clarified such functions. He disagreed with Leibniz that a special function was only applicable for positive numbers, and showed that i was applicable for both negative and positive numbers, only with a difference of a constant. When Euler here (the offered item) came out with the correct form for the logarithm, it was not generally accepted. - Enestrom, Euler Bibliography E 168.‎

Referencia librero : 36103

‎"CAYLEY, ARTHUR & GIUSEPPE VERONESE.‎

‎Sur quelques théorèmes de la géométrie de position (Cayley) (+) Behandlung der projectivischen Verhältnisse der Räume von verschiedenen Dimensionen durch das Princip des Projicirens und Schneidens. 2 vols. - [THE CAYLEY-VERONESE CLASS OF CONFIGURATIONS.]‎

‎Berlin, G. Reimer, 1846. - Leipzig, B.G. Teubner, 1881. 4to and 8vo. Cayley's paper in ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, Bd. 31: Drittes Heft.1846"". Pp. (179-)268,(2) and 1 plate. The whole issue (Drittes Heft) present with titlepage, stitched without wrappers. Cayley's paper pp. 213-226. - Veronese's paper in ""Mathematische Annalen. In Verbindung mit C. Neumann...hrsg. von Felix Klein und Adolph Meyer. XIX. Band. 2 Heft. 1881."" Pp. (161-)234. The whole issue (2. Heft) present with orig. printed wrappers. No backstrip. Veronese's paper pp. (161-)234.‎

‎Both papers first edition and first apperance in print of these two main papers in the history of projective geometry.""Cayley, in his paper ""Sur quelques théorèmes de la géométrie de position"", (the paper offered) first calls attention to the figures obtained by taking the section, by a plane or 3-dimensional space, of the complete n-point (viz., n points, and the (n/2) lines, (n/3) plans etc. dtermined by them) in a flat spaceof v dimensions. Later Veronese discusses more fully the nature of this class of configurations thus obtained in r dimensions (the second paper offered). Both Cayley and Veronese state that these same configurations can also be obtained as projections of higher-dimensional figures."" (Walter B. Carver). Veronese ""in particular may be considered the main founder of the projective geometry of hyperspaces with n dimensions, which had previously been linear algebra presented geometrically, rather than geometry.""(DSB). - An: Veronese-paper see Sommerville Bibliography of Non-Euclidean Geometry, 1881:3.This issue of ""Crelle's Journal"" contains one more paper of Cayley: ""Problème de géometrie analytique."", pp. 227-230.‎

Referencia librero : 41240

‎"PEANO, GIUSEPPE.‎

‎Démonstration de l'intégrabilité des équations différentielles ordinaires. - [THE PROOF OF THE EXISTENCE THEOREM - INTRODUCING THE AXIOM OF CHOICE]‎

‎Leipzig, B.G. Teubner, 1890. Orig. printed wrappers, no backstrip. A small offsetting to upper left corner of frontwrapper. A small tear to endwrapper repaired. In ""Mathematische Annalen. Gegenwärtig hrsg. von Felix Klein, Walter Dyck, Adolph Mayer, 36. Band, 2. Heft."" Pp. (153-)320. The whole issue (Heft 2) with orig.wrappers. Peano's paper: pp. 182-288.‎

‎First edition and the first appearance of this fundamental paper in which Peano gives the proof of the so-called ""Peano-Existence-Theorem"" and at the same time contains the first explicit statement of ""The axiom of choice"".The Peano-Existence-Theorem, or ""Cauchy-Peano-Theorem"" guarantees the existence of solutions to certain initial value problems. He first published the theorem in 1886 in ""Sull'integrabilita della equazioni differenziali del primo ordine"" in Atti Accad. Sci. Torino, 21, with an incorrect proof. The new correct proof appeared in this paper, as offered.""Peano's work in analysis began in 1883 with an article on the integrability of functions. The article of 1890 (the paper offered) contains notions of integrals and areas. Peano wasthe first to show that the first-order differential equation y' = f(x,y) is solvable on the sole assumption that f is continuous. His first proof dates from 1886, but its rigor leaves something to be desired. In 1890 this result was generalized to systems of differential equations using a different method of proof. This work is also notable for containing the first explicit statement of the axiom of choice. Peano rejected the axiom of choice as being outside the ordinary logic used in mathematical proofs."" (Hubert T Kennedy in DSB).‎

Referencia librero : 41242

‎BEHNKE, HEINRICH u. FR. SOMMER.‎

‎Theorie der Analytischen Funktionen einer Komplexen veränderlichen. Dritte Aufl.‎

‎Bln., N.Y., 1965. Orig. cloth. X, 603 pp.‎

Referencia librero : 4133

‎"HILBERT, DAVID.‎

‎Die logischen Grundlagen der Mathematik. - [IMPORTENT HILBERT-PAPER ON METAMATHEMATICS]‎

‎Berlin, Julius Springer, 1923. Later full cloth. In: ""Mathematische Annalen begründet durch Alfred Clebsch und Carl Neumann."", 88. Bd. (4),312 pp. Hilbert's paper: pp. 151-165. The whole volume offered.‎

‎First edition as a continuation of his paper from 1922 ""Neubegründung der Mathematik. Erste Mitteilung"".""This articlee, delivered as a lecture to the deutsche Naturforscher Gesellschaft in Leipzig, September 1922, is a sequel to (neubegründung...), and brings Hilbert's proof theory to maturity. Hilbert here introduces several technical refinements and clarification to his theory. Specifically: (i) he improves the formal system by adding a special sign for formal negation...(ii) he refines his account of the distinction between formal language and the metalanguage....(iii) he outlines a consistency proof for an elementary, quantifier-free formal system of number-theory. (iv) he begins to extend his proof theory to analysis and set theory....sketches a strategy for proving the consistency of a version of Zermel's axiom of choice for real numbers...(etc. etc). (William Ewald in from Kant to Hilbert, vol. II, pp.1134-35).‎

Referencia librero : 41351

‎"HILBERT, DAVID.‎

‎Ueber die Theorie des relativquadratischen Zahlkörpers. - [A MAIN WORK ON ALGEBRAIC NUMBER-THEORY]‎

‎Leipzig, B.G. Teubner, 1898. Orig. printed wrappers, no backstrip. In: ""Mathematische Annalen begründet durch Alfred Clebsch und Carl Neumann."", 51. Bd., 1. Heft. The whole issue offered (=Heft 1). IV,160 pp. Hilbert's paper pp. 1-127.‎

‎First edition of Hilbert's famous report on algebraic numbers.""The work on algebraic number theory was climaxed in the nineteenth century by Hilbert's famous report on algebraic numbers. This report is primarely an account of what had been done during the century. However Hilbert reworked all of this earlier theory and gave a new, elegant and powerfull methods of securing these results. He had begun to create new ideas in algebraic number theory from about 1892 on and one of the new creations on Galoisian number fields was also incorporated in the report."" (Morris Kline in ""Mathematical Thoughts..."" pp. 825).‎

Referencia librero : 41356