‎Mathematics‎

‎"BOOLE, GEORGE.‎

‎On Simultaneous Differential Equations of the First Order in which the Number of the ariables exceeds by more than one the umber of the Equations. Received June 19, - Read June 19, 1862.‎

‎London, Taylor and Francis, 1862. 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862. Vol. 152 - Part I. Pp. 225-252. A very faint dampstain to upper corners on the last 2 leaves, otherwise clean and fine, wide-margined..‎

‎First appearance of one of Boole's last papers.George Boole is mostly known for his ""An Investigation on the Laws of Thought"" 1854 and his developments of a form of symbolic logik, called Boolean Algebra. But he also did importent work on the Calculus, Differential Equations and the heory of probabilities.‎

Bookseller reference : 42127

‎"BOOLE, GEORGE. - BOOLE'S LAST WORK.‎

‎On the Differential Equations which determine the form of the Roots of Algebraic Equations. Received April 27, - Read May 26, 1864.‎

‎(London, Taylor and Francis, 1865). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1864. Vol. 154 - Part III. Pp. 733-755. Clean and fine.‎

‎First printing of Boole's last paper, - Boole, the founder of Computer science.George Boole is mostly known for his ""An Investigation on the Laws of Thought"" 1854 and his developments of a form of symbolic logic, called Boolean Algebra. But he also did importent work on the Calculus, Differential Equations and the Theory of probabilities.‎

Bookseller reference : 42985

‎"BOOLE, GEORGE.‎

‎Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order (+) On certain theorems in the calculus of variations (+) On the integration of linear differential equatio... - [FIRST PAPERS BY BOOLE]‎

‎Cambridge, Macmillan, Barclay, and Macmillan, 1840-1846. 8vo. Bound in recent brown full cloth with gilt letting to spine. In ""The Cambridge Mathematical Journal, Vol. 1-2, Second edition"". Light writing in pencil to title page and very light miscolouring to borders of pages, otherwise a fine and clean copy. VI, 311, (1), VIII, (2), II, 284 pp. + folded plates.‎

‎First printing of four early papers by the influential British mathematician and philosopher. As the inventor of Boolean logic-the basis of modern digital computer logic-Boole is regarded in hindsight as a founder of the field of computer science. His earliest published paper was the ""Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order."" Printed in the Cambridge Mathematical Journal in February 1840 (Volume 2, no. 8, pp. 64-73), and it led to a friendship between Boole and D.F. Gregory, the editor of the journal, which lasted until the death of the latter in 1844.In 1840 he began to contribute to the recently founded Cambridge Mathematical Journal and also to the Royal Society, which awarded him a Royal Medal in 1844 for his papers on operators in analysis"" he was elected a fellow of the Royal Society in 1857.""In papers in the Cambridge Mathematical Journal in 1841 and 1843 [The present], Boole dealt with linear transformations. The algebraic fact had been partly perceived by Lagrange and by Gauss, but Boole's argument drew attention to the (relative) invariance of the discrimiant ab - h2, and also to the absolute invariants of the transformation. This was the starting point of the theory of invariants, so rapidly and extensively developed in the second half of the nineteenth century."" (DSB)‎

Bookseller reference : 45091

‎"BOLLÉE, LÉON. - THE INVENTION OF ""THE MILLIONAIRE CALCULATOR""‎

‎Sur une nouvelle machine à calculer.‎

‎(Paris, Gauthier-Villars, 1889). 4to. No wrappers. Disbound. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 109, No 20. Pp. (723-) 758 (entire issue offered). Bollée's paper: pp. 737-739. Disbound but clean.‎

‎First printing of the paper in which Bollée describes his invention of a new calculating machine, later called ""The Millionaire"", based on a multiplying mechanism which was capable of performing multiplication directly instead of using repeated addition. As it allows multiplication by any digit it was used by government agencies ans scientists, especially astronomers, well into the twentieths century.Bollée did not produced his machine comercially, ""... but in 1893 Otto Steiger of Munich patented a calculator based on Bollée's approach, which was manufactured between 1895 and 1935 by the firm Hans W. Egli of Switzerland and marketed under the name of ""Millionaire"".... Forty-six hundred ""Millionaires"" were sold, primarly in Europe."" (Hook & Norman ""Origins of Cyberspace"" : 288).‎

Bookseller reference : 48744

‎"BOOLE, GEORGE. (+) ARTHUR CAYLEY.‎

‎The Theory of Linear Transformations (+) On The Reduction of the General Equation of the n-th Degree (Sequel to a Memoire on the Theory of Linear Transformations) [Boole] (+) Note on Mr. Cockle's Solution of a Cubic Equation [Cayley]. - [THE VERY FIRST BOOLEAN DETERMINANT]‎

‎Cambridge, Macmillan and Co., 1851. 8vo. Bound with the original front wrapper in contemporary half calf with black and red title labels to spine with gilt lettering. In ""The Cambridge and Dublin Mathematical Journal"", Vol. VI [6], (Being Vol. X [10], of the Cambridge Mathematical Journal), 1851. Bookplate pasted on to pasted down front free end-paper and library code written in hand to lower part of spine. Library cards in the back. First two leaves detached, but present (Title page and index page). Otherwise a fine and clean copy. Pp. 87-106"" Pp. 106-141. [Entire volume: IV, 293 pp.].‎

‎First printing of these two important paper by Boole and Cayley's famous note to include the very first Boolean determinant: ""...the Hessian, or as it ought to be termed, the first Boolean Determinant"" (P. 192).‎

Bookseller reference : 47440

‎"BOLZANO, BERNARD.‎

‎Versuch einer objectiven Begründung der Lehre von den drei Dimensionen des Raumes. (Aus dem Abhandlungen der k. böhm. Gesellschaft der Wissenschaften (V Folge, Bd. 3).) - [BOLZANO'S FIRST WORK ON SPACE AND TIME]‎

‎Prag [Prague], 1843. 4to. Uncut in the original printed light pink wrappers, with a dicreet new black cloth back-strip. A bit of brownspotting and minor chipping to edges pf wrappers, but overall a very nice copy of this fairly fragile publication. 15, (1) pp.‎

‎The very rare first edition, off-print (separately paginated), of this important treatise on space and time, which constitutes an important part of Bolzano's philosophical-logical theory. The present paper constitutes the first public formulation of these controversial ideas on time and space, with which Bolzano sets out to establish a foundation of mathematics which is non-empirical. By uniting mathematics and philosophy and applying both to the question of space and time, Bolzano here brings both sciences to a higher level of completeness, acknowledging that his theories depart from the those of Hegel, Kant, Schelling, etc. As always, Bolzano grabs the essence of the question and the terms that he is treating and retraces the concepts that must be used, establishing their original inner connection. In the present paper, the question of space, time, and thought are treated in order to establish the precise and full nature of space, a theme which Bolzano had apparently been working on for many years but previously only discussed with a very small number of intimate acquaintances, and now publishes on for the first time. The concept of space plays an important rôle in Bolzano's ontology and is closely linked to his mathematical and philosophical logic, in which the ""space-position"" plays a part in the demarcation of that which is purely mathematical and logical. Furthermore, for Bolzano, truth is constituted by true propositions (which state things as they are), and his canonical form of all propositions entails that ""[a] proposition is true iff the object has the property (the attribute) which belongs to the subject of the proposition. Moreover, empirical propositions must contain determinations of space and time. Without these determinations, the sentence ""It is snowing"" has no truth value, it is just a propositional form which does not correspond to a complete proposition"" ""in order to be true, [such propositions] require the addition of such specifications as to time (and often place as well), 'It is snowing today, in this place'"" (SEP).‎

Bookseller reference : 41020

‎"BOLTZMANN, LUDWIG. - DEFENDING THE ATOMIC VIEWPOINT.‎

‎Über die Integrale linearer Differentialgleichungen mit periodischen Coëfficienten.‎

‎Wien, Karl Gerold's Sohn, 1868. 8vo. Uncut and unopened in orig. printed wrappers. In: ""Sitzungsberichte der kaiserlichen Akademie der Wissenschaften"", 58. Band, 1. Heft - Juni. Pp. (1-) 155 a. 7 plates.(Entire issue offered). Boltzmann's paper: pp. 54-59. Clean and fine.‎

‎First apperance of an importent paper in which Boltzmann from a mathematical point of view defends atomism. ""Throughout his career, even in his works on subjects other than kinetic theory Boltzmann was concerned with the mathematical problems arising from the atomic nature of matter. Thus, an early paper with the title ""Über die Integrale linearer Differentialgleichungen mit periodischcn Koeffizienten"" (1868) turned out to be an investigation of the validity of Cauchy’s theorem on this subject, which is needed to justify the application of the equations for an elastic continuum to a crystalline solid in which the local properties vary periodically from one atom to the next."" (DSB). The issue contains an importent paper by JOHANN JOSEPH LOSCHMIDT ""Ableitung des Potentiales bewegter elektrischer Massen aus dem Potentiale für die Ruhestand"", pp. 7-14, in which he attempted to derive the Weber-Ampère law from that of Coulomb, and, in accordance with Kirchhoff, to derive Ohm’s law from hydrodynamic flow laws, analogous to Poiseuille’s law.‎

Bookseller reference : 47990

‎"BOHR, HARALD.‎

‎Lösung des absoluten Konvergenzproblems einer allgemeinen Klasse Dirichletscher Reihen.‎

‎[Berlin, Stockholm, Paris, Beijer, 1913] 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 36, pp. 197-240.‎

‎"BOLLÉE, LÉON. - THE INVENTION OF ""THE MILLIONAIRE CALCULATOR""‎

‎Sur une nouvelle machine à calculer.‎

‎(Paris, Gauthier-Villars, 1889). 4to. No wrappers. Disbound. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 109, No 20. Pp. (723-) 758 (entire issue offered). Bollée's paper: pp. 737-739. Disbound but clean.‎

‎"BOLZANO, BERNARD.‎

‎Paradoxien des Unendlichen. Herausgegeben aus dem schriftlichen Nachlasse des Verfassers, von Dr. Fr. Prihonsky. - [THE FIRST WORK ON INFINIT NUMBERS AND SET THEORY]‎

‎Leipzig, 1851. 8vo. Original printed wrappers. Re-stitched and with a new paper backstrip perfectly matching the wrappers. Possibly lightly washed (?). Housed in a custom-made red cloth box with a gilt red morocco title-label to spine. XII, (2), 134 pp.‎

‎"BOOLE, GEORG - FOUNDING MODERN DIGITAL COMPUTER SCIENCE.‎

‎The Calculus of Logic.‎

‎Cambridge, Macmillan, Barclay, and Macmillan, 1848. No wrappers as extracted from ""The Cambridge and Dublin Mathematical Journal. Edited by W. Thomson."" Vol. III. Pp. 183-198. Having the titlepage (2) pp. to the entire volume.‎

‎"BOOLE, GEORG. - THE THEORY OF INVARIANTS INITIATED.‎

‎Exposition of a general Theory of linear Transformations. Part I-II. (November 1841 a. May 1842).‎

‎Cambridge, E. Johnson, 1843. 8vo. Unbound without wrappers. In: ""The Cambridge Mathematical Journal"", Vol. III. IV,292 pp. (Entire volume offered). Boole's paper: pp. 1-20 a. 106-119.‎

‎"BOOLE, GEORGE.‎

‎On Simultaneous Differential Equations of the First Order in which the Number of the ariables exceeds by more than one the umber of the Equations. Received June 19, - Read June 19, 1862.‎

‎London, Taylor and Francis, 1862. 4to. No wrappers as extracted from ""Philosophical Transactions"" 1862. Vol. 152 - Part I. Pp. 225-252. A very faint dampstain to upper corners on the last 2 leaves, otherwise clean and fine, wide-margined..‎

‎"BOOLE, GEORGE.‎

‎Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order (+) On certain theorems in the calculus of variations (+) On the integration of linear differential equatio... - [FIRST PAPERS BY BOOLE]‎

‎Cambridge, Macmillan, Barclay, and Macmillan, 1840-1846. 8vo. Bound in recent brown full cloth with gilt letting to spine. In ""The Cambridge Mathematical Journal, Vol. 1-2, Second edition"". Light writing in pencil to title page and very light miscolouring to borders of pages, otherwise a fine and clean copy. VI, 311, (1), VIII, (2), II, 284 pp. + folded plates.‎

‎"BOOLE, GEORGE. - BOOLE'S LAST WORK.‎

‎On the Differential Equations which determine the form of the Roots of Algebraic Equations. Received April 27, - Read May 26, 1864.‎

‎(London, Taylor and Francis, 1865). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1864. Vol. 154 - Part III. Pp. 733-755. Clean and fine.‎

‎"BOSSUT, (CHARLES)‎

‎Usages de la Differentiation des Parametres, pour la Solution de plusieurs Problèmes de laa méthode inverse des Tangentes.‎

‎(Paris, Imprimerie Royale, 1755). 4to. Extract from ""Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome II. Pp. 435-451 a. 1 folded engraved plate.‎

‎"BROUWER, L. E. J. [LUITZEN EGBERTUS JAN]. (+) DAVID HILBERT.‎

‎[Brouwer:] Beweis des ebenen Translationssatzes (+) Zur Invarianz des n-dimensionalen Gebiets (+) Beweis der Invarianz der geschlossene Kurve (+) [Hilbert:] Begründung der Kinetischen Gastheorie. - [DISCOVERY OF THE ""INVARIANCE OF DOMAIN""-THEOREM]‎

‎Leipzig, B.G. Teubner, 1912. 8vo. Bound in half cloth with the original printed wrappers. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 68. Band. 3. Heft."" Entire issue offered.Black title-label in leather with gilt lettering to spine. Small library-label pasted on to top of spine. Small library stamp to title page and a few numbers written on front wrapper. Internally very fine and clean. [Brouwer:] Pp. 37-54" Pp. 55-6" Pp. 422-25 [Entire issue: (4), 595 pp.].‎

‎First printing of three important papers by Brouwer. In ""Zur Invarianz des n-dimensionalen Gebiets"" Brouwer introduced his ""Invariance of domain"" which is a theorem in topology about homeomorphic subsets of Euclidean space.""The existence of one-to-one correspondences between numerical spaces Rn for different n, shown by Cantor, together with Peano's subsequent example (1890) of a continuous mapping of the unit segment onto the square, had induced mathematicians to conjecture that topological mappings of numerical spaces Rn would preserve the number n (dimension). In 1910 Brouwer proved this conjecture for arbitrary n."" (DSB)‎

Bookseller reference : 44950

‎"BRACONNIER, JEAN.‎

‎L'analyse harmonique dans les groupes abeliens. [Monographies de l""Enseignment mathematique, No 5].‎

‎Geneve, L'Enseignement Mathematique, (1956). 8vo. Original light blue wrappers. 48, (2) pp. Slight miscolouring to wrapper, otherwise a nice and clean copy.‎

Bookseller reference : 42865

‎"BRILL, ALEXANDER VON (+) MAX NOETHER.‎

‎Ueber die algebraischen Functionen und ihre Anwendung in der Geometrie. - [THE BRILL-NOETHER THEORY]‎

‎Leipzig, B. G. Teubner, 1874. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 7., 1874. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Title-page and index-page with nicks and repairs. Otherwise fine and clean. Pp. 269-316. [Entire volume: IV, 638 pp.].‎

‎First printing of this important paper in which the Brill-Noether theory was presented for the first time. In the theory of algebraic curves, Brill-Noether theory, is the study of special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a ""larger than expected"" linear system of divisors.‎

Bookseller reference : 47190

‎"BRILL, ALEXANDER VON (+) MAX NOETHER.‎

‎Ueber die algebraischen Functionen und ihre Anwendung in der Geometrie. - [THE BRILL-NOETHER THEORY]‎

‎Leipzig, B. G. Teubner, 1874. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 7., 1874. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Title-page and index-page with nicks and repairs. Otherwise fine and clean. Pp. 269-316. [Entire volume: IV, 638 pp.].‎

‎"BROUWER, L. E. J.‎

‎Besitzt jede reelle Zahl eine Dezimalbruchentwicklung. (In ""Mathematische Annalen. 83-84. Band. 1921""). - [THE BEGINNING OF THE ""FOUNDATIONAL DEBATE""]‎

‎Berlin, Julius Springer, 1921. 8vo. Bound with the original wrappers in dark blue full cloth. A very nice and clean copy. [Brouwer:] Pp. 201-10. [Entire issue: (4), 319, (4), 320 pp.].‎

‎"BUÉE, (ADRIEN). - INFLUENTIAL WORK ON IMAGINARY NUMBERS.‎

‎Mémoire sur les Quantités imaginaires. Communicated by William Morgan. Read June 20, 1805.‎

‎(London, W. Bulmer and Co., 1806). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1803 - Part I. Pp. 23-88 a. 1 folded engraved plate.‎

‎First printing of Buée's memoir on imaginary numbers, an influential work containing original ideas. He shows how imaginary numbers can be represented geometrically.‎

Bookseller reference : 45114

‎"BURNSIDE, WILLIAM.‎

‎Theory of Groups of Finite Order. - [GROUP THEORY]‎

‎Cambridge, University Press, 1897. 8vo. Original publishers cloth with gilt spine lettering. Extremeties slightly worn, else fine. Owners signature on front free end paper. Other wise clean throughout. Uncut, mostly unopend. A fine copy. XVI,388 pp. Text illustrated.‎

‎"BÉZOUT, (ÉTIENNE). - BÉZOUT'S THEOREM.‎

‎Théorie Générale des Équations algebraiques.‎

‎Paris, Ph.-D. Pierres, 1779. 4to. Nice recent vellum, titlelabel with gilt lettering on spine. (4),XXVIII,471 pp. Wide-margined, clean and fine.‎

‎"CAYLEY, (ARTHUR)‎

‎A Memoir on the Theory of Reciprocal Surfaces. Received November 12, 1868, - Read January 14, 1869.‎

‎(London, Taylor and Francis, 1870). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1869 - Vol. 159 - Part I. Pp. 201-229. Clean and fine.‎

‎First printing of the paper which ""contains some extensions of dr. Salmon's theory of Reciprocal Surfaces‎

Bookseller reference : 45118