‎Mathematics‎

‎"MACWILLIAMS, JESSIE.‎

‎Permutation Decoding of Systematic Codes. - [FIRST PUBLICATION OF PERMUTATION DECODING]‎

‎New York, American Telephone and Telegraph Company, 1964. 8vo. Volume XLIII (63), January, Number 1, part 2, 1964 of ""The Bell System Technical Journal"". In the original blue printed wrappers. Previous owner's stamps to front wrapper. A part from minor light spotting to front wrapper, a very nice and clean copy. Pp. 485-505. [Entire issue: Pp. 339-563].‎

‎First publication of MacWilliam's important paper on permutation decoding.""MacWilliams (1917-1990) was a mathematician who contributed to the field of coding theory. She was born in Stoke-on-Trent, England and studied at the University of Cambridge, receiving her BA in 1938 and her MA in the following year. She spent most of her career at Bell Labs, where she worked on error-correcting codes and co-wrote 'The Theory of Error-Correcting Code with Neil Sloane'."" (Codings: Webster's Quotations, 42 p.)The issue contains the following papers.1. Darlington, Sidney. Demodulation of Wideband, Low-Power FM Signals. Pp. 339-374.2. Froehlich, F.E." Anderson, R.R. Data Transmission over a Self-Contained Error Detection and Retransmission Channel. Pp. 375-398.3. Sunde, E.D. Intermodulation Distortion in Analog FM Troposcatter Systems. Pp. 399-435.4. Harris, S.E. DeGrasse, R.W. Schulz-Dubois, E.O. Cutoff Frequencies of the Dielectrically Loaded Comb Structure as Used in Traveling-Wave Masers. Pp. 437-484.5. MacWilliams, Jessie. Permutation Decoding of Systematic Codes. Pp. 485-505.6. Gordon, Eugene I. Optical Maser Oscillators and Noise. Pp. 507-539.7. Wood, Elizabeth A. The 80 Diperiodic Groups in Three Dimensions. Pp. 541-559.‎

Bookseller reference : 43550

‎"CHURCH, ALONZO (+) EMIL L. POST.‎

‎[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) [Post:] Finite combinatory processes-formulation I. [In ""Journal of Symbolic Logic"", Volume 1, number 1 + 3, 1936] - [THE FOUNDATION FOR MODERN COMPUTER LOGIC]‎

‎Wisconsin, The Association for Symbolic Logic, 1936. Lev8vo. Entire volume one of ""Journal of Symbolic Logic"" (i.e. number 1-4), March, June, September, December 1936) BOUND WITH ALL THE ORIGINAL WRAPPERS in a blue half cloth with gilt lettering to spine. Crossed-out library paper-label to lower part of spine and top left corner of front board. Two library stamps (in Chinese) to back of front free end-paper. Chinese library-stamp (red) and stamped inventory-number lower part of all four front wrappers. Minor bumping to lower corner of nr. 4, otherwise internally a very fine and clean copy of the entire volume. [Church:] Pp. 40-1"" 101-2. [Post:] Pp. 103-5. [Entire volume: 218 pp.].‎

‎First publication of Church's seminal paper in which he proved the solution to David Hilbert's ""Entscheidungsproblem"" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's ""Entscheidungsproblem"" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous ""On Computable Numbers"" by a few months. ""Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis."" (Hook & Norman: Origins of Cyberspace, 250) The volume also contains first printing of Post's seminal paper, in which he, simultaneously with but independently of Turing, describes a logic automaton, which very much resembles the Turing machine. The Universal Turing Machine, which is presented for the first time in Turing's seminal paper in the Proceedings of the London Mathematical Society for 1936, is considered one of the most important innovations in the theory of computation and constitutes the most famous theoretical paper in the history of computing. ""Post [in the present paper] suggests a computation scheme by which a ""worker"" can solve all problems in symbolic logic by performing only machinelike ""primitive acts"". Remarkably, the instructions given to the ""worker"" in Post's paper and to a Universal Turing Machine were identical."" (A Computer Perspective, p. 125).""The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper [the paper offered]. Post's paper was intended to fill a conceptual gap in Alonzo Churchs' paper on ""An unsolvable problem of elementary number theory"" (Americ. Journ. of Math. 58, 1936). Church's paper had answered in the negative Hilbert's question as to whether a definite method existed for proving the truth or falsity of any mathematical statement (the Entscheidungsproblem), but failed to provide the assertion that any such definite method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be written in the form of instructions to a mindless worker operating on an infinite line of ""boxes"" (equivalent to Turing's machine's ""tape""). The worker would be capable only of reading the instructions and performing the following tasks... This range of tasks corresponds exactly to those performed by a Turing machine, and Church, who edited the ""Journal of Symbolic Logic"", felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and ascertaining that ""the present article... although bearing a later date, was written entirely independently of Turing's"" (p. 103)."" (Origins of Cyberspace, pp. 111-12).Even though Post's work to some degree has been outshined by Turing's, the present paper is of seminal importance in the history of the foundation for modern computer logic and the ideological basis for the modern computer.The volume also contains the following important papers by W. V. Quine:1. Toward a Calculus of Concepts. Pp. 2-25.2. Set-theoretic Foundations for Logic. Pp. 45-57.Hook & Norman, Origins of Cyberspace, 2002: 250 + 356 Charles & Ray Eames, A Computer Perspective, 1973: 125.‎

Bookseller reference : 43552

‎"(LEIBNITZ, GOTTFRIED WILHELM).‎

‎De linee super linea incessu, ejusque tribus speciebus motu radent motu provolutionis et composito ex ambobus (+) Excerptum ex epistola G.G.L. pro hypothesi physica motus planetarii olim (Febr.1689) hic Actis inserta, ad Amicum scripsit.‎

‎Leipzig, Grosse & Gleditsch, 1706. 4to. Contemp. full vellum. Faint hand-written title to spine. Two small stamps to title-page and one stamp to front free end-paper. Library label pasted on to pasted down front free end-paper. As usual with various browning to leaves and plates. The entire volume of ""Actorum Eruditorum Anno MDCCVI"" offered. [Leibniz's paper:] Pp. 10-15 + 1 engraved plate" 446-51 pp. [Entire volume: (2), 590 pp.].‎

‎First publication of two Leibniz papers. In the first paper, Leibniz's calculates the curve for a rolling without sliding body (Pura provolutio). The second paper is a correction to Leibniz's 1689-paper.Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume.‎

Bookseller reference : 43900

‎"BERNOULLI, JACOBI (JACOB).‎

‎Analysis magni problematis Isoperimetrici. - [BERNOULLI'S SOLUTION TO THE ISOPERIMETRIC PROBLEM]‎

‎Leipzig, Gross & Fritsch, 1701. 4to. Contemporary full vellum. Handwritten title on spine. A small stamp to title page and page . Pasted library label to pasted down front free end-paper. In: ""Nova Actorum Eruditorum Anno MDCCI"". Pp 213-228 + 1 engraved plate. [Entire volume: (2), 581 pp. + 8 engraved plates].‎

‎First publication of Jacob Bernoulli influential dissertation in which he published the first correct solution to the isoperimetric problem both Johann Bernoulli and Leibniz had been seeking without success. The paper influenced both Leonhard Euler in writing his first research paper and British mathematician Brook Taylor to begin a dispute which has later been referred to as Taylor versus Continental mathematicians. ""It [the dissertation] was considered as a prodigy of sagacity and invention: and indeed, if the time be considered, it will not be too much to assert, that a more difficult problem never was solved."" (Bossut. A general history of mathematics. 341 p.).The isoperimetric problem is an ancient problem which dates back to antiquity and can be described as which curve, if any, maximizes or minimizes the area of its enclosed region?Euler, who had been taught by Johann Bernoulli, published his first paper in 1726 which was a note on the construction of isochronous curves in a resistant medium.DSB II, 48b.The following papers by Johann Bernoulli are also contained in the present volume:1. Disquisitio Catoptrico-Dioptrica exhibens Reflexionis et Refractionis naturam ex aequilibrii fundamento deductam. Pp 19-26.2. Novaratio construendi radios osculi seu curvanturae in Curvis quibusvis etc. Pp. 136-40.3. Multisectio Anguli vel Arcus, duplici aequatione universali exhibita. Pp. 170-75.‎

Bookseller reference : 44002

‎"LACHLAN, R.‎

‎On Systems of Circles and Spheres. Communicated by A. Cayley. Received February 23, - Read March 11, 1886.‎

‎(London, Harrison and Sons, 1887). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1886 - Vol. 177 - Part II. Pp. 481-625. Clean and fine.‎

‎First edition of an importent study on the geometry of circles, treating circles as vectors and using basic ideas from linear algebra.‎

Bookseller reference : 44042

‎"BERNOULLI, JOHANN.‎

‎Perfectio regulae suae editae in Libro Gall. Analyse des infiniment petits art. 163. pro determinando valore fractionis, cujus Numerator et Denominator certo casu evanescunt‎

‎Leipzig, Grosse & Gleditsch, 1704. 4to. In: ""Acta Eruditorum Anno MDCCIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 375-80. [Entire volume: (2), 592 pp. + six engraved plates.].‎

‎First printing of Bernoulli's paper on infiniti series. Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume.‎

Bookseller reference : 44107

‎"BERNOULLI, JOHANN.‎

‎Methodus commoda et naturalis reducendi Quadraturas transcendentes cujusvis gradus ad Longitudines Curvarum algebraicarum.‎

‎Leipzig, Grosse & Gleditsch, 1724. 4to. In: ""Acta Eruditorum Anno MDCCXXIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 356-66. [Entire volume: (2), 543, (43) pp. + five engraved plates.].‎

‎First printing of one of the famous Swizz mathematician Johann Bernoulli's papers. He is known for his contributions to the infinitesimal calculus and educated Leonhard Euler in his youth.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 44109

‎"BERNOULLI, NICLAUS.‎

‎De trajectoriis curvas ordinatim positione datas ad angulos rectos vel alia date lege secantibus.‎

‎Leipzig, Grosse & Gleditsch, 1718. 4to. In: ""Acta Eruditorum Anno MDCCXVIII"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 248-262. [Entire volume: Pp. (4), 564, (40) + five engraved plates.].‎

‎First printing of Bernoulli's paper on trajectories. The volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 44195

‎"KEILL, IOANNES [JOHN KEILL] (+) CHRISTIANUS WOLFFIUS [CHRISTIAN WOLFF].‎

‎Epistola ad Clarissimum Virum Christianum Wolfium in Academia Regio Fridericiana Mathematum Professorem [Keill] (+) Responsio ad epistolam viri clarissimi Johannis Keill (+) Monitum circa experimentum de circulatione aeris per poros ligni [Wolf].‎

‎Leipzig, Grosse & Gleditsch, 1710. 4to. In: ""Acta Eruditorum Anno MDCCX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 11-15" Pp. 78-80 Pp. 80-1. [Entire volume: Pp. (4), 535, (37) + seven engraved plates.].‎

‎First publication of the dispute between the mathematician Keill and philosopher Wolf about the existence of vacuum. Wolf is widely regarded the most eminent German philosopher between Leibniz and Kant.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 44263

‎"EULER, [LEONHARD].‎

‎Reflexions sur un probleme de geometrie traite par quelques geometres et qui es neanmoins impossible (+) Recherches physiques sur la diverse refrangibilite des rayons de lumiere. - [EULER ON LIGHT RAYS]‎

‎(Berlin, Haude et Spener, 1756). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome X, pp. 173-199" pp. 200-226.‎

‎First printing of two Euler-papers in which he occupies himself with an unsolvable geometric problem and the physics of the different refrangibilities of light rays, a field Euler made important and original contributions to. Euler's wave theory of light, published in 1746, was based on an analogy between sound and light to a more and more mathematical elaboration on that notion. His wave theory degenerated, and it was not until Fresnel introduced transverse waves and an elaborate notion of interference that the wave theory again progressed. He was the second after Christian Huygens to proposed a wave theory of light, and thereby one of the earliest to argue against Newton's particle theory of light. His 1740s papers on optics helped ensure that the wave theory of light proposed by Christian Huygens would become the dominant mode of thought until the development of the quantum theory of light.See Eneström E220, E221.‎

Bookseller reference : 44265

‎"EULER, [LEONHARD].‎

‎Recherches sur la veritable courbe que decrivent les corps jettes dans l'air ou dans un autre fluide quelconque.‎

‎(Berlin, Haude et Spener, 1755). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome IX, pp. 321-352.‎

‎First printing of this Euler-paper in which he examines curves of airborne bodies. Euler describes how the forces acting on a cannonball give different differential equations for the ascending branch than for descending branch. See Eneström E217.‎

Bookseller reference : 44267

‎"HERMANNUS, JACOBUS [HERMANN, JAKOB].‎

‎De nova accelerationis lege, qua gravia versus terram seruntur, suppositis Motu siurno terrae et vi gravitatis constanti.‎

‎Leipzig, Grosse & Gleditsch, 1709. 4to. In: ""Acta Eruditorum Anno MDCCIX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 404-11. [Entire volume: Pp. (2), 547, (45) + eleven engraved plates.].‎

‎First printing of Swiss mathematician Jakob Hermann's paper on gravity. Hermann was a talented mathematician who was taught by Jakob Bernoulli and became friends with Leibnitz. (DSB VI, Pp. 304b-5a).The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 44269

‎ACTA ERUDITORUM - [VARIOUS AUTHORS, SEE BELOW].‎

‎Actorum Eruditorum. Supplementa. Tomus I.‎

‎Leipzig, Grosse & Gleditsch, 1692. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. (4), 639, (5) pp. + drvrn engraved plates.].‎

‎First printing of this issue of the important and exceedingly influential journal Acta Eruditorum containing the following papers:1. Giannettasius, Nicolaus Parthenius. Piscatoria et nautica (Neapoli 1686, Rezension). Pp.1-5. 2. Eschinardus, Franciscus. Epistola ... in qua discursus physico-mathematici quidam continentur/Lettera ... nella quale si contengono alcuni discorsi fisico-mathematici (Romae 1681, Rezension). Pp. 5-9. 3. de Bonnatis, Antonius Franciscus. Universa astrosophia naturalis (Patavii 1687, Rezension). Pp. 9-12. 4. de Beatiano, Julius Caesar. Mercurius heraldicus Fecialis Venetus/Il Mercurio araldico in Italia" L'araldo Veneto (Venetiis 1686, Rezension). Pp. 12-14.5. Anonymus. Tentamen anatomicum, in quo clare explicatur constructio organorum, eorumque operatio mechanica /Essais d'anatomie ... (Lugduni Batavorum 1686, Rezension). Pp. 48-9.6. Starkey, Georgius. Medulla verae chymiae/Het pit der waare chymie ... (Leowardiae 1687, Rezension). Pp. 49-51.7. Thiers, Ioannes Baptista. Tractatus de ludis et recreationibus/Traité des jeux es des divertissements (Parisiis 1686, Rezension). Pp. 51-55.8. Lamy, Bernardus Elementa geometriae seu mesurae corporis/Les elemens de geometrie, ou de la mesure du corps ... (Parisiis 1685, Rezension). Pp. 94-5.9. Griendelius ab Ach, Ioannes Franciscus. Micrographia nova (Norimbergae 1687, Rezension). Pp. 95-6.10. Picardus (de la Hire (ed.)). Tractatus de libellatione/Traité du nivellement ... (Parisiis 1686, Rezension). Pp. 96-9.11. Bio" Moschus (de Longepierre (conv.)). Idyllia Bionis et Moschi/Les idylles de Bion et de Moschus (Parisiis 1686, Rezension). Pp. 99-102.12. Leeuwenhoek, Antonius Anatomia. Seu interiora rerum cum animaliusm tum inanimatarum, ope et beneficio exquisitissimorum microscopiorum detecta (Lugduni Batavorum 1687, Rezension). Pp. 102-6.13. Agricola, Ioannes (Jungkens, Ioannes Helfricus (ed.)). Notae in Poppii medicamenta chymica/Deutliche und wohlgegründete Anmerckung über die Chymische Artzeneyen Johannis Poppii ... (Noribergae 1686, Rezension). Pp. 106-10. 14. Lemee, Franciscus.Tractatus de statuis/Traité des statues (Parisiis 1688, Rezension)Pp. 110-1.15. Rajus, Ioannes. Historiae plantarum tomus II. (Londini 1688, Rezension). Pp. 111-13.16. Redus, Franciscus. Bacchus in Hetruria/Bacco in Toscana (Florentiae 1685, Rezension). Pp. 113-118.17. Botelerius, Nathaniel. De servitiis et expeditionibus nauticis dialogi sex/Six Dialogues about Sea-Services (Londini 1685, Rezension). Pp. 125-6. 18. Aurelius Prudentius Clemens (Chamillardus, Stephanus (ed.)). Opera (Parisiis 1687, Rezension). Pp. 126-37.19. Boyle, Robertus. Nova experimenta circa frigus .../New Experiments and Observations touching Cold, or an Experimental History of Cold begun ... (Londini 1683, Rezension). Pp. 137-44. 19. Halleius, Edmundus. De constructione problematum solidorum ... dissertatiuncula (Übernahme aus: Transactiones philosophicae Anglicanae, 1687, Junius/Augustus, nr. 188, p. 335.). Pp. 144-151.20. Mariotte (de la Hire (ed.)). De motu aquarum/Traité du mouvement des eaux et des autres corps fluides (Parisiis 1686, Rezension).21. Cornelius, Thomas. Progymnasmata physica (Neapoli 1688, Rezension).22. P.V.D. Observationes excerptae ex praelectionibus ... Theodori Craanen (Lugduni Batavorum 1687, Rezension).23. Starkey, Georgius. Pyrotechnia asserta et illustrata/Pyrotechnia, ofte vuur-stook-kunde vastgesteld en opgehelderd ... (Amstelodami 1687, Rezension).24. de Zeidlern, Sebastianus Christianus. Institutiones medicae (Pragae 1687, Rezension).25. Anonymus. Observationes nova, seu civile Gallorum super lingua vernacula bellum/Nouvelles observations, ou guerre civile des Francois sur la langue (Parisiis 1688, Rezension). 26. Aelianus, Claudius (Schefferus, Ioannes" Kuhnius, Joachim). Variae historiae libri XIV./Klaudiou Ailianou poikiles historias biblia id' (gr.) (Argentorati 1685, Rezension).27. Strausius, Laurentius. Isagoge physica (Ulmae 1684, Rezension).28. Meyerus, Cornelius. Ars restituendi Romae navigationem sui Tiberis hactenus intermissam/L'arte di restituire a Roma la tralasciata navigatione suo Tevere ... (Romae 1685, Rezension). 29. Werdmuellerus, Ioannes Jacobus. Lapis Lydius architectorum militarium/Der Probier-Stein der Ingenieure ... (Francofurti ad Moenum 1685, Rezension).30. Sütteringus, Daniel. Georgius Rimplerus contra J. Jac. Werdmüllerum defensus/Der in Wien todte ehrliche Sachse ... (Dresdae 1687, Rezension).(vgl. p. 243.) 31. Scanavacca, Bartholomaeus. Nova inventio describendi ... horologia solaria/Novissima inventione per disegnare ... (Patavii 1688, Rezension).32. Hookius, Robertus. Contenta discursus mechanici, comcernentis descriptionem optimae formae velorum horizontalium pro usu molarum, nec non fundamentum ... (Übernahme aus: Transactiones philosophicae Anglicanae, 1681, December, nr. 3, p. 61.).33. Brownius, Eduardus. Relatio de anatome struthiocameli (Übernahme aus: Transactiones philosophicae Anglicanae, 1682, Februarius, nr. 5, p. 147.).34. Jaegerus, Ioannes Wolfgangus. Tractatus moralis de juramentis (Stutgardiae 1687, Rezension).35. Jaegerus, Ioannes Wolfgangus. Tractatus de legibus (Tubingae 1688, Rezension).36. Brown, Thomas Opera/The Works ... (Londini 1686, Rezension).37. Deckherrus, Ioannes. De scriptis adepostis, pseudepigraphis et suppostitiis conjecturae (Amstelodami 1686, Rezension).38. Newhouse, Daniel. Universa ars nautica/The whole Art of Navigation ... (Londini 1686, Rezension).39. Listerus, Martinus Relatio ... de miro quodam et monstroso animali ... per vomitum ejecto (Übernahme aus: Transactiones philosophicae Anglicanae, 1682, Martius, nr. 6, p. 164.).40. Weichardus, Ioannes. ... methodus statuas ex metallo fundendi (Übernahme aus: Transactiones philosophicae Anglicanae, 1687, Januarius, nr. 186, p. 259.).41. P.T. Chemia rationalis (Lugduni Batavorum 1687, Rezension).42. de Gottignies, Aegidius Franciscus. Logistica universalis (Neapoli 1687, Rezension).43. Bellorius, Ioannes Petrus. Veterum illustrium philosophorum, poetarum, rhetorum et oratorum imagines (Romae 1685, Rezension).44. Menetrejus, Claudius" Holstenius, Lucas" Bellorius, Ioannes Petrus Symbolica Dianae Ephesiae statua" Epistola de verubus Dianae Ephesiae statua" Notae in numismata apibus insignita (Romae 1688, Rezension).45. Smith, Ioannes Discursus completus de natura, usu et recta tractatione baroscopii/A compleat Discourse of the Nature, Use and right Managing of the Baroscope or Quick-Silver Weather Glaß (Londini 1688, Rezension).45. Schmidt, Samuel. Hodegus epistolicus (Quedlinburgi 1688, Rezension).46. Plot, Robertus. Discursus de lampadibus antiquorum sepulcralibus (Übernahme aus: Transactiones philosophicae Anglicanae, 1684, December, nr. 166, p. 806.).47. Nicasius, Claudius. De numo pantheo Hadriani imperatoris (Lugduni 1689, Rezension).48. Nicasius, Claudius. Explicatio veteris monumenti .../Explication d'un ancien monument trouvé en Guienne dans de diocese d'Ausch (Parisiis 1689, Rezension).49. Commelinus, Ioannes. Catalogus plantarum horti medici Amstelodamensis. Pars I. (Amstelodami 1689, Rezension).50. Eschinardus, Franciscus. Cursus physico-mathematici pars I. (Romae 1689, Rezension).51. Gouye. Observationes physico-mathematicae, e regno Siam ... missae/Observations physiques et mathematiques, envoyées de Siam (Parisiis 1688, Rezension).52. Bartolus, Daniel Operum ... ea, quae moralia inscribuntur/Delle opere ... le morali (Romae 1684, Rezension).53. Weisenbornius, Ioannes. Nucleus artis logicae (Hildesiae 1689, Rezension).54. Seldenus, Janus. Colloquia mensalia/Table-Talk (Londini 1689, Rezension).55. Anonymus. Dissertatio de arthritide/Dissertation sur la goutte ... (Parisiis 1689, Rezension).(vgl. p. 591.) 56. de Villemandy, Petrus. Manuductio ad philosophiae Aristotelicae, Epicureae et Cartesianae parallelismum (Amstelodami 1685, Rezension).57. Averanus, Benedictus. Orationes (Florentiae 1688, Rezension).58. Wallerus, Richardus. Observationes de cicindela volante (Übernahme aus: Transactiones philosophicae Anglicanae, 1685, Januarius, nr. 167, p. 841.)59. Hookius, Robertus. Descriptio inventi, cuius auxilio divisiones barometri ad datam quamlibet proportionem ampliare licet (Übernahme aus: Transactiones philosophicae Anglicanae, 1686, December, nr. 185, p. 241.)60. Bernier, Ioannes. Conamina physica/Essais de Medecine (Parisiis 1689, Rezension).61. Foy-Vaillant, Ioannes. Numismata aerea imperatorum, augustorum et caesarum, in coloniis, municipiis et urbibus ... percussa (Parisiis 1688, Rezension).62. Harduinus, Ioannes. Antirrheticus de nummis antiquis (Parisiis 1689, Rezension).63. Mortonus, Richardus. Phthisiologia (Londini 1689, Rezension).64. Perraltius. Tentamina physica. Tomus IV./Essais de physique ... (Parisiis 1688, Rezension).65. Floyerus, Ioannes. Lapis Lydius medicamentorum/Pharmako-Basanos (gr.), or, the Touchstone of Medicines (Londini 1687" 1691, Rezension).66. Porschon, A. Tractatus novus de purpura, morbillis et variolis/Nouveau traitté du pourpre, de la rougeole et petite verole ... (Parisiis 1688, Rezension).67. Alexander Phoebammon Minutianus (Normannus, Laurentius (ed.)). De figuris sententiae atque elocutionis libri duo De sedibus argumentorum" De schematibus oratoriis/Peri ton tes dianoias schematon, kai peri ton tes lexeos schematon ... (gr.) (Upsaliae 1690, Rezension) 518 68. Hickesius, Georgius. Institutiones grammaticae Anglo-Saxonicae et Moeso-Gothicae (Oxonii 1689, Rezension).69. Solski, Stanislaus. Praxis nova et expeditissima geometrice mensurandi distantias, altitudines et profunditates (Cracoviae 1688, Rezension).70. Goad, Ioannes. Astro-Meteorologia sana (Londini 1690, Rezension).71. Ovidius Naso, Publius (Crispinus, Daniel (ed.)). Opera (Lugduni 1689, Rezension).72. Solski, Stanislaus. Geometra et architectus Polonus/Geometra y architekt Polski (Cracoviae 1683"1686 1690, Rezension).73. Aristarchus Pappus (Wallis, Ioannes). De magnitudine et distantiis solis et lunae liber Secundi libri mathematicae collectionis fragmentum/Peri megethon kai apostematon heliou kai selenes biblion ... (gr.) Tou tes synagioges bibliou b' apospasma (gr.) (Oxoniae 1688, Rezension).74. Fabrettus, Raphael. De columna Trajani syntagma (Romae 1683, Rezension).75. Giannettasius, Nicolaus Parthenius. Halieutica (Neapoli 1689, Rezension).76. Piso, Homobonus. Ultio antiquitatis in sanguinis circulationem (Cremonae 1690, Rezension).77. Rigordus Graverolus. Dissertatio historica de numo aliquo/Dissertation historique sur une medaille d'herodes Antipas (Parisiis 1689, Rezension).78. Bayle, Fridericus. Dissertatio quaestiones quasdam physicas et medicas explanans/Dissertations sur quelques questions de physique et de medecine ... (Tolosae 1688, Rezension)79. Paragallus, Casparus. Disquisitio circa causam terrae motuum /Ragionamento ... intorno alla cagione de tremonti (Neapoli 1689, Rezension).80. Anonymus. Responsum ad dissertationem de arthritide/Response a la dissertation sur la goutte (Parisiis 1690, Rezension).(vgl. p. 429.) 81. Desroches. Dictionarium nauticum/Dictionaires de termes propres de marine (Parisiis 1687, Rezension).82. de Launay. Praecepta necessaria in eorum consignata gratiam, qui herniis laborant/Instructions necessaires pour ceux qui sont incommodés des décentes ... (Parisiis 1690, Rezension).83. le Monnier, L. tractatus novus de morbo Venereo/Nouveau traitté de la maladie venerienne ... (Parisiis 1689, Rezension).84. Capuanus, Leonardus. De medicamentorum incertitudine discursus/Ragionamenti ... intorno alla incertezza de' medicamenti (Neapoli 1689, Rezension)‎

Bookseller reference : 44274

‎"L'HOPITAL (L'HOSPITAL) LE MARQUIS DE.‎

‎Solution d'un Probléme Physico-Mathematique.‎

‎(Paris, Jean Boudot, 1703). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1700"". Pp. 9-21 and 1 folded engraved plate.‎

‎First appearance of a paper in mathematical physics in which L'Hospital - best known by his draft of the first treatise oof the differential calculus - in which he applies the new mathematical tool, the calculus to physics. ""L'Hospital was a major figure in the early development of the calculus on the continent of Europe. he advanced its cause not only by his scientific works but also by his many contacts, including correspondence with Leibniz, Jean Bernouilli, and with Huygens. Fontenelle tells us that it was he who introduced Huygens to the new calculus.""(DSB).‎

Bookseller reference : 44386

‎"WIENER, NORBERT.‎

‎Nonlinear Problems in Random Theory.‎

‎New York: The Technology Press of the Massachussetts Institute of Technology, John Wiley and Sons, Inc, 1958. 8vo. In the original green embossed full cloth with the original wrappers. Previous owner's stamp to front free end-paper. Wrappers with some wear, otherwise a very fine and clean copy. IX, (1), 131 pp.‎

‎First edition, with author's signature to title page, of this seminal work within modelling of physiological systems. The book is ""an examination of the role of nonlinear processes in physics, mathematics, electrical engineering, physiology and communications theory."" (OOC 1004).""Wiener's seminal ideas on systems and cybernetics have shaped the entire field of systems science and have inspired it tremendous in the last 50 years. [...] Furthermore, Wiener's specific mathematical ideas for modeling nonlinear dynamic systems in a stochastic context, presented in his seminal monograph [the present], have provided great impetus to our collective efforts for modeling physiological systems."" (Marmarelis, Nonlinear dynamic modeling of physiological systems. P. 142).See Origins of Cyberspace 1004.‎

Bookseller reference : 44426

‎"HILBERT, DAVID.‎

‎Ueber die Vollen Invariantensysteme.‎

‎Leipzig, B.G. Teubner, 1893. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet 1893 durch Alfred Clebsch und Carl Neumann. 42. Band. 3. Heft."" Entire issue offered. [Hilbert:] Pp. 314-73. [Entire issue: Pp. 314-604].‎

‎First printing of Hilbert's fundamental landmark paper in which he ""INTRODUCED STUNNING NEW IDEAS WHICH HAVE DEEPLY INFLUENCED THE DEVELOPMENT OF MODERN ALGEBRA AND ALGEBRAIC GEOMETRY."" (Buchberger. Gröbner bases and applications. P. 63). The ideas presented in the present paper was introduced in his 1890-paper, but here he ""called attention to the fact that his earlier results failed to give any idea of how a finite basis for a system of invariants could actually be construted. [...] To show how these drawbacks could be overcome, Hilbert thus adopted an even more general standpoint [...]. He described the guiding idea of this culminating paper of 1893 as invariants could actually be constructed"". (Hendricks. Proof theory: history and philosophical significance. P. 59) Hilbert's first work on invariant functions led him to the demonstration in 1888 of his famous finiteness theorem. Twenty years earlier, Paul Gordan had demonstrated the theorem of the finiteness of generators for binary forms using a complex computational approach. Attempts to generalize his method to functions with more than two variables failed because of the exceedingly complicated calculations involved. Hilbert realized that it was necessary to take a completely different path. Hilbert sent his results to the Mathematische Annalen. Gordan, the expert on the theory of invariants for the Mathematische Annalen, did not appreciate the revolutionary nature of Hilbert's theorem and rejected the article. His - now famous - comment was: Das ist nicht Mathematik. Das ist Theologie. (i.e. This is not Mathematics. This is Theology).Klein, on the other hand, recognized the importance of the work immediately, and guaranteed that it would be published without the slightest alterations. Encouraged by Klein and by the comments of Gordan, Hilbert extended his method in a second article, providing estimations on the maximum degree of the minimum set of generators, and he sent it once more to the Annalen. After having read the manuscript, Klein wrote to him, saying: ""WITHOUT DOUBT THIS IS THE MOST IMPORTANT WORK ON GENERAL ALGEBRA that the Annalen has ever published.""Later, after the usefulness of Hilbert's method was universally recognized, Gordan himself said: ""I have convinced myself that even theology has its merits"".(Klein. Development of mathematics in the 19th century. P. 311).‎

Bookseller reference : 44428

‎"HILBERT, DAVID.‎

‎Ueber die Endlichkeit des Invariantensystems für binäre grundformen (+) Ueber Büschel von binären Formen mit vorgeschriebener Functionaldeterminante. - [""WITHOUT DOUBT THIS IS THE MOST IMPORTANT WORK ON GENERAL ALGEBRA""]‎

‎Leipzig, B.G. Teubner, 1888. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet 1888 durch Rudolf Friedrich Alfred Clebsch. XXXIII.[33] Band. 2. Heft."" Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 223-6"" Pp.227-36 [Entire issue: Pp. 161-316].‎

‎First printing of Hilbert's exceedingly important and groundbreaking paper in which he proved his famous Basis Theorem that is, if every ideal in a ring R has a finite basis, so does every ideal in the polynomial ring R[x]. Hilbert had thus connected the theory of invariants to the fields of algebraic functions and algebraic varieties. When Felix Klein read the paper he wrote ""I do not doubt that this is the most important work on general algebra that the Mathematische Annalen has ever published.""Hilbert submitted a paper proving the finite basis theorem to Mathematische Annalen. However Gordan was the expert on invariant theory for the journal and he found Hilbert's revolutionary approach difficult to appreciate. He refereed the paper and sent his comments to Klein:""The problem lies not with the form ... but rather much deeper. Hilbert has scorned to present his thoughts following formal rules, he thinks it suffices that no one contradict his proof ... he is content to think that the importance and correctness of his propositions suffice. ... for a comprehensive work for the Annalen this is insufficient.""Gordan rejected the article. His - now famous - comment was: Das ist nicht Mathematik. Das ist Theologie. (i.e. This is not Mathematics. This is Theology).However, Hilbert had learnt through his friend Hurwitz about Gordan's letter to Klein and Hilbert wrote himself to Klein in forceful terms:""... I am not prepared to alter or delete anything, and regarding this paper, I say with all modesty, that this is my last word so long as no definite and irrefutable objection against my reasoning is raised.""At the time Klein received these two letters from Hilbert and Gordan, Hilbert was an assistant lecturer while Gordan was the recognised leading world expert on invariant theory and also a close friend of Klein's. However Klein recognised the importance of Hilbert's work and assured him that it would appear in the Annalen without any changes whatsoever, as indeed it did. Hilbert expanded on his methods in a later paper, again submitted to the Mathematische Annalen [1893] and Klein,after reading the manuscript, wrote to Hilbert saying:-I do not doubt that this is the most important work on general algebra that the Annalen has ever published.Later, after the usefulness of Hilbert's method was universally recognized, Gordan himself said: ""I have convinced myself that even theology has its merits"".(Klein. Development of mathematics in the 19th century. P. 311).Sometimes Hilbert's first publication of the Basis Theorem is referred to as being published in the paper ""Zur Theorie der algebraischen Gebilde"" in Göottinger Nachrichten in 1888. This, however, was published in December 1888 and the present issue was published in March.‎

Bookseller reference : 44430

‎"KILLING, WILHELM.‎

‎Die Zusammensetzung der stetigen endlichen Transformationsgruppen. - [THE FOUNDATION OF A STRUCTURE THEORY FOR LIE ALGEBRAS]‎

‎Leipzig, B.G. Teubner, 1888. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet 1888 durch Rudolf Friedrich Alfred Clebsch. XXXIII. [33] Band. 1. Heft."" Entire issue offered. Wrappers with a few nicks, internally fine and clean. [Killing:] Pp. 1-48. [Entire issue: Pp. IV,160 pp].‎

‎First publication of Killing's seminal paper in which he laid the foundation of a structure theory for Lie algebras.""In particular he classified all the simple Lie algebras. His method was to associate with each simple Lie algebra a geometric structure known as a root system. He used linear transformation, to study and classify root systems, and then derived the structure of the corresponding Lie algebra from that of the root system.""(Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences)Unfortunately for Killing a myth arose that his work was riddled with error, which later has been proved untrue. ""As a result, many key concepts that are actually due to Killing bear names of later mathematicians, including ""Cartan subalgebra"", ""Cartan matrix"" and ""Weyl group"". As mathematician A. J. Coleman says, ""He exhibited the characteristic equation of the Weyl group when Weyl was 3 years old and listed the orders of the Coxeter transformation 19 years before Coxeter was born.""The theory of Lie groups, after the Norwegian mathematician Sophus Lie, is a structure having both algebraic and topological properties, the two being related.‎

Bookseller reference : 44433

‎COURANT, R. und D. HILBERT.‎

‎Methoden der Mathematischen Physik. 2 Bde. Zweite verbesserte Auflage.‎

‎Berlin, Julius Springer, 1931-37. (Reprinted 1943). 2 orig. full cloth. XIV,1),469(XIV),(6),549 pp. Internally clean and fine.‎

Bookseller reference : 44476

‎"CANTOR, GEORG.‎

‎Bemerkung mit Bezug auf den Aufsatz: Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen in Math. Annalen. Bd. XXXIII, p. 154. - [CANTOR ON NUMBER THEORY]‎

‎Leipzig, B.G. Teubner, 1889. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet 1889 durch Rudolf Friedrich Alfred Clebsch. XXXIII.[33] Band. 3. Heft."" Entire issue offered. Internally very fine and clean. [Cantor:] P. 476. [Entire issue: Pp. (1), 318-476, (1)].‎

‎First printing of Cantor's important comment to Illigens paper from the same year: ""Zur Weierstrass'-Cantor'schen Theorie der Irrationalzahlen"". He states that: ""The squareroot of 3 is thus only a symbol for number which has yet to to be found, but is not its definition. The definitions is, however, satisfactorily given by my method as, say (1.7, 1.73, 1.732, ...). [From the present paper]. Cantor is famous for his work on infinite numbers.‎

Bookseller reference : 44494

‎"KLEIN, FELIX.‎

‎Zur Nicht-Euklidischen Geometrie (+) Ueber die Nullstellen der hypergeometrischen Reihe.‎

‎Leipzig, B.G. Teubner, 1890. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXXVII. [37]. Band. 4. Heft."" Entire issue offered. Internally very fine and clean. [Klein:] Pp. 544-72"" 573-90. [Entire issue: Pp. pp. 465-604].‎

‎First printing of Klein's important contribution to non-Euclidean geometry. Klein saw a fundamental unity in the subject of non-Euclidean geometry. Rather than a heterogeneous collection of abstruse mathematics, non-Euclidean geometry was in Klein's view a ""concrete discipline"".For over two millennia geometry had been the study of theorems which could be proved from Euclid's axioms. However, in the beginning of the 19th century it was proved that there exist other geometries than that of Euclid. Motivated by the emergence of the new geometries of Bolyai, Lobachevsky, and Riemann, Klein proposed to define a geometry, not by a set of axioms, but instead in terms of the transformations that leave it invariant" according to Klein, a geometric structure consists of a space together with a particular group of transformations of the space. A valid theorem in that particular geometry is one that holds under this group of transformations. This controversial idea did not only give a more systematic way of classifying the different geometries, but also gave birth to new geometric structures such as manifolds. Landmark Writtings in Western Mathematics 1640-1940, p.544-52.‎

Bookseller reference : 44503

‎"KLEIN, FELIX.‎

‎Neue Untersuchungen im Gebiete der elliptischen Functionen.‎

‎Leipzig, B.G. Teubner, 1886. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXVI. [26]. Band. 3. Heft."" Entire issue offered. Internally very fine and clean. [Klein:] Pp. 455-464. [Entire issue: Pp. 309-464].‎

‎First printing of Klein's paper on elliptic functions. ""One of the leading mathematicians of his age, Klein made many stimulating and fruitful contributions to almost all branches of mathematics, including applied mathematics and mathematical physics. Moreover, his extensive activity contributed greatly to making Göttingen the chief center of the exact sciences in Germany. An opponent of one sided approaches, he possessed an extraordinary ability to discover quickly relationships between different areas of research and to exploit them fruitfully."" (DSB).‎

Bookseller reference : 44526

‎"WEYL, HERMANN.‎

‎Über die Konvergenz von Reihen, die nach Orthogonalfunktionen fortschreiten.‎

‎Leipzig, B.G. Teubner, 1909. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 67 Band. 2. Heft."" Entire issue offered. Internally very fine and clean. [Weyl:] Pp. 225-45. [Entire issue: Pp. 145-280].‎

‎First printing of Weyl's paper on the convergence of series which continue as orthogonal functions. ""Very few of Weyl's 150 published books and papers-even those chiefly of an expository character-lack an original idea or afresh viewpoint. The influence of his works and of his teaching was considerable: he proved by his example that an ""abstract"" approach to mathematics is perfectly compatible with ""hard"" analysis and, in fact, can be one of the most powerful tools when properly applied."" (DSB)‎

Bookseller reference : 44528

‎"HILBERT, DAVID.‎

‎Hermann Minkowski. - [HILBERT'S OBITUARY OVER MINKOWKI]‎

‎Leipzig, B.G. Teubner, 1910. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 68. Band. 4. Heft."" Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 445-71. [Entire issue: Pp. 445-572].‎

‎First printing of Hilbert's obituary over Minkowki. They had a life long friendship.""Minkowski was born of German parents who returned to Germany and settled in Königsberg [now Kaliningrad, R.S.F.S.R.] when the boy was eight years old. His older brother Oskar became a famous pathologist. Except for three semesters at the University of Berlin, he received his higher education at Köningsberg, where he became a lifelong friend of both Hilbert, who was a fellow student, and the slightly older Hurwitz, who was beginning his professorial career. Hilbert’s education at Königsberg and his close friendship with Hermann Minkowski both stimulated his interest in physics."" (DSB).‎

Bookseller reference : 44530

‎"HILBERT, DAVID.‎

‎Ueber die gerade Linie als kürzeste Verbindung zweier Punkte. (Aus einem an Herrn F. Klein gerichteten Briefe). - [FIRST PUBLICATION OF THE HILBERT METRIC]‎

‎Leipzig, B.G. Teubner, 1895. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 46. Band. 1. Heft.""Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 91-96. [Entire issue: IV, 160 pp].‎

‎First printing of Hilbert's groundbreaking paper in which ""Hilbert's Metric"" (or Hilbert's projective metric) - and the metric in general - was introduced. The Hilbert metric an a closed convex cone that can be applied to various purposed in non-Euclidean geometryThe usefulness of Hilbert's metric were made clear in 1957 by Garrett Birkhoff who showed that the Perron-Frobenius theorem for non-negative matrices and Jentzch's theorem for integral operators with positive kernel could both be proved by an application of the Banach contraction mapping theorem in suitable metric spaces. (Serrin. Hilbert's Matric. P. 1).‎

Bookseller reference : 44580