‎Mathematics‎

‎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

‎"LEVI-CIVITA, T. [TULLIO].‎

‎Sulla integrazione della equazione di Hamilton-Jacobi per separazione di variabili.‎

‎Leipzig, B.G. Teubner, 1904. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 59. Band. 3. Heft.""Entire issue offered. Internally very fine and clean. [Levi-Civita:] Pp. 383-387. [Entire issue: Pp. 321-448].‎

‎First printing of Levi-Civita's paper on the integration of the Hamilton-Jacobi equation.""Levi-Civita’s approximately 200 memoirs in pure and applied mathematics deal with analytical mechanics, celestial mechanics, hydrodynamics, elasticity, electromagnetism, and atomic physics."" (DSB).‎

Bookseller reference : 44726

‎NERNST, W. & A. SCHÖNFLIES.‎

‎Einführung in die mathematische Behandlung der Naturwissenschaften. Mit 68 im Text befindlichen Figuren. Dritte Auflage.‎

‎München & Leipzig, Wolff, 1901. Contemp. hcalf. XII,340 pp., textillustr.‎

‎Third edition of the famous textbook which by 1931 had passed through 11 editions.‎

Bookseller reference : 44744

‎"HAUSDORFF, F. [FELIX].‎

‎Grundzüge einer Theorie der geordneten Mengen. - [THE GENERALIZATION OF CANTOR'S CONTINUUM HYPOTHESIS]‎

‎Leipzig, B. G. Teubner, 1908. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet 1908 durch Alfred Clebsch und Carl Neumann. 65. Band. 4. Heft."" Entire issue offered. Wrappers with a few nicks, internally fine and clean. [Hausdorff:] Pp. 435-505. [Entire issue: Pp. 433-575].‎

‎First printing of Hausdorff important paper in which a generalization of Cantor's Continuum Hypothesis was presented for the first time. This is equivalent to what is now called the Generalized Continuum Hypothesis.The continuum hypothesis is a hypothesis, put forth by Georg Cantor in 1877, about the possible sizes of infinite sets. It states: ""There is no set whose cardinality is strictly between that of the integers and that of the real numbers.""Felix Hausdorff is considered to be one of the founders of modern topology and he contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.‎

Bookseller reference : 44768

‎"HEISENBERG, W. [WERNER].‎

‎Über quantentheoretische Kinematik und Mechanik.‎

‎(Berlin, Julius Springer, 1926). 8vo. Without wrappers. Extracted from ""Mathematische Annalen. Begründet 1868 durch Alfred Clebsch und Carl Neumann. 95. Band"". Pp. 683-704.‎

‎First printing. This paper was written as a mathematical exposition of the Three-Man-Paper 'Zur Quantenmechanik II' by Born, Jordan, and Heisenberg from the same year.‎

Bookseller reference : 44772

‎"CARNAP, RUDOLF.‎

‎Foundations of Logic and Mathematics.‎

‎Chicago, The University of Chicago Press, (1939). 8vo. In the original blue printed wrappers. A very nice and clean copy - near mint. VIII, 71 pp.‎

‎First printing of Carnap's seminal publication of his semantical period. Here Carnap presents a clear and detailed account of the application of logic and mathematics in empirical science and the central importance of the analytic/synthetic distinction herein.Carnap thought that the logic of science could be fruitfully applied to the problems of quantum theory as well. In particular, the final sections of Foundations of Logic and Mathematics (1939, 24, 25) suggest that the vexed question of the ""interpretation"" of the wave-function can be resolved by appreciating that theories of modern mathematical physics operate with ""abstract"" terms which are implicitly defined, in the manner of Hilbert, in an axiomatic system (and thus require no ""intuitive"" or ""visualizable"" meaning) but which still relate to empirical phenomena (experimental measurements) indirectly. (Cambridge Companion to Carnap).These thoughts anticipate Carnap's later conception of the ""partial interpretation"" of theoretical terms.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.‎

Bookseller reference : 44775

‎"MAUPERTUIS, PIERRE LOUIS MARIE de - FORMEY, JEAN HENRI S.‎

‎Eloge de Monsieur Maupertuis.‎

‎Berlin, Haude et Spener, 1766. 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Année 1759, tome XV. Titlepage to tome XV a. pp. 464-512. Titlepage with a stamp and engraved vignette.‎

Bookseller reference : 44785

‎"HARTREE, DOUGLAS R.‎

‎The ENIAC, an Electronic Computing Machine. - [""FIRST PAPER ON AN ELECTRONIC DIGITAL COMPUTER PUBLISHED IN A LARGE-CIRCULATION""]‎

‎London, Macmillan & Co., 1946. 8vo. Without wrappers. Extracted from ""Nature. No. 4015, Saturday, October 12, 1946, Vol. 158"". A fine and clean copy. [Hartree:] Pp. 500-6. [Entire offered issue: Pp. 495-528].‎

‎First printing of this ""first paper on an electronic digital computer published in a large-circulation international scientific journal."" (OOC).The ENIAC was the first general-purpose electronic computer. It was a Turing-complete [computationally universal] digital computer capable of being reprogrammed to solve a full range of computing problems.""Hartree, a British mathematician, first learned of ENIAC [Electronic Numerical Integrator And Computer] in 1945, when he saw the as-yet uncompleted machine during a visit to the Moore School. In 1946 he returned to the Moore School as a participant in the Moore School lectures, advising on nonmilitary uses of ENIAC"" during this time he became the first Englishman to work with the machine. He was the first to bring news of ENIAC to Great Britain, publishing the above article in Nature shourtly after his return from the United States. Although he himself invented no new calculating devices, Hartree's promotion of electronic digital calculating methods in scientific computation helped to stimulate the development of more powerful computers like Cambridge University's EDSAC."" (OOC).The ENIAC was compared to today's standard rather large: It was 100 feet long, 10 feet high, and 3 deep and contained 18,000 vacuum tubes, about 70,000 resistors, 10,000 capacitors, and 6,000 switches. It consumed 140 kilowatts of power, so much power that, when operated, the lights in a nearby town dimmed.See: Hook & Norman. Origins of Cyberspace 648.‎

Bookseller reference : 44828

‎"FABER, G.‎

‎Über stetige Funktionen. (In ""Mathematische Annalen. 66. Band. 1909""). - [FIRST PUBLICATION OF THE 'HIERARCHICAL BASIS' WITHIN MATHEMATICS]‎

‎Berlin, Julius Springer, 1909. 8vo. Bound with the original wrappers in black full cloth. A small white barcode pasted on to top left corner of front board. Library stamp pasted on the pasted down front free end-paper and stamp to verso of title page. A very nice and clean copy. [Faber:] Pp. 81-94. [Entire issue: IV, 575, (1) pp.].‎

‎First printing of Faber's important paper in which he introduces the 'hierarchical basis' and uses it for the representation of functions. Faber was building on the idea of Archimedes who computed approximately using a hierarchy of polygonal approximations of a circle. In the 1980s Faber's idea became an important ingredient for the efficient solution of partial differential equations.The issue contain the following papers of interest:Weyl, H. Singuläre Integralgleichungen. Pp. 273-324.Weyl, H & F. Jerosch. Über die Konvergenz von Reihen, die nach periodischen Funktionen fortschreiten. Pp. 67-80.And many other papers by contemporary mathematicians.‎

Bookseller reference : 44834

‎"SCHOENFLIES, ARTHUR MORITZ.‎

‎Beiträge zur Theorie der Punktmengen I-I (+) Beiträge zur Theorie der Punktmengen II (+) Beiträge zur Theorie der Punktmengen III. - [SCHOEFLIES FAMOUS STUDIES IN TOPOLOGY]‎

‎Leipzig, B.G. Teubner, 1904, 1906. 8vo. In ""Mathematische Annalen, 58. Band, 1904" 59. Band, 1904" 62. Band, 2. Heft, 1906"". 58. Band and 62. Band in the original printed wrappers, without backstrips. Date written with pencil to both front wrappers. 59. Band bound in half cloth with the original wrappers, with wear to spines. All three issue internally very fine and clean. Pp: 195-234" Pp. 129-160" Pp.286-328.‎

‎First printing of this influential series of papers by Schoenflies, his ""fundamental researches into the topological aspects of point set theory"" (Anderson. Who gave you the epsilon? P. 144).""The greater part of Schoenflies' original contributions to topology is contained in three papers [The offered] and is devoted to plane topology. He proved the topological invariance of the dimension of the square, and he invented the notions and theorems that are connected with the characterization of the simple closed curve in the plane by its dividing the plane into two domains of which it is the everywhere attainable boundary. There are numerous gaps and wrong statements in this part of Schoenflies' work, and these errors led L. Brouwer to some of his startling discoveries."" (DSB).‎

Bookseller reference : 44917

‎"DEDEKIND, VON R.‎

‎Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind. - [FIRST PRINTING OF DEDEKIND GROUP / HAMILTONIAN GROUP]‎

‎Leipzig, B.G. Teubner, 1897. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. 48. Band. 4. Heft."" Entire issue offered. Minor soiling to back wrapper, internally fine and clean. [Dedekind:] Pp. 548-61. [Entire issue: 433-606, (2) pp.].‎

‎First printing of Dedekind groups, named named after Richard Dedekind, who investigated them in proving a form of the above structure theorem (for finite groups). He named the non-abelian ones after William Rowan Hamilton, the discoverer of quaternions.In group theory, a Dedekind group is a group G such that every subgroup of G is normal. All abelian groups are Dedekind groups. A non-abelian Dedekind group is called a Hamiltonian group‎

Bookseller reference : 44919

‎"TINSEAU (D'AMONDANS, CHARLES de).‎

‎Sur quelques Propriètés des Solides renfermés par des Surfaces composées de Lignes droites.‎

‎(Paris, Moutard, Panckoucke, 1780). 4to. Extract from ""Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans"", Tome IX. Pp. 625-642 and 2 folded engraved plates.‎

‎First appearance of an importent papwer in the history of analytic geometry.""Two of the three memoirs that constitute Tinseau’s oeuvre deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruled surfaces, the study of the properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space. In these two papers the equation of the tangent plane at a point of a surface was first worked out in detail (the equation had been known since Parent), methods of descriptive geometry were used in determining the perpendicular common to two straight lines in space, and the Pythagorean theorem was generalized to space (the square of a plane area is equal to the sum of the squares of the projections of this area on mutually perpendicular planes). (DSB). Although Tinseau published very little, his papers are of great interest as additions to Monge’s earliest works. Indeed, Tinseau appears to have been Monge’s first disciple.‎

Bookseller reference : 44932

‎"ZERMELO, ERNST FRIEDRICH FERDINAND.‎

‎Beweis, dass jede Menge wohlgeordnet werden kann. (Aus einem an Herrn Hilbert gerichteten Briefe). - [INTRODUCING BOTH ""THE AXIOM OF CHOICE"" AND ""THE WELL-ORDERING THEOREM""]‎

‎Leipzig, B.G. Teubner, 1904. 8vo. Bound in half cloth with five raised bands and gilt lettering to spine. In ""Mathematische Annalen. Begründet 1868 durch von A. Clebsch und C. Neumann. 59. Band."" Small bar-code pasted on to top left corner of front wrapper. Two library labels pasted on to pasted down front free end-paper and a small stamp to verso of title page. Pp. 514-16.‎

‎First appearence of this fundamental paper in metamathematics and mathematical logic in which he introduced both ""The Axiom of Choice"" and ""his sensational proof of the well-ordering theorem"" (DSB). By this paper Zermelo contributed decisively to the development of set-theory. Zermelo took up the problem, left over by Cantor, of what to do about the comparison of sets that are not well-ordered. ""In 1904 (the paper offered) he proved....that every set can be well-ordered. To make the proof he had to use what is now known as the axiom of choice (Zermelo's axiom), which states that given any collection of nonempty, disjoined sets, it is possible to choose one member from each set and so make up a new set. The axiom of choce, the well-ordering theorem, and the fact that any two sets may be compared as to size, are equivalent principles.""(Morris Kline). A controversy arose around ""The axiom of Choice"", from Bertrand Russell, Tarski, Frege, Hilbert, Brouwer and others, mainly, and of course importent, over how to interpret the words ""choose"" and ""exists"".The issue also contain the following papers of interest:David Hilbert. Über das dirichletsche prinzip. Pp. 161-186.Lie, Sophus. Drei Kapitel aus dem unvollendeten zweiten Bande der Geometrie der Berührungstransformationen. Pp. 193-313.Schoenflies, A. Beitrage zur Theorie der Punktmengen II, Pp. 129-160.‎

Bookseller reference : 44952