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Motives and problems of the arithmetization of mathematics in the first half of the 19th century - Cauchy's analysis in the view of the mathematician Martin Ohm

literature

  1. Abel, N. H .: Développement de (cos x)n et de (sin x)n en séries de ... Universitetsbiblioteket i Oslo. Manuscrits d'Abel. Cahier numéro V. Signature: MS nO 435 in-folio, undated, pp. 3–11

  2. Abel, NH: Investigations on the series: \ (1 + \ frac {m} {1} x + \ frac {{m (m - 1)}} {{1 \ cdot 2}} x ^ 2 + \ frac { {m (m - 1) (m - 2)}} {{1 \ cdot 2 \ cdot 3}} x ^ 2 + ... \) in: Journal for pure and applied mathematics 1 (1826), 311-339. Reprint: A. Wangerin (Ed.). Leipzig 1895

    Google Scholar

  3. Abel, N. H .: Correspondence d'Abel. In: Mémorial publié à l'occasion du centenaire de sa naissance. Kristiania 1902

  4. Archive of mathematics and physics with special regard to the needs of teachers in higher education institutions. Edited by J. A. Grunert. Greifswald 1841 ff.

  5. Bekemeier, B .: The "Arithmetization of Mathematics" - A basic theoretical program of mathematics in the 19th century. In: Bekemeier u.a .: Science and Education in the Early 19th Century II, Materials and Studies of the IDM, Vol. 30. Bielefeld 1982, 1-96

  6. Bekemeier, B .: Martin Ohm (1792–1872): University mathematics and school mathematics in the new humanist educational reform. Studies on the history of science, society and education 3. Göttingen 1986

  7. Biermann, K. R .: Mathematics and its lecturers at the Berlin University 1810–1920. Berlin 1973

  8. Boehm, C .: Overview of volumes 14, 15, 16, 16 * of the first series. In: Leonardi Euleri Opera Omnia I16, Part 2. Basel 1935, VII-LXXIII

  9. Bohlmann, G .: Overview of the most important textbooks on infinitesimal calculus from Euler up to the present day. Annual report of the DMV 6 (1897), 91–110

    Google Scholar

  10. Bolzano, B .: The binomial theorem, and as a consequence of it the polynomial, and the series that are used to calculate the logarithms and exponentials, more precisely than previously proven. Prague 1816

  11. Bolzano, B .: Purely analytical proof of the theorem that between every two values ​​that give an opposite result there is at least one real root of the equation. 1817. Reprint: A. Kolman: Bernard Bolzano. Berlin 1963, 175-207

    Google Scholar

  12. Boutroux, P .: The ideal of science for mathematicians. Authorized German edition with explanatory notes by H. Polloczek-Geiringer. Leipzig and Berlin 1927

  13. v. Braunmühl, A .: Lectures on the history of trigonometry. 2 parts. Stuttgart 1900-1903. Unchanged reprographic reprint: Wiesbaden 1971

    Google Scholar

  14. Bredow, F .: De potestatibus sinuum et cosinuum quae secundum sinus aut cosinus multiplicium arcuum procedunt dissertatio, Breslau 1829

  15. Bulletin universel des sciences et de l'industrie publ. par la Société pour la Propagation des Connaissances Scientifiques et Industrielles. Section 1: Bulletin des sciences mathématiques, astronomiques, physiques et chimiques, éd. Férussac 1824ff (= "Bulletin de Férussac")

  16. Burkhardt, H .: Trigonometric series and integrals up to about 1850. In: Encyklopadie der Mathematischen Wissenschaften with inclusion of their applications. Leipzig 1904–1916. 2nd vol., 1st part, 2nd half, 819-1354

  17. Burkhardt, H .: On the use of divergent series in the period 1750–1860. In: Math. Annals 70 (1910/11), 169–206

    Google Scholar

  18. Cantor, M .: Obituary to Oskar Schlömilch. Biblioteca mathematica 3rd volume, 2nd volume (1901), 260–281

    Google Scholar

  19. Cassirer, E .: The problem of knowledge in modern philosophy and science, 1st vol. Darmstadt 1974

  20. Cauchy, A. L .: Cour d'analysis de l'école royale polytechnique. I.re Lot. Analysis algébrique. Paris 1821. Reprint: Oeuvres complètes d'Augustin Cauchy, IIe série, tome III. Paris 1897

  21. Cauchy, A. L .: Sur le développement des fonctions en séries et sur l'intégration des equations différentielles ou aux différences partielles. Bulletin de la Sociéte Philomatique, 1822, 49-54. Reprint: Oeuvres complètes d'Augustin Cauchy, IIe série, tome II, 276-282

  22. Cauchy, A. L .: Résumé des leçons données à l'école royale polytechnique sur le calcul infinitésimal. Paris 1823. Reprint: Oeuvres complètes d'Augustin Cauchy, IIe série, tome IV, 3-261. Paris 1899

  23. Cauchy, A. L .: Sur l'analyse des sections angulaires. In: Exercises de mathématiques. Paris 1826. Reprint: Oeuvres complètes d'Augustin Cauchy, IIe série, tome VI, 11-22

  24. Cauchy, A. L .: Leçons sur les applications du calcul infinitésimal à la géométrie. Paris 1826a. Reprint: Oeuvres complètes d'Augustin Cauchy, IIe série, tome V.

  25. Cauchy, A. L .: A. L. Cauchy's Textbook of Mathematical Analysis. 1st part. Algebraic Analysis. Translated from the French by C. L. A. Huzler. Königsberg 1828 (= German translation by Cauchy 1821)

  26. Cauchy, A. L .: Leçons sur le calcul différentiel. Paris 1829. Reprint: Oeuvres complètes d'Augustin Cauchy, IIe série, tome IV, Paris 1899, 263–609

  27. Cauchy, A. L .: Lectures on differential calculus combined with Fourier's method of solving certain equations. Translated from French by Dr. E. H. Schnuse. Braunschweig 1836 (= German translation by Cauchy 1829)

  28. Cauchy, A. L .: Lectures on the applications of calculus to geometry. German edited by Dr. E. H. Schnuse. Braunschweig 1840 (= German translation by Cauchy 1826a)

  29. Cauchy, A. L .: Lectures on the applications of calculus to geometry. Additions. German edited by Dr. E. H. Schnuse. Brunswick 1846

  30. Cauchy, A. L .: Algebraic Analysis. German edited by Carl Itzigsohn. Berlin 1885 (= German translation by Cauchy 1821)

  31. Crelle, A. L .: Solution d'une difficulté connue que présente la théorie des fonctions angulaires, relativement au développement des puissances fractionnaires des cosinus. Annales de mathématiques pures et appliquées 13 (1822/23), 213–241

    Google Scholar

  32. Crelle, A. L. (Ed.): J. L. Lagranges mathematical works. German ed. v. ..., 3 vol. Berlin 1823

  33. Crelle, A. L .: Attempt of a general theory of the analytical faculties, according to a new method of development; prepared by an attempt at a critical examination of the powers, logarithms and exponential quantities and accompanied by remarks and discussions relating to the theory of angle functions. Berlin 1823a

  34. Crelle, A. L .: Recherches sur les expressions des puissances des cosinus et sinus en cosinus et sinus des arcs multiples, et sur les expressions réciproques. Journal for pure and applied mathematics 5 (1830), 197–221

    Google Scholar

  35. Dedekind, R .: Continuity and irrational numbers. 2nd edition Braunschweig 1892

  36. Dhombres, J .: Quelques aspects de l'histoire des équations fonctionelles liés à l'évolution du concept de fonction. Arch. Hist. Ex. Sci. 36 (1986), 91–181.

    Google Scholar

  37. Dieudonné, J. (ed.): Abrégé de l'histoire des mathématiques 1760–1900, 2 vol. Paris 1978

  38. Dirichlet, P. G. L .: About the representation of completely arbitrary functions by sine and cosine series. 1837. Reprinted in: Werke, Vol. 1, ed. by L. Kronecker. Berlin 1889, 133-160

  39. Dirksen, E. H .: Organon of the entire transcendent analysis. First part. Transcendent Elementary Doctrine. Berlin 1845

    Google Scholar

  40. du Bois-Reymond, P .: About the scope of the Taylor series expansion. Mathematical annals 21 (1883), 109–117

    Google Scholar

  41. Dugac, P .: Eléments d'analysis de Karl Weierstrass. In: Arch. Hist. Ex. Sci. 10 (1973), 41–176

    Google Scholar

  42. Dugac, P .: Richard Dedekind et les fondements des mathématiques. Paris 1976

  43. Eccarius, W .: The technician and mathematician August Leopold Crelle (1780–1855) and his contribution to the promotion and development of mathematics in 19th century Germany. Diss. Eisenach 1974

    Google Scholar

  44. Ettingshausen, A. v .: About the formulas which represent the powers of the sine or cosine of an arc of a circle by the sines and cosines of the multiples of this arc. Journal of Physics and Mathematics 1 (1826), 96–110

    Google Scholar

  45. Ettingshausen, A. v .: On the use of the method of indefinite coefficients in the expansion of the powers of the cosine of an arc according to the cosines of its multiples. Journal of Physics and Mathematics 1 (1826a), 374-379

    Google Scholar

  46. Ettingshausen, A. v .: Lectures on higher mathematics. 2Bd. Vienna 1827

  47. Euler, L .: Introductio in analysin infinitorum. Tomus primus. Lausanne 1748. Reprint: Leonardi Euleri Opera omnia I8

  48. Euler, L .: Subsidium calculi sinuum. Novi commentarii academiae scientiarium Petropolitanae 5 (1754/55), 1760, 164-204. Reprint: Leonardi Euleri Opera Omnia I14, 542–584.

    Google Scholar

  49. Euler, L .: De seriebus divergentibus. Novi commentarii academiae scientiarium Petropolitanae 5 (1754 / 55a), 1760, 205-237. Reprint: Leonardi Euleri Opera Omnia I14, 585–617

    Google Scholar

  50. Euler, L .: Observationes generales circa series quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur. Nova acta academiae scientiarium Petropolitanae 7 (1789), 1793, 87-98. Reprint: Leonardi Euleri Opera Omnia I16, 163–177

    Google Scholar

  51. Euler, L .: Dilucidationes super formulis, quibus sinus et cosinus angulorum multiplorum exprimi solent, ubi simul ingentes difficultates diluuntur. Nova acta academiae scientiarium Petropolitanae 9 (1791), 1795, 54-80. Reprint: Leonardi Euleri Opera Omnia I16, 282–310

    Google Scholar

  52. Fichte, J. G .: Deduced plan of a higher educational institution to be established in Berlin, which is in proper connection with an academy of sciences. 1807. In: Weischedel, W. (Ed.): Idea and Reality of a University. Berlin 1970, 30-105

    Google Scholar

  53. Freudenthal, H .: Cauchy. In: C. C. Gillispie (ed.): Dictionary of Scientific Biography, vol. III. New York 1971, 131-148

  54. Fries, J. F .: The mathematical natural philosophy processed according to the philosophical method: an experiment. Heidelberg 1822. Reprographic reprint: J. F. Fries, Complete Writings, ed. v. G. König and L. Geldsetzer, Vol. 13. Aalen 1979

  55. Grabiner, J. V .: Is mathematical truth time-dependent? American Mathematical Monthly 81 (1974), 354–365

    Google Scholar

  56. Grabiner, J. V .: The Origins of Cauchy's Theory of the Derivative. In: Historia Mathematica (1978), 379-409

  57. Grabiner, J. V .: The Origins of Cauchy's Rigorous Calculus. Cambridge / Mass. 1981

  58. Grassmann, H .: The linear expansion theory. Leipzig 1844. Reprint: New York 1969

  59. Grattan-Guinness, I .: Bolzano, Cauchy and the "New Analysis" of the Early Nineteenth Century. Arch. Hist. Ex. Sci. 6 (1969–70), 372–400

    Google Scholar

  60. Grattan-Guinness, I .: The Development of the Foundations of Mathematical Analysis from Euler to Riemann. Cambridge / Mass. 1970

  61. Grattan-Guinness, I (ed.): From the Calculus to Set Theory, 1630-1910. London 1980

  62. Hilbert, D .: About the Infinite, 1925. Reprint: D. Hilbert: Hilbertiana. Darmstadt 1964

    Google Scholar

  63. Hindenburg, C. F. (Ed.): The polynomial theorem, the most important theorem of all analysis: together with some related and other theorems, revised and presented by v. Tetens, ... Promoted for printing and with notes, also a short abstract d. combinatorial method and its application to analysis provided by C. F. Hindenburg. Leipzig 1796 (= collection of combinatorial-analytical treatises 1)

  64. Holmboe, B. (ed.): Oeuvres complètes d'Abel, mathématicien. Christiania 1839

  65. Jahnke, H. N .: On the relationship between education and scientific thinking using the example of mathematics. A controversy about the mathematical curriculum of the Prussian grammar schools 1829-30 and their methodological context, in: Bekemeier / Jahnke / Lohmann / Otte / Schminnes (ed.): Science and education in the early 19th century I, materials and studies of the IDM, vol . 27. Bielefeld 1982, 2–225

  66. Jahnke, H. N .: On the historical meaning of the concept of the indirect application of the sciences. In: Steiner / Winter (Hrsg.): Mathematikdidaktik, Bildungsgeschichte, Wissenschaftsgeschichte. Cologne 1985, 48-53

  67. Yearbooks for Scientific Criticism, ed. v. d. Society for Scientific Criticism in Berlin, Aug. 1827, No. 153-160, review v .: 1) F. W. Spehr: Neue Principien des Fluentencalcüls. 2) A. L. Cauchy: Resumé des leçons données à l'Ecole royale Polytechnique sur le calcul infinitésimal (Author: Dirksen)

  68. Yearbooks for Scientific Criticism, ed. v.d. Society for Scientific Criticism 1829, 2nd Vol., Col. 211-222. Review of A. L. Cauchy's textbook on algebraic analysis. Translated from the French by C. L. B. Huzler (Author: Dirksen)

  69. Knopp, K .: Theory and Application of Infinite Series. 5th edition Berlin 1964

  70. Koppe, C .: The beginnings of pure mathematics for school lessons. Vol. 1, 2, 3, 4, 1st ed. Essen 1836–38

  71. Koppelmann, E .: The Calculus of Operations and the Rise of Abstract Algebra. Arch. Hist. Ex. Sci. 8 (1971/72), 155–242

    Google Scholar

  72. Kronecker, L .: Letter to Georg Cantor dated August 21, 1884. In: Meschkowski, H .: Problems of the infinite. Work and life of Georg Cantor. Braunschweig 1967, 237-239

  73. Kummer, E.E .: De cosinuum et sinuum potestatibus evolvendis. Dissertation. Hall 1832

    Google Scholar

  74. Kummer, E. E .: About infinitely different developments of the powers of cosines and sines. Journal for pure and applied mathematics 14 (1835), 110–122

    Google Scholar

  75. Kummer, E. E .: Review of: 'The spirit of mathematical analysis and its relationship to school; First treatise ‘by Martin Ohm. Berlin 1842. In: Yearbooks for Scientific Criticism 1842, Sp. 209–216

  76. Lacroix, S. F .: Traité du calcul différentiel et du calcul intégral. 3 vol., 2nd edition. Paris 1810-1819

  77. Lagrange, J. L .: Leçons sur le calcul des fonctions, nouvelle édition. Paris 1806. Reprint: Oeuvres de Lagrange X

  78. Lakatos, I .: Proofs and Refutations. The Logic of Mathematical Discovery. Edited by John Worrall and Elie Zahar. Cambridge 1976

  79. Lakatos, I .: Cauchy and the continuum: the significance of non-standard analysis for the history and philosophy of mathematics. In: Lakatos, I .: Mathematics, Science and Epistemology. Philosophical Papers, vol. 2. Cambridge 1978, 43-60

    Google Scholar

  80. Lambert, J. H .: Attachment to the architectonics or theory of the simple and the first in the philosophical and mathematical knowledge. 2 vol. Riga 1771. Reprint: J. H. Lambert, Philosophische Schriften, ed. v. H.-W. Arndt, Vol. III and IV. Hildesheim 1965

  81. Laugwitz, D .: Cauchy and Infinitesimals. Reprint No. 911 of the Department of Mathematics, Technical University. Darmstadt 1985

  82. Lorey, W .: The study of mathematics at German universities since the beginning of the 19th century. Treatises on mathematical instruction in Germany III, 4th Leipzig and Berlin 1916

  83. Manning, K. R .: The Emergence of the Weierstrassian Approach to Complex Analysis. Arch. Hist. Ex. Sci. 14 (1974/75), 297–383

    Google Scholar

  84. Mehrtens, H .: The skeleton of modern algebra. On the formation of mathematical terms with Richard Dedekind. In: C. J. Scriba (Ed.): On the emergence of new directions of thought and work in natural science. Festschrift for the 90th birthday of Hans Schimank. Göttingen 1979, 25-43

    Google Scholar

  85. Minkowski, H .: Peter Gustav Lejeune Dirichlet and its importance for today's mathematics. Annual report of the DMV 14 (1905), 149–163

    Google Scholar

  86. Nový, L .: Origins of Modern Algebra. Leyden 1973

  87. Ohm, G. S .: Basic lines for an expedient treatment of geometry as a higher educational tool in preparatory educational establishments. Erlangen 1817

  88. Ohm, M .: De elevatione serierum infinitarum secundi ordinis ad potestatem exponentis indeterminati. Dissertation, Erlangen 1811

    Google Scholar

  89. Ohm, M .: Elementary number theory for use in schools and self-learners. Erlangen 1816

  90. Ohm, M .: Critical illuminations of mathematics in general and Euclidean geometry in particular. Berlin 1819

  91. Ohm, M .: Attempt of a perfectly consistent system of mathematics, first and second part. Also under the title: Textbook of Arithmetic, Algebra and Analysis. According to its own principles. Initially edited for his lectures. Berlin 1822

  92. Ohm, M .: Essays from the field of higher mathematics. Berlin 1823

  93. Ohm, M .: The pure elementary mathematics less abstract, but more vivid. 3 vols., Berlin 1825/26. 2nd edition Berlin 1834ff

  94. Ohm, M .: Sur la transformation des fonctions trigonométriques, et principalement sur les développemens de (2 cos x)m. Bulletin de Férussac 1826, tome V, no. 160, 250-252

  95. Ohm, M .: An attempt at a short, thorough and clear instruction that can also be understood by non-mathematicians, 10-14 year old boys in lower middle classes of a grammar school; in the upper classes of a learned preparatory school, as well as in higher civil and technical preparatory schools, to enable an easy, thorough and scientific study of mathematics. As an introduction to his elementary mathematics, also for self-learners as a comment on the same ... Berlin 1827

  96. Ohm, M .: Review of: 'Textbook of Mathematical Analysis' by A. L. Cauchy (translated by C. L. A. Huzler). Koenigsberg 1828; in: Leipziger Literatur-Zeitung, No. 255, October 1829a, 2033–38

  97. Ohm, M .: Textbook of the entire higher mathematics in two volumes. For use in the upper classes of grammar schools and other higher educational institutions, as well as for self-teaching, edited and provided with many examples from ... Leipzig 1839

  98. Ohm, M .: De nonnullis seriebus infinitis summandis. Berlin 1839a

  99. Ohm, M .: The spirit of mathematical analysis and its relationship to school. First treatise Berlin 1842. Second treatise Erlangen 1846

  100. Olivier, L .: Development of an arbitrary power of a cosine by the cosine of multiple arcs. Journal for pure and applied mathematics 1 (1826), 16–36

    Google Scholar

  101. Otte, M., & Steinbring, H .: Problems of the concept development - on the concept of continuity. Didactics of mathematics 1 (1977), 16–25

    Google Scholar

  102. Otte, M .: Texts and Means. Zentralblatt für Didaktik der Mathematik 15 (1983), 183–194

    Google Scholar

  103. Pagani, M .: Eclaircissements sur le développement de cosm x, en fonction des sinus et cosinus d'arcs multiples. Annales de mathématiques pures et appliquées 13 (1822/23), 94–101

    Google Scholar

  104. Pagani, M .: Note sur le développement des puissances de sinus et de cosinus, en séries de sinus et de cosinus d'arcs multiples. Bulletin de Férussac 1826, tone V, No. 7, 4-12

  105. Peacock, G .: A Treatise on Algebra. Cambridge 1830

  106. Peacock, G .: Report on the Recent Progress and Present State of Certain Branches of Analysis. In: Report of the Third Meeting of the British Association for the Advancement of Science; Held at Cambridge in 1833. London 1834, 185–352

  107. Peano, G .: Sulla formula di Taylor. Atti Accad. Sci. Torino 27 (1891/2), 40-46. German translation in: A. Genocchi, differential calculus and basics of integral calculus, ed. v. G. Peano, translated by G. Bohlmann and A. Schepp. Leipzig 1899

    Google Scholar

  108. Plana, G .: Sur le développement des puissances des cosinus en cosinus d'arcs multiples. Annales de mathématiques pures et appliquées 11 (1820/1), 84–90

    Google Scholar

  109. Poggendorff, J. C .: Biographical-literary concise dictionary for the history of exact science I, II. Leipzig 1863

  110. Poinsot, L .: Recherches sur l'analyse des sections angulaires. Paris 1825

  111. Poinsot, L .: Note sur l'article inseré nO 124 du Bulletin précédent, et intitulé: Observations relatives au développement des puissances de sinus et de cosinus, en séries de sinus ou de cosinus d'angles multiples. Bulletin de Férussac 1825a, tome IV, No. 194, 221-222

  112. Poisson, S. D .: Note sur le développement des puissances des sinus et des cosinus en séries de sinus ou de cosinus d'arcs multiples. Correspondance sur l'Ecole Polytechnique vol. 2, No. 3, Janvier 1811, 212-217

    Google Scholar

  113. Poisson, S. D .: Observations relative au développement des puissances de sinus et de cosinus, en séries de sinus ou de cosinus d'angles multiples. Bulletin de Férussac 1825, tome IV, no. 124, 140-150

  114. Poisson, S. D .: Addition à l'article sur le développement des puissances de cosinus et de sinus, inseré dans le 'Bulletin' de Septembre dernier. Bulletin de Férussac 1825 a, tome IV, No. 295, 344–352

  115. Pringsheim, A .: On the theory of Taylor's series and the analytic functions with a limited area of ​​existence. Mathematical annals 42 (1893), 153–184

    Google Scholar

  116. Pringsheim, A .: About the necessary and sufficient conditions of the Taylor-s theorem for functions of a real variable. Mathematical annals 44 (1894), 57–82

    Google Scholar

  117. Pringsheim, A .: On the history of Taylor's theorem. Bibliotheca Mathematica. Journal of the History of Mathematical Sciences. Third episode. First volume. Leipzig 1900, 433–479

  118. Reiff, R .: History of the Infinite Rows. Munich 1889. Reprinted in 1969

  119. Richenhagen, G .: Carl Runge (1856–1927): From pure mathematics to numerics. Studies on the scientific, social and educational history of mathematics 1. Göttingen 1985

  120. Riemann, B .: About the representability of a function by a trigonometric series. 1854. In: Weber, H. (Ed.): Bernhard Riemann's Collected Mathematical Works and Scientific Legacy. Leipzig 1902, 227-271

  121. Saigey, J. F .: Report on Poinsot's reading in the Académie des sciences of May 19, 1823. Bulletin de Férussac 1824, tome II, No. 21, 12-13

  122. Saigey, J. F .: Paper on: Recherches sur l'analyse des sections angulaires, par M. Poinsot. Bulletin de Férussac 1825, tome IV, nos. 193 and 294, 216-220 and 338-344

  123. Scharlau, W .: The origins of pure mathematics. In: Jahnke / Otte (eds.): Epistemological and social problems of the sciences in the early nineteenth century. Dordrecht 1981, 331-347

  124. Schleiermacher, F. D .: Dialectics. 1822. Ed. R. Odebrecht 1942. Reprogr. Reprint: Darmstadt 1976

  125. Schleiermacher, F. D .: Occasional thoughts on universities in the German sense. In addition to an appendix about a new one to be set up. 1808. In: Weischedel, W. (Ed.): Idea and Reality of a University. Berlin 1970, 106-192

    Google Scholar

  126. Schlömilch, O .: Against Herr Doctor Barfuss. Archive of Mathematics and Physics 5 (1844), 374–400

    Google Scholar

  127. Schlömilch, O .: Handbook of mathematical analysis. First part: Algebraic Analysis. Jena 1845

  128. Schubring, G .: Mathematics and teacher training: Plans for a polytechnic in Berlin: In: Historical Studies in the Physical Sciences 12 (1981) 1, 161–194

    Google Scholar

  129. Spalt, D .: On the Myth of Mathematical Reason. An archeology for the fundamental dispute of analysis or documentation of a futile search for the unity of mathematical reason. Darmstadt 1981

  130. Stein, J. P. W .: Sur quelques cas de développement des fonctions, et en particulier sur le développement des puissances fractionnaires des sinus et cosinus. Annales de mathématiques pures et appliquées 15 (1824/25), 150–157

    Google Scholar

  131. Steiner, J .: Systematic development of the interdependence of geometric shapes, taking into account the work of old and new geometries on porisms, projection methods, geometry of position, transversals, duality and reciprocity, etc. Berlin 1832. Reprint: A. J. v. Oettingen (ed.). Leipzig 1896

  132. Sylow, L .: Les études d'Abel et ses découvertes. In: Niels Henrik Abel. Mémorial published à l'occasion du centenaire de sa naissance. Kristiania 1902

  133. Turner, R. S .: The Growth of Professorial Research in Prussia. 1818 to 1845 - Causes and Context. In: Historical Studies in the Physical Sciences 3 (1971), 137–182

    Google Scholar

  134. Woodhouse, R .: The Principles of Analytical Calculation. Cambridge 1803

  135. Youschkevitch, A. P .: The Concept of Function up to the Middle of the 19th Century. In: Arch. Hist. Ex. Sci. 16 (1976/77), 37–85

    Google Scholar

  136. Zerner, M .: Sur l'analysis des traités d'analysis: les fondements du calcul différentiel dans les traités français, 1870–1914. Cahier de didactique des mathématiques, number 30. Paris 1986

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    Hans Niels Jahnke

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Jahnke, H.N. Motives and problems of the arithmetization of mathematics in the first half of the 19th century - Cauchy's analysis in the view of the mathematician Martin Ohm. Arch. Hist. Exact Sci.37, 101-182 (1987). https://doi.org/10.1007/BF00348355

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