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Graßmann’s life

  • Hans-Joachim Petsche

Abstract

The Graßmann family had lived in Pomerania for centuries. Like his father, Hermann Graßmann spent his whole life in Stettin, except for three years in Berlin as a student and one year as a teacher at the Berlin School of Commerce. He was very involved in the life of his hometown. Civic life and culture in Stettin made a lasting impression on Hermann Graßmann’s worldview and political positions.

Keywords

Extension Theory Sion Theory Mathematical Productivity Constitutional Monarchy Petty Bourgeoisie 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    Quoted from Wehrmann 1906, p. 199.Google Scholar
  2. 2.
    See Wehrmann 1911.Google Scholar
  3. 3.
    Wehrmann 1911, p. 363.Google Scholar
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    Friedrich Engels: North-and South-German Liberalism (12 April 1842). MECW, vol. 2, p. 265.Google Scholar
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    See Wehrmann 1906, p. 241.Google Scholar
  6. 6.
    See in this context: Wehrmann 1894, Runze 1910, Rühl 1887, p. 18–23.Google Scholar
  7. 7.
    See also Wehrmann 1911, p. 404.Google Scholar
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    See Wehrmann 1911, p. 451.Google Scholar
  12. 12.
    In 1822, the “Chamber” had 226 members. By 1872, the number increased to 728. — See Wehrmann 1911, p. 451.Google Scholar
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    See Wehrmann 1911, p. 468.Google Scholar
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    Ibidem, p. 82.Google Scholar
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    Mehring 1973, p. 105.Google Scholar
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    See Scherwatzky 1939, p. 201.Google Scholar
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  25. 25.
    Ibidem, p. 156.Google Scholar
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    See Wehrmann 1911, p. 490sqq.Google Scholar
  28. 28.
    See Runze 1910.Google Scholar
  29. 29.
  30. 30.
    Runze 1907 lists some of the school’s most noteworthy pupils.Google Scholar
  31. 31.
    H. Müller 1926, p. 15. See also A. Müller 1878 and M. Wehrmann 1911, p. 489sqq.Google Scholar
  32. 32.
    See also Klein 1926, p. 173.Google Scholar
  33. 34.
    R. Graßmann 1876c, p. 21/22.Google Scholar
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    G. L. Graßmann 1868 and the Allgemeine Deutsche Biographie, vol. 9, p. 593-594, give a list of his other publications.Google Scholar
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    See G. L. Graßmann 1868 and R. Graßmann 1876c, p. 19sqq.Google Scholar
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    R. Graßmann 1876c, p. 26. See also: Curriculum vitae, by Justus Graßmann, reprinted in Scheibert 1937, p. 33sqq.Google Scholar
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    See in this context J. Graßmann’s discourses for the “akademische Erinnerungsfeste” (1846).Google Scholar
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    See in this context and on the influence on J. Graßmann of the Romantic philosophy of nature Heuser 1996. J. Graßmann probably did not appreciate the fact that Klügel’s presentation of combinatorics in Halle followed the Hindenburg school. Later he rejected this approach and relied directly on Leibniz. See KRY, p. 175.Google Scholar
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    See, for more details, Wehrmann 1911, p. 415sqq.Google Scholar
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    Karl Marx: Introduction to A Critique of Hegel’s Philosophy of Right (1844). MECW, vol. 3, p. 177.Google Scholar
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    For more information on the “Turnverein” movement, see “The life of Schleiermacher” in chapter 2, section 3.Google Scholar
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    König 1973, p. 41.Google Scholar
  44. 46.
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  45. 47.
    These are J. Graßmann 1817, 1824, 1835.Google Scholar
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    Scheibert 1937, p. 36.Google Scholar
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    Scheibert 1854, p. 160/161.Google Scholar
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    Becker /Hofmann 1951, p. 327/328.Google Scholar
  50. 54.
    These are, on the one hand, the “Curriculum vitae et studiorum ratio” from 17 December 1831, submitted to the Berlin commission for the first examination for teachers (25 half-folios) and, on the other, a curriculum vitae in German from 23 March 1833. Graßmann submitted the latter when he took theology exams in Stettin (15 half-folios). Both texts (Graßmann 1831, 1833) can be found in the Pomeranian Library Szczecin. Engel mentions scientific documents left behind by Graßmann (BIO, p. 373) which the author of the present book has been unable to uncover. Gert Schubring’s search for additional Graßmann manuscripts was likewise unsuccessful (see Schubring 1996c). The Möbius archive in Leipzig, which possessed letters of Graßmann’s, was completely destroyed during the Second World War. Therefore the present book must largely rely on the extensive documentation of Graßmann’s life in (BIO). Recently discovered material on Graßmann and his family will be published in autumn 2009 in a book of Graßmann sources.Google Scholar
  51. 55.
    Graßmann 1831, translation from Latin.Google Scholar
  52. 56.
    Graßmann 1833.Google Scholar
  53. 57.
  54. 58.
  55. 59.
  56. 60.
  57. 61.
    Justus Graßmann is reputed to have said that “Hermann was more given to study than Robert, but Robert was more talented” (Scheibert 1937, p. 68).Google Scholar
  58. 62.
    H. Graßmann’s secondary-school diploma, quoted from BIO, p. 17.Google Scholar
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  60. 64.
    Heinrici 1889, p. 49.Google Scholar
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    See Wirzberger 1973, p. 78. For more information on Schleiermacher, see chapter 2, section 3.Google Scholar
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  66. 70.
    See the entry G. A. Strauß in Lenz 1910a, 1910b, 1918.Google Scholar
  67. 71.
    See Wirzberger 1973, p. 78.Google Scholar
  68. 72.
    Letter to Robert Graßmann on 26 November 1836. Quoted from BIO, p. 21.Google Scholar
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  70. 74.
    BIO, p. 24.Google Scholar
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    For details on the excellent standards of philological research at Berlin University, see Wirzberger 1973.Google Scholar
  72. 76.
    See the entry F. v. Raumer in Lenz 1910a, 1910b, 1918.Google Scholar
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  75. 79.
    Ueberweg 1923, p. 274. — See also the entry H. Ritter in Lenz 1910a, 1910b, 1918.Google Scholar
  76. 81.
    Graßmann 1833.Google Scholar
  77. 85.
    Graßmann 1833.Google Scholar
  78. 86.
    Quoted from BIO, p. 150.Google Scholar
  79. 87.
    Ibidem, p. 150.Google Scholar
  80. 88.
    Justus Graßmann, Hermann Graßmann’s oldest son, confirmed the following information. — See BIO, p. 29.Google Scholar
  81. 90.
    Graßmann 1833.Google Scholar
  82. 91.
  83. 92.
    On 18 April 1847 Graßmann wrote the following letter to Saint-Venant, clarifying the rights to his discoveries by claiming that he had conceived the basic concepts of his Extension Theory as early as 1832: “Comme je lisais l’extrait de votre mémoire sur les sommes et les différences géométriques publié dans les Comptes rendus, je fus frappé par la ressemblance merveilleuse, qu’il y a entre les résultats, qui y sont communiqués et les découvertes faites par moi-même depuis l’année 1832 ”. (Quoted from BIO, p. 42/43).Google Scholar
  84. 94.
    See BIO, p. 39.Google Scholar
  85. 95.
    BIO, p. 40.Google Scholar
  86. 96.
    Graßmann’s diploma, issued on 31 December 1831; quoted from BIO, p. 41.Google Scholar
  87. 97.
    Quoted from BIO, p. 41.Google Scholar
  88. 98.
    See Engel’s explanations in BIO, p. 44.Google Scholar
  89. 99.
    Biermann 1973, p. 39.Google Scholar
  90. 100.
    BIO, p. 46.Google Scholar
  91. 101.
    Report of the director of the School of Commerce K. F. Klöden to the school’s administrative committee, dated 17 October 1834; quoted from BIO, p. 46.Google Scholar
  92. 102.
    Contract between the director of the trade school Klöden and J. Steiner, dated 14 October 1834; quoted from BIO, p. 48.Google Scholar
  93. 103.
    Biermann 1973, p. 38.Google Scholar
  94. 104.
    Quoted from BIO, p. 49.Google Scholar
  95. 105.
    BIO, p. 49.Google Scholar
  96. 106.
    In a letter to his father of 25 January 1835, Graßmann wrote the following on his corrections in the textbook: “ ... I noted a few misspellings in some formulas, which I immediately, though apprehensively, corrected ...”. Quoted from BIO, p. 51.Google Scholar
  97. 107.
    Letter from Hermann Graßmann to his father, 24 January 1835. Quoted from BIO, p. 53.Google Scholar
  98. 108.
    Letter from Hermann Graßmann to his father, 9 March 1835. Quoted from BIO, p. 53.Google Scholar
  99. 109.
    Ibidem, p. 54.Google Scholar
  100. 110.
    Letter from Hermann Graßmann to his brother Robert, 9 March 1835. Quoted from BIO, p. 54/55.Google Scholar
  101. 111.
    Letter from Hermann Graßmann to his brother Robert, 24 February 1836. Quoted from BIO, p. 60/61.Google Scholar
  102. 112.
    Petition to the Stettin city council by Hermann Graßmann, concerning a teaching position at the Ottoschule, dated 5 January 1836. Quoted from BIO, p. 58.Google Scholar
  103. 113.
    See BIO, p. 59.Google Scholar
  104. 114.
    Letter from Hermann Graßmann to his brother Robert, 24 February 1836. Quoted from BIO, p. 61.Google Scholar
  105. 117.
    Letter from Möbius to H. Graßmann, 17 June 1854. Quoted from BIO, p. 66.Google Scholar
  106. 118.
    Graßmann’s diploma, issued 12 July 1839. Quoted from BIO, p. 69.Google Scholar
  107. 119.
    This was the position Graßmann was hoping to obtain at the “Friedrich-Wilhelmsschule”, which was to be established in October 1840 — the following year. See BIO, p. 67 (footnote).Google Scholar
  108. 120.
    Graßmann’s request to the Berlin scientific examination commission, 28 February 1839. Quoted from BIO, p. 67/68.Google Scholar
  109. 121.
    Quoted from BIO, p. 69.Google Scholar
  110. 122.
    Letter of Graßmann’s accompanying his examination thesis, 20 April 1840. Quoted from BIO, p. 69.Google Scholar
  111. 123.
    Graßmann’s diploma, issued 1 Mai 1840. Quoted from BIO, p. 70.Google Scholar
  112. 124.
  113. 125.
    See BIO, p. 79.Google Scholar
  114. 126.
    Graßmann’s diploma, issued 1 Mai 1840. Quoted from BIO, p. 70.Google Scholar
  115. 127.
    Graßmann’s letter to the Prussian minister of culture and education Eichhorn, May 1847. Quoted from BIO, p. 124/125.Google Scholar
  116. 128.
    See: H. Graßmann 1878, p. 5.Google Scholar
  117. 129.
    This is how his brother Robert Graßmann remembered it. — See BIO, p. 73 (footnote).Google Scholar
  118. 132.
    See F. Engel in: GW11, xii.Google Scholar
  119. 133.
    For more information on Conrad (1796–1861), see BIO, p. 68.Google Scholar
  120. 134.
    See BIO, p. 75 (footnote).Google Scholar
  121. 135.
    The text is structured along the lines of unfolding symmetrical oppositions. The theory of language splits up into a theory of forms and a theory of concepts. Graßmann viewed the theory of concepts as a system of representations and defined it as the double opposition of sign and cognitive form on the one hand, and cognitive form and external reality, on the other. He described language as the totality of forms and ideas. At the same time, language was also the subject’s construction and a representation of reality. See in this context Erika Hültenschmidt (1995), the first analysis of this text.Google Scholar
  122. 136.
    Schlegel 1878, p. 10.Google Scholar
  123. 137.
    See BIO, p. 90.Google Scholar
  124. 138.
    See BIO, p. 90 (footnote).Google Scholar
  125. 139.
    See the index of H. Graßmann’s writings in BIO, p. 356.Google Scholar
  126. 141.
    M. Cantor and A. Leskien: “Hermann Graßmann”. In: Allgemeine Deutsche Biographie 1875sqq., vol. 9, p. 596.Google Scholar
  127. 142.
    Concerning Barycentric Calculus (Möbius 1827), see Wußing 1984, p. 35–44.Google Scholar
  128. 143.
    Letter from Graßmann to Möbius, 10 October 1844. Quoted from BIO, p. 99.Google Scholar
  129. 144.
    Letter from Möbius to Graßmann, 2 February 1845. Quoted from BIO, p. 100.Google Scholar
  130. 145.
    Letter from Apelt to Möbius, 3 September 1845. Quoted from BIO, p. 101.Google Scholar
  131. 146.
    See the letter from Baltzer to Möbius, 26 October 1846. Quoted from BIO, p. 101sq.Google Scholar
  132. 147.
    Letter from Gauß to Graßmann, 14 December 1844. Quoted from GW12, p. 397/398, editor’s note.Google Scholar
  133. 148.
    Letter from Grunert to Graßmann, 9 December 1844. Quoted from BIO, p. 103.Google Scholar
  134. 149.
    Letter from Gauß to Graßmann, 14 December 1844. Quoted from GW12, p. 397/398, editor’s note.Google Scholar
  135. 150.
    See Stanke 1974, p. 18sq.Google Scholar
  136. 151.
    See Jaworski/Detlaf 1972, p. 413. For more information on Graßmann’s theory of electrodynamics, see Sturm/Schröder/Sohncke 1879, p. 33sq. See also Müller/Pouillet 1932, p. 403, and Reif/Sommerfeld 1898sqq, p. 462.Google Scholar
  137. 152.
    Letter from Clausius to Graßmann, 15 May 1877. Quoted from BIO, p. 105. Clausius’ “beloved and admired teacher” was Justus Graßmann, who had known Clausius as a pupil during his time at the Stettin “Gymnasium”. — See also GW22, p. 255sqq.Google Scholar
  138. 154.
    Letter from Möbius to Graßmann, 9 June 1853. See BIO, p. 106. Möbius was referring to the following texts: H. Graßmann 1848a, 1851a, 1851b, 1851c, 1852.Google Scholar
  139. 155.
    Klein 1926, p. 180.Google Scholar
  140. 156.
    Klein 1926, p. 181. — See also Klein 1928, p. 132sq.Google Scholar
  141. 158.
    Letter from Möbius to Graßmann, 2 February 1845. Quoted from BIO, p. 109.Google Scholar
  142. 159.
    Quoted from GW11, p. 415/416, editor’s note.Google Scholar
  143. 160.
    See GW11, p. 417–420.Google Scholar
  144. 162.
    Quoted from BIO, p. 111.Google Scholar
  145. 163.
    Expert opinion on Graßmann’s contribution to the prize question by Möbius. Quoted from BIO, p. 112.Google Scholar
  146. 164.
    Ibidem, p. 113.Google Scholar
  147. 165.
    Ibidem, p. 114.Google Scholar
  148. 166.
    In an appendix to Graßmann’s treatise (Möbius 1847), Möbius attempted to give a geometrical interpretation of these “pseudo-magnitudes”. In subsequent works, Graßmann himself dropped some of these “pseudo-magnitudes”. — See chapter 3, section 4.Google Scholar
  149. 167.
    Letter from Drobisch to Graßmann, 8 July 1846. Quoted from BIO, p. 115/116.Google Scholar
  150. 169.
    Letter from Graßmann to the Prussian minister of culture and education Eichhorn, Mai 1847. Quoted from BIO, p. 125.Google Scholar
  151. 170.
    Ibidem, p. 125.Google Scholar
  152. 171.
    “Written assessment by Prof. Kummer on the mathematical writings of secondary-school teacher Hermann Graßmann from Stettin and his intentions of carrying out academic research”, 12 June 1847. Quoted from BIO, p. 126.Google Scholar
  153. 172.
    Ibidem, p. 126.Google Scholar
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    Ibidem, p. 127.Google Scholar
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  156. 175.
  157. 176.
    Communiqué from the Stettin school administration to the ministry of culture and education, 31 July 1847. Quoted from BIO, p. 130.Google Scholar
  158. 177.
    Letter from Eichhorn to H. Graßmann, 4 September 1847. Quoted from BIO, p. 130.Google Scholar
  159. 178.
    Wehrmann 1911, p. 471/472.Google Scholar
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    See Wehrmann 1911, p. 470sqq.Google Scholar
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    Letter from Graßmann to Möbius, 22 May 1853. Quoted from BIO, p. 160.Google Scholar
  162. 181.
    See Dahlmann 1835, p. 80sq.Google Scholar
  163. 182.
    Dahlmann 1835, p. 179/180. Concerning his rejection of democracy and despotism, see Dahlmann 1835, p. 13sqq.Google Scholar
  164. 183.
    Karl Marx: The Bourgeoisie and the Counter-Revolution (December 1848). MECW, vol. 8, p. 162.Google Scholar
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  171. 191.
    Letter from Graßmann to Möbius, 22 Mai 1853. Quoted from BIO, p. 160.Google Scholar
  172. 192.
    H. Graßmann, “Die Früchte des Berliner Barrikadenkampfes”. In: Königlich privilegierte Stettinische Zeitung, 15 April 1848. Quoted from BIO, p. 138/140.Google Scholar
  173. 193.
    R. Graßmann 1890a, p. xxi/xxii (footnote).Google Scholar
  174. 195.
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    Ibidem, p. 2/1.Google Scholar
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    Ibidem, p. 2/1.Google Scholar
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    Ibidem, p. 2/2.Google Scholar
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    Ibidem, p. 23/2.Google Scholar
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    Ibidem, p. 2/2.Google Scholar
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    Ibidem, p. 10/1.Google Scholar
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    Ibidem, p. 17/1.Google Scholar
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    Ibidem, p. 28/2.Google Scholar
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    Ibidem, p. 27/1.Google Scholar
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    See Friedrich Engels: The Constitutional Question in Germany (1847). MECW, vol. 6, p. 78.Google Scholar
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    Deutsche Wochenschrift 1848, p. 23/2.Google Scholar
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    Marx /Engels: The German Ideology (1845/46). MECW, vol. 5, p. 195.Google Scholar
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    Heine 2007, p. 114.Google Scholar
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  196. 218.
    Karl Marx: Introduction to A Contribution to the Critique of Hegel’s Philosophy of Right (1844). MECW, vol. 3, p. 185.Google Scholar
  197. 219.
    See R. Graßmann 1890a, p. xxi, footnote.Google Scholar
  198. 220.
    Letter from Graßmann to Möbius, 22 May 1853. Quoted from BIO, p. 160/161.Google Scholar
  199. 221.
    See Scheibert 1937, p. 45–50.Google Scholar
  200. 222.
    Ibidem, p. 49.Google Scholar
  201. 223.
    BIO, p. 248.Google Scholar
  202. 224.
    Letter from Graßmann to Möbius, 22 May 1853. Quoted from BIO, p. 161.Google Scholar
  203. 225.
    See the letter from Möbius to Graßmann, 9 June 1853. Extracts in: BIO, p. 162/163.Google Scholar
  204. 226.
    Bellavitis believed to have shown that Graßmann’s methods for generating third-order curves (H. Graßmann 1848a) were not generally valid. But Graßmann gave the unconditional proof of their generality and, at the same time, uncovered Bellavitis’ mistakes (see H. Graßmann 1855g). Bellavitis only learned about Graßmann’s article in August of 1859. He immediately reacted publicly to his mistake and informed Graßmann in a letter on 26 March 1860. — See BIO, p. 106.Google Scholar
  205. 227.
    According to Engel, Arithmetic and the second Extension Theory (A2) were published in 1860 and 1861. For editorial reasons, the dates were changed to 1861 and 1862. — See BIO, p. 225 and 230.Google Scholar
  206. 229.
    Knoblauch had proposed Graßmann for full membership in the Society for Natural Science Research (“Naturforschende Gesellschaft”) in the town of Halle. Graßmann was made a member on 6 February 1864. — See BIO, p. 267, footnote.Google Scholar
  207. 230.
    See Helmholtz 1855.Google Scholar
  208. 231.
    See, for more details, Turner 1995.Google Scholar
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    H. Graßmann 1853, p. 161.Google Scholar
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    Ibidem, p. 162.Google Scholar
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    Ibidem, p. 163.Google Scholar
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    Ibidem, p. 168.Google Scholar
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    Ibidem, p. 171.Google Scholar
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    See also Wußing 1977, p. 41sqq.Google Scholar
  215. 238.
    Friesler 1953, p. 93.Google Scholar
  216. 239.
    Letter from Graßmann to Möbius, 22 May 1853. Quoted from BIO, p. 162.Google Scholar
  217. 240.
    Concerning the importance of Graßmann’s approach for Helmholtz’ theory of sensation, see Lenoir 2004.Google Scholar
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  220. 243.
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    See the article by M. Cantor and A. Leskien in Allgemeine Deutsche Biographie, vol. 9, 1875sqq, p. 597.Google Scholar
  224. 247.
    See Junghans 1978, p. 251sq.Google Scholar
  225. 248.
    BIO, p. 244/245. This section also offers more information on Graßmann’s law of comparative philology.Google Scholar
  226. 249.
    See also Elfering 1995.Google Scholar
  227. 250.
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    G. Schubring (1991) has written a very noteworthy introduction to what it meant to be a teacher of mathematics in the 19th century.Google Scholar
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    Quoted from Schubring 1991, p. 169.Google Scholar
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    For more information on Graßmann as a teacher and on the Stettin “Gymnasium”, see BIO, p. 255sqq, Bartholdy 1907, Delbrück 1877, Heintze 1907, Müller 1909, Runze 1907, Runze 1910, Schlegel 1878, Wandel 1888, Wehrmann 1894. See also the summary in Schwartze 1996.Google Scholar
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    Quoted from BIO, p. 161.Google Scholar
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    Möbius was referring to the following articles: “Sur les clefs algébriques”. In: Comptes Rendus 36 (1853), p.70–75 and p. 129–136. “Sur les avantages que présente, dans un grand nombre de questions, l’emploi des clefs algébriques”. In: Comptes Rendus 36 (1853), p. 161–169. And Möbius was also thinking of Saint-Venant’s text: “De l’interprétation (géométrique) des clefs algébriques et des déterminants”. In: Comptes Rendus 36 (1853), p. 582sqq.Google Scholar
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Copyright information

© Birkhäuser Verlag AG 2009

Authors and Affiliations

  • Hans-Joachim Petsche
    • 1
  1. 1.PotsdamGermany

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