Augustus De Morgan: Historian of science

History of Science

Volumn 34, Issue 104, 1996, Pages 232-240

  Rice, Adrian ^a  

^a MIDDLESEX UNIVERSITY   (United Kingdom)

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EID: 0040415259     PISSN: 00732753     EISSN: None     Source Type: Journal    
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References (199)

1. An exception is J. L. Richards, "Augustus De Morgan, the history of mathematics, and the foundations of algebra", Isis, lxxviii (1987), 7-30. It should also be noted that historians of science still make use of De Morgan's work on Newton.
2. The best bibliography of De Morgan's work is in G. C. Smith, The Boole-De Morgan correspondence 1842-1864 (Oxford, 1982), 141-7.
3. Additional works are cited in S. E. De Morgan, Memoir of Augustus De Morgan (London, 1882), 401-15.
4. Letter from G. Peacock to S. Hunter Christie, 16 Oct. 1847. Royal Society Archives: RR.1.57.
5. W. W. Rouse Ball, A history of the study of mathematics at Cambridge (Cambridge, 1889), 133.
6. See I. Grattan-Guinness, "Some British eccentrics: The historians of mathematics in the British Isles" (contribution to forthcoming volume on the history of historians of mathematics, in preparation under the editorship of C. J. Scriba and J. W. Dauben).
7. For a discussion of the historical work of Montucla, as well as that of other eighteenth- and nineteenth-century historians of science (including Delambre, Colebrooke and Whewell), see Rachel Laudan, "Histories of the sciences and their uses: A review to 1913", History of science, xxxi (1993), 1-34.
8. C. Hutton, A mathematical and philosophical dictionary (2 vols, London, 1795-96), i, p. vi.
9. C. Hutton, A mathematical and philosophical dictionary (1795-96), i, p. vi. Ibid.
10. For an evaluation of John Wallis the historian, see J. F. Scott, "John Wallis as a historian of mathematics", Annals of science, i (1936), 335-57.
11. Hutton, ", Annals of science, op. cit. (ref. 7), i, 95.
12. ", Annals of science, Ibid., i, 248.
13. ", Annals of science, Ibid., ii, 151.
14. ", Annals of science, Ibid., i, 485.
15. A. De Morgan, "Delambre", in Gallery of portraits: with memoirs, iv (London, 1835), 165-9, p. 167.
16. P. C. Enros, "The Analytical Society (1812-1813): Precursor of the renewal of Cambridge mathematics", Historia mathematica, x (1983), 24-47.
17. G. Peacock, "Arithmetic", Encyclopaedia metropolitana, i (London, 1845), 369-523, p. 477.
18. S. E. De Morgan, Memoir of Augustus De Morgan (London, 1882), 393.
19. Memoir of Augustus De Morgan (Ibid., 21.
20. It is worth mentioning that De Morgan's religious scruples, strong though they undoubtedly were, did not prevent him actually taking his B.A. degree, which required acceptance of the thirty-nine Articles of Faith. It can only be assumed that he took the oath under (silent) protest.
21. A. Rice, "Inspiration or desperation? Augustus De Morgan's appointment to the chair of mathematics at London University in 1828", to appear.
22. A. De Morgan, "Polytechnic School of Paris", Quarterly journal of education, i (1831), 57-74, p. 73.
23. For example: (a) A. De Morgan, "On the syllogism III", Transactions of the Cambridge Philosophical Society, x (1858), 173-230, pp. 175 and 181, note;
24. (b) A. De Morgan, Syllabus of a proposed system of logic (London, 1860), 41, note, and 44, note;
25. A. De Morgan, "On the syllogism IV", Transactions of the Cambridge Philosophical Society, x (1860), 331-58.
26. This is now housed in the University College archives (MS. ADD. 7). Its first page contains a charming preamble in which De Morgan says: "Such account as I can give of my family is contained in two books. The first is well known by the name of Genesis, ascribed by Jewish tradition to Moses. The second is this book itself, which my own handwriting will identify as compiled by me. Moses gave no account of his materials: I have given what I could. Moses wrote in Hebrew: I in English. Moses was a public writer, I am a private one. Many are the oppositions between me and Moses...."
27. A. De Morgan, "A budget of paradoxes", The Athenaeum, no. 1876 (10 Oct. 1863), 466;
28. A. De Morgan, A budget of paradoxes (London, 1872), 2.
29. De Morgan, A budget of paradoxes (op. cit. (ref. 24, 1863), 467;
30. De Morgan, A budget of paradoxes (op. cit. (ref. 24, 1872), 7.
31. A. De Morgan, "Some account of James Dodson F.R.S.", Journal of the Institute of Actuaries and Assurance magazine, xiv/5 (October 1868), 341-64.
32. A. De Morgan, "Old arguments against the motion of the Earth", Companion to the almanac for 1836, 5-20, p. 18.
33. A. De Morgan, "Copernicus, Nicolaus", Penny cyclopaedia, vii (London, 1837), 498-501, p. 499.
34. A. De Morgan, "On the opinion of Copernicus with respect to the light of the planets", Monthly notices of the Royal Astronomical Society, vii (1847), 290-3, p. 293.
35. De Morgan, "Copernicus, Nicolaus" (ref. 28), 499.
36. A. De Morgan, "The progress of the doctrine of the Earth's motion between the times of Copernicus and Galileo, being notes on the ante-Galilean Copernicans", Companion to the almanac for 1855, 5-25, pp. 6, 7.
37. Companion to the almanac for 1855, Ibid., 22.
38. De Morgan, "Copernicus, Nicolaus" (ref. 28), 501.
39. De Morgan, "Copernicus, Nicolaus" (op. cit. (ref. 27), 5.
40. "Copernicus, Nicolaus" (Ibid., 17.
41. De Morgan, "Copernicus, Nicolaus" (op. cit. (ref. 31), 12.
42. In his analysis of the views of Francis Bacon, De Morgan defends his anti-Copernicanism from a conviction that he was no more pro-Ptolemy than pro-Aristotle. "In his [Bacon's] ideas of astronomy he perfectly agrees with Ramus, but goes further. It is degraded, he says, by being placed among the mathematical arts, when it should be the noblest part of physics.... We rather suspect, putting all the passages together, that when Bacon impugnes that doctrine as manifestly false which he elsewhere propounds for inquiry, he is taking, for the moment, an advocate's license, in aggravation of the case against the Ptolemaic system.... The whole of what he has said on this subject, when put together, does not justify Hume's assertion that he rejected the Copernican system 'with the most positive disdain.' Like so many others of his day, his view is of one colour or another, according as he is thinking of astronomy or of physics.... We are not among the strongest admirers of Bacon, yet we cannot help thinking that, on this point, he has not been fairly represented" ("Copernicus, Nicolaus" (ibid., 11).
43. De Morgan, "Copernicus, Nicolaus" (op. cit. (ref. 27), 11.
44. De Morgan, "Copernicus, Nicolaus" (op. cit. (ref. 31), 12.
45. A. De Morgan, "Brahe, Tycho", Penny cyclopaedia, v (London, 1836), 323-7, p. 326.
46. A. De Morgan, "Notices of English mathematical and astronomical writers between the Norman Conquest and the year 1600", Companion to the almanac for 1837, 21-44, p. 35.
47. Companion to the almanac for 1837, Ibid., 35.
48. Companion to the almanac for 1837, Ibid., 21.
49. Letter from A. De Morgan to J. F. W. Herschel, 21 July 1845. Royal Society Archives: HS.6.224.
50. A. De Morgan, "An account of the speculations of Thomas Wright of Durham", Philosophical magazine, 3rd ser., xxxii (1848), 241-52, p. 250.
51. Philosophical magazine, 3rd ser., Ibid., 241.
52. De Morgan, Philosophical magazine, 3rd ser., op. cit. (ref. 24), 90.
53. A. De Morgan, Newton: his friend: and his niece (London, 1885), 130.
54. D. Brewster, The life of Sir Isaac Newton (London, 1831), 2.
55. The life of Sir Isaac Newton (Ibid., 117.
56. The life of Sir Isaac Newton (Ibid., 218.
57. The life of Sir Isaac Newton (Ibid., 338.
58. The life of Sir Isaac Newton (Ibid., 218.
59. For a summary of the Newton-Flamsteed dispute, see R. S. Westfall, Never at rest: A biography of Isaac Newton (Cambridge, 1980), 541-50, 655-66.
60. J. Gascoigne, "From Bentley to the Victorians: The rise and fall of British Newtonian natural theology", Science in context, ii (1988), 219-56, p. 219.
61. R. Yeo, "Genius, method, and morality: Images of Newton in Britain, 1760-1860", Science in context, ii (1988), 257-84, p. 271.
62. G. N. Cantor, "Between rationalism and romanticism: Whewell's historiography of the inductive sciences", in M. Fisch and S. Schaffer (eds), William Whewell: A composite portrait (Oxford, 1991), 67-86, p. 80.
63. W. Whewell, History of the inductive sciences (London, 1837), ii, 198.
64. S. E. De Morgan, Memoir of Augustus De Morgan (London, 1882), 256.
65. A. De Morgan, "Newton", The Cabinet Portrait Gallery of British worthies, xi (London, 1846), 78-117, p. 98.
66. William Whiston (1667-1752) succeeded Newton as Lucasian Professor of Mathematics at Cambridge in 1703. He was removed from his chair in 1710 on the grounds of being an Arian. In 1720, Newton used his position as President of the Royal Society to block a proposal to make him a Fellow.
67. De Morgan, "Newton" (ref. 60), 100.
68. A report published by the Royal Society in 1712, when Newton was President, which concluded that not only was Newton the first inventor of the calculus (or method of fluxions), but that it was certainly possible for Leibniz to have received hints that materially affected the creation of his own algorithm.
69. A. De Morgan, "On a point connected with the dispute between Keill and Leibnitz about the invention of fluxions", Philosophical transactions of the Royal Society, cxxxvi (1846), 107-9, p. 107.
70. Philosophical transactions of the Royal Society, Ibid., 108.
71. Philosophical transactions of the Royal Society, 108. Ibid.
72. Philosophical transactions of the Royal Society, 108. Ibid.
73. De Morgan, Philosophical transactions of the Royal Society, op. cit. (ref. 48), 132.
74. A. De Morgan, "On the additions made to the second edition of the Commercium Epistolicum", Philosophical magazine, 3rd ser., xxxii (1848), 446-56, p. 447.
75. A. De Morgan, "A comparison of the first and second editions of the Commercium Epistolicum", 1-12, f. 11. Royal Society Archives: AP.29.2.
76. Letter from S. Hunter Christie to A. De Morgan, 25 Feb. 1848. Pasted in J. Collins, Commercium epistolicum... (London, 1712), University of London Library, shelf mark: [De M] L (BP 1), Secondary Strong Room.
77. Referee's report from G. Peacock to S. Hunter Christie, 16 Oct. 1847. Royal Society Archives: RR.1.57.
78. Ibid.
79. Letter from S. Hunter Christie to A. De Morgan, 25 Feb. 1848. Pasted in Collins, Commercium epistolicum... (ref. 71).
80. This did not prevent its being cited in C. R. Weld, A history of the Royal Society (London, 1848), i, 417, note 38.
81. De Morgan, A history of the Royal Society (op. cit. (ref. 48), 135.
82. A. De Morgan, handwritten note, dated 10 Oct. 1848, in Collins, Commercium epistolicum... (ref. 71).
83. De Morgan, Commercium epistolicum... (op. cit. (ref. 69), 450.
84. Commercium epistolicum... (Ibid., 447.
85. De Morgan, Commercium epistolicum... (op. cit. (ref. 64), 108.
86. A. De Morgan, "A short account of some recent discoveries in England and Germany relative to the controversy on the invention of fluxions", Companion to the almanac for 1852, 5-20, p. 8.
87. C. I. Gerhardt (ed.), Leibnizens mathematische Schriften (2 vols, Berlin, 1849-50).
88. De Morgan, Leibnizens mathematische Schriften op. cit. (ref. 81), 17.
89. Leibnizens mathematische Schriften Ibid., 17-18.
90. D. Brewster, Memoirs of the life, writings, and discoveries of Sir Isaac Newton (Edinburgh, 1855), ii, 75.
91. Memoirs of the life, writings, and discoveries of Sir Isaac Newton (Ibid., i, p. xiii.
92. Memoirs of the life, writings, and discoveries of Sir Isaac Newton (i, p. xiii. Ibid.
93. D. Brewster, The life of Sir Isaac Newton (London, 1831), 218;
94. D. Brewster, Memoirs of the life, writings, and discoveries of Sir Isaac Newton (Edinburgh, 1855), ii, 83.
95. P. Theerman, "Unaccustomed role: The scientist as historical biographer - two nineteenth century portrayals of Newton", Biography, viii (1985), 145-62, pp. 146, 158-9.
96. Letter from A. De Morgan to Lord Brougham, 16 May 1855. University College London Archives: Brougham Correspondence, no. 10,299.
97. Letter from W. Whewell to A. De Morgan, 2 Sept. 1856. University of London Library: MS 775/370/34/1.
98. A. De Morgan, Review of Brewster's Memoirs of the life of Sir Isaac Newton, North British review, xxiii (1855), 307-38, p. 310.
99. Memoirs of the life of Sir Isaac Newton, North British review, Ibid., 337.
100. Letter from A. De Morgan to D. Brewster (?), n.d., Royal Astronomical Society Archives.
101. De Morgan, op. cit. (ref. 92), 321.
102. S. E. De Morgan, op. cit. (ref. 59), 263.
103. For an assessment of Brewster's historical work, see J. R. R. Christie, "Sir David Brewster as an historian of science", in A. D. Morrison-Low and J. R. R. Christie (eds), Martyr of science: Sir David Brewster 1781-1868 (Edinburgh, 1984), 53-56.
104. Letter from A. De Morgan to J. F. W. Herschel, 29 August 1867. Royal Society Archives: HS.6.396.
105. A. De Morgan, "Lord Halifax and Mrs. Catherine Barton", Notes and queries, 1st ser., viii, no. 210 (5 Nov. 1853), 429-33, p. 429.
106. Notes and queries, 1st ser., Ibid., 429.
107. Notes and queries, 1st ser., Ibid., 432.
108. Notes and queries, 1st ser., 432.Ibid.
109. A. De Morgan, "Lord Halifax and Mrs. Catherine Barton", Notes and queries, 2nd ser., ii, no. 35 (30 Aug. 1856), 161-3, p. 161.
110. ", Notes and queries, 2nd ser., Ibid., 163.
111. S. E. De Morgan, ", Notes and queries, 2nd ser., op. cit. (ref. 59), 264.
112. F. Manuel, A portrait of Isaac Newton (Cambridge, Mass., 1968), p. viii,
113. quoted in Theerman, A portrait of Isaac Newton (op. cit. (ref. 89), 154.
114. Letter from G. Peacock to A. De Morgan, 8 Sept. 1856. University of London Library: MS 775/370/28.
115. Yeo, op. cit. (ref. 56), 278-9.
116. R. Yeo, Defining science: William Whewell, natural knowledge, and public debate in early Victorian Britain (Cambridge, 1993), 144.
117. De Morgan, Defining science: William Whewell, natural knowledge, and public debate in early Victorian Britain (op. cit. (ref. 48), 140.
118. J. L. Richards, "Augustus De Morgan, the history of mathematics, and the foundations of algebra", Isis, lxxviii (1987), 7-30, p. 17.
119. A. De Morgan, Arithmetical books (London, 1847), p. xiv.
120. Arithmetical books (Ibid., p. xvii.
121. G. Libri, Histoire des sciences mathematiques en Italie (Paris, 1838), ii, 46.
122. A. De Morgan, "On the invention of the signs + and -; and on the sense in which the former was used by Leonardo da Vinci", Philosophical magazine, 3rd ser., xx (1842), 136-7.
123. A. De Morgan, "On the early history of the signs + and -", Transactions of the Cambridge Philosophical Society, xi (1864), 203-12, p. 203.
124. A. De Morgan, "History of the signs + and -", The Athenaeum, no. 1925 (17 Sept. 1864), 376.
125. De Morgan, The Athenaeum, op. cit. (ref. 116), 203.
126. Letter from A. De Morgan to J. F. W. Herschel, 13 Sept. 1864. Royal Society Archives: HS.6.374.
127. De Morgan, op. cit. (ref. 117), 376.
128. Graves had also been a colleague of De Morgan at University College from 1839 to 1843, when he held the Professorship of Jurisprudence.
129. Letter from J. T. Graves to A. De Morgan, 27 Sept. 1864. University of London Library: MS 321/3.
130. De Morgan, op. cit. (ref. 117), 376.
131. De Morgan, op. cit. (ref. 116), 210.
132. Ibid., 212.
133. De Morgan, op. cit. (ref. 112), 19.
134. De Morgan, op. cit. (ref. 116), 206.
135. Ibid., 210.
136. For a pertinent criticism of De Morgan's opinions in this area, see J. W. L. Glaisher, "On the early history of the signs + and - and on the early German arithmeticians", Messenger of mathematics, li (1921-22), 1-148.
137. A. De Morgan, "On some points in the history of arithmetic", Companion to the almanac for 1851, 5-18.
138. A. De Morgan, "Viga Ganita", Penny cyclopaedia, xxvi (London, 1843), 318-25.
139. A. De Morgan, "On ancient and modern usage in reckoning", Companion to the almanac for 1850, 5-34, p. 11.
140. Companion to the almanac for 1850, Ibid., 13.
141. Companion to the almanac for 1850, Ibid., 17.
142. Companion to the almanac for 1850, Ibid., 26.
143. Companion to the almanac for 1850, 26.Ibid.
144. A. De Morgan, Companion to the almanac for 1850, op. cit. (ref. 112), pp. vi, vii.
145. A. De Morgan, "On the earliest printed almanacs", Companion to the almanac for 1846, 1-31, p. 1.
146. A. De Morgan, "Cocker, Edward", Penny cyclopaedia, vii (London, 1837), 312.
147. Letter from J. O. Halliwell to A. De Morgan, n.d., pasted in J. Hawkins, Cocker's Arithmetick, 20th edn (London, 1700), University of London Library, shelf mark: [De M] L1 [Cocker], Secondary Strong Room.
148. Historical Society of Science [prospectus] (London, 1840?).
149. Historical Society of Science [List of Members] (London, 1840?), 5-9.
150. Letter from A. De Morgan to A. Lovelace, July (?) 1840. Bodleian Library, Oxford. Dep. Lovelace Byron 170, ff. 1-2.
151. For a selection of letters from Ada to De Morgan, see B. A. Toole, Ada: the enchantress of numbers: a selection from the letters of Lord Byron's daughter and her description of the first computer (Mill Valley, Calif., 1992).
152. Other articles on Halliwell and the Historical Society of Science include H. W. Dickinson, "J. O. Halliwell and the historical society of science", Isis, xviii (1932), 127-32,
153. and T. Hornberger, "Halliwell-Phillips and the history of science", Huntingdon Library quarterly, xii (1949), 391-9.
154. See Statement in answer to reports which have been spread abroad against Mr. James Orchard Halliwell (London, 1845)
155. and A. N. L. Munby, The history and bibliography of science in England: The first phase, 1833-1845 (Berkeley, 1968).
156. J. O. Halliwell (ed.), A collection of letters illustrative of the progress of science in England from the reign of Queen Elizabeth to that of Charles the Second (London, 1841), p. ix.
157. A. De Morgan, "References for the history of the mathematical sciences", Companion to the almanac for 1843, 40-65, pp. 40, 41.
158. Letter from A. De Morgan to J. F. W. Herschel, 11 Jan. 1847. Royal Society Archives: HS.6.233.
159. De Morgan, op. cit. (ref. 112), p. i.
160. Letter from G. Peacock to A. De Morgan, 2 April 1847. University of London Library: MS 776/3, f.19.
161. De Morgan, op. cit. (ref. 112), p. xiv.
162. Ibid., p. ii.
163. R. Witt, Arithmetical questions... (London, 1613).
164. See De Morgan, Arithmetical questions... (op. cit. (ref. 112), 33.
165. Arithmetical questions... (Ibid., p. xxviii.
166. Arithmetical questions... (Ibid., p. xxviii.
167. Arithmetical questions... (Ibid., 96.
168. De Morgan, Arithmetical questions... (op. cit. (ref. 81), 8.
169. A. De Morgan, "On the difficulty of correct descriptions of books", Companion to the almanac for 1853, 5-19, p. 5.
170. De Morgan, Companion to the almanac for 1853, op. cit. (ref. 137), 1.
171. De Morgan, Companion to the almanac for 1853, op. cit. (ref. 158), 16.
172. For a criticism of De Morgan's views concerning the first English translation of Euclid, see R. C. Archibald, "The first translation of Euclid's Elements into English and its source", American mathematical monthly, lvii (1950), 443-52.
173. De Morgan, ", American mathematical monthly, op. cit. (ref. 158), 11.
174. ", American mathematical monthly, Ibid., 12.
175. De Morgan, ", American mathematical monthly, op. cit. (ref. 112), p. iii.
176. Letter from A. De Morgan to Lord Brougham, 13 Aug. 1863. University College London Archives: Brougham Correspondence, no. 10,307.
177. A. De Morgan, op. cit. (ref. 24, 1872), 301.
178. Ibid., 255.
179. S. E. De Morgan, "Editor's Preface", ibid., p. vi.
180. Editor's Preface", Ibid., p. v.
181. R. Yeo, Defining science: William Whewell, natural knowledge, and public debate in early Victorian Britain (Cambridge, 1993), 149.
182. Richards, Defining science: William Whewell, natural knowledge, and public debate in early Victorian Britain (op. cit. (ref. 111), 17.
183. A. De Morgan, "Speech of Professor De Morgan, President, at the first meeting of the Society, January 16th, 1865", Proceedings of the London Mathematical Society, 1st ser., 1 (1866), 1-9, p. 8.
184. A. De Morgan (ed. by P. Heath), On the syllogism, and other logical writings (London, 1966), pp. xi-xxiv.
185. De Morgan, On the syllogism, and other logical writings (op. cit. (ref. 112), p. ii.
186. For a treatment of religious inclination with respect to English nineteenth-century mathematicians (including De Morgan, Peacock and Whewell), see J. L. Richards, "God, truth, and mathematics in nineteenth century England", in M. J. Nye et al. (eds), The invention of physical science (Amsterdam, 1992), 51-78.
187. I. Todhunter, A history of the mathematical theory of probability from the time of Pascal to that of Laplace (Cambridge and London, 1865), p. xii.
188. I. Todhunter, A history of the mathematical theories of attraction and the figure of the Earth, from the time of Newton to that of Laplace (London, 1873), ii, 29.
189. W. W. Rouse Ball, A short account of the history of mathematics, 3rd edn (London, 1901), 482;
190. Rouse Ball, A short account of the history of mathematics, 3rd edn (op. cit. (ref. 4), 133.
191. W. W. Rouse Ball, "Augustus De Morgan", The mathematical gazette, viii (1915-16), 42-45, p. 43.
192. The mathematical gazette, Ibid., 44.
193. D. E. Smith, Rara arithmetica, 4th edn (New York, 1970), p. xii.
194. Smith was less complimentary, however, about De Morgan's historical articles, describing them as "not only eccentric but unreliable" (D. E. Smith, History of mathematics, i (New York, 1958), 462).
195. P. E. B. Jourdain, "Editor's Preface", in A. De Morgan, Essays on the life and work of Newton (Chicago and London, 1914), p. x.
196. Rouse Ball, Essays on the life and work of Newton (op. cit. (ref. 4), 133.
197. De Morgan, Essays on the life and work of Newton (op. cit. (ref. 171), 6.
198. De Morgan, Essays on the life and work of Newton (op. cit. (ref. 129), 14.
199. De Morgan, Essays on the life and work of Newton (op. cit. (ref. 31), 21.