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Letters from Smith to the editor of the Athenaeum, William Hepworth Dixon, arguing against Augustus De Morgan on the quadrature of the circle.

Manuscript volume, 15th or 16th century, containing the 'Perspectiva Communis' of John Peckham, in three parts, beginning 'Inter philosophie consideracionis studia ... '. Bound (perhaps from the first) with two printed works, the Arithmetica of Jordanus Nemorarius, edited by Jacques le Fêvre (Johannes Higman and Wolfgang Hopyl, Paris, 1496), and the Geometria speculatiua of Bradwardine (Paris, 1495).

Manuscript volume, 17th century, containing: Mohammed Ibn Al-Hussain Karkhi, Kitab al-kafi fi 'ilm al-hisab wa-'ilm al-misahah wa-al-khawafi (Treatise on arithmetic, geometry, land surveying etc)

Manuscript volume, late 15th century, containing a mathematical treatise, with ink diagrams.

Arithmeticae et Astronomicae Auctores Varii: 15th century (possibly 1468) mathematical and astronomical treatises by various authors. Earlier texts written in Italy by one hand; others written by Heinrich Langenstein and Paul of Olmütz (?). Full page diagram of the zodiac on folio 47r.

Archives of the London Mathematical Society, 1853-1994, the bulk comprising c500 letters to Thomas Archer Hirst, 1853-1892, mainly in his capacity as a member of the LMS, including a letter inviting him to the first meeting of the Society, and also reflecting his travels in Europe, including letters from prominent European mathematicians. The letters include several from Henry M Bompas, 1865, 1874-1879; Arthur Cayley, 1858-1891 and undated; Michel Chasles, 1858-1871 and undated; Luigi Cremona, 1864-1892 and undated; Augustus De Morgan, 1861-1869; Georges-Henri Halphen, 1875-1879; Amédée Mannheim, 1866-1891; Julius Plücker, 1866-1868; William Roberts, 1859-1865 and undated; George Salmon, 1858-1878; [Hermann Cäsar Hannibal?] Schubert, 1877-1884; Henry John Stephen Smith, 1865-1876 and undated; William Spottiswoode, 1862, 1865, 1883; Cyparissos Stephanos, 1877-1887; Rudolf Sturm, 1874-1892; James Joseph Sylvester, 1859-1888 and undated; Barnaba Tortolini, 1858-1863; Richard Townsend, 1865-1878; John Van Voorst, 1864-1867; and there are a few letters from Hirst himself. The archive also includes a bound notebook containing a manuscript catalogue of the LMS library by R A Sampson, 1891-1893; miscellaneous administrative correspondence and papers, 1964-1975; membership lists, 1966-1972; binder of papers of H T J Norton on mathematics, with correspondence, largely to E H Neville, regarding their disposition in the LMS archive in c1938, and also including bibliographical material on elliptic functions, apparently compiled by Neville [1930s-1950s]; miscellaneous letters and papers on research, 1986, 1992-1994.

Papers of James Lighthill, 1970s-1990s including working papers; lecture notes and transcripts; conference papers; off prints of articles; drafts and proofs of publications by Lighthill; correspondence; personal awards and honours; papers relating to the Royal Society; audio cassettes and papers relating to the International Union of Theoretical and Applied Mechanics.

'Elements of statics', a volume written for publication at the proposal of the Society for the Diffusion of Useful Knowledge, though it was never actually published. De Morgan used it as evidence of his work and knowledge when applying for the Mathematics Chair at University College London in 1827.

Augustus De Morgan's mathematical tracts, copied by John Power Hicks from the original manuscripts in the Library of University College London.

Mathematical fragments, letters, and papers.

Student's notes on lectures on Algebraic Geometry and the Calculus, given by Augustus De Morgan at University College London from 11 March to 13 May 1847.

Manuscript of De Morgan's introductory lecture delivered at the opening of classes in mathematics at University College London on 5 November 1828. Appended are notes for another lecture.

Notes for an introductory lecture in the Faculty of Arts and Laws at University College London.

Correspondence between Augustus De Morgan and George Boole, Professor of Mathematics at Queen's College Cork, dated 1842-1864. The collection also includes letters from John Stuart Mill, and letters from various correspondents mostly dated 1846-1848.

Notes on physics and mathematics.

Undated mathematical fragments.

Undated lecture notes on geometry: two closely written sheets pasted onto an otherwise unused notebook.

Thirteen volumes of manuscript notes and calculations about magic squares.

Twenty-three manuscript notebooks on mathematical statistics which include 'The theory of deviation from an average', the introduction to 'An algebra of evolution', and 'Problems relating to the mathematical treatment of statistics: periodicity and deviation'.

Manuscript volume, 1694: Rechenbuch. An arithmetic book containing problems, including calculations for finding the date of Judgement Day, the Golden Number, etc, together with astrological information. Some of the problems are set out in verse.

Notebooks on lectures on mathematics, languages and political economy attended by Bagehot when a student at University College London.