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Draft of a paper entitled 'Sur une propriété générale d'une certaine classe de fonctions transcendantes (par Mr.N.H.Abel de Christiana)', apparently in the hand of Niels Henrik Abels hand, later printed as 'Remarques sur quelques propriétés generales d'une certaine sorte de fonctions transcendantes' in Oeuvres complètes de N.H.Abel...redigées...par B.Holmboe (1859), vol.I (section XV), pp.288-98.

The collection, 1835-1850, contains letters and printed papers, notices and unpublished printed material, which Airy received during his time as a member of the Senate of the University of London. The Airy correspondence has a special importance because much of the early archival material of the University of London was destroyed and so often the only record of its activities is in the Senate and Committee Minutes. Airy was particularly interested in the constitution of the University, the developments of the mathematics syllabus, the syllabuses for certificates in hydrography and civil engineering and the introduction of the religious examination.

Notebook compiled by Jonathan Baker containing mathematical problems and tables, dated 29 July 1765. The notebook was also used for entering his accounts between 1782 and 1796, with some later, more general, additions to 1800, mostly relating to his work as a cobbler, but also accounts of household expenses and rents received. The accounts mention places between Cirencester and Newnham.

Manuscript transcript by Richard Bateman, 1612, of a work by Benedictus Victorius Faventius containing a calculator or computer for increasing or diminishing figures, which was printed by Benedict Hector, bookseller of Bologna, in 1512. The text was copied by Bateman from a treatise of a revised edition by Dom. Gaetanus, Doctor of Medicine.

Letter from Henry Peter Brougham of [Westmorland] to [Augustus] De Morgan, 11 Sep [1857]. Referring to an article in Notes and Queries [2nd series, Volume 4] and discussing mathematical subjects. Autograph, with signature.

Nine foolscap pages of handwritten mathematical calculations and notes by Arthur Cayley entitled 'Areal Co-ordinates' (December 1891)

Letter from Michel Chasles of Paris to Augustus De Morgan, 17 May 1850. On mathematical matters.

Autograph, with signature.

Letter from Michel Chasles of Paris to Augustus De Morgan, 31 Aug 1852. On mathematical matters.

Autograph, with signature.

Letter from Michel Chasles of Paris to Augustus De Morgan, 4 Oct 1852. On mathematical matters.

Autograph, with signature.

Letter from Michel Chasles of Paris to Augustus De Morgan, 8 Apr 1848. On algebraical formulae.

Autograph, with signature.

Letter from Josiah Latimer Clark of Westminster Chambers, 11 Victoria Street, London to Sydney Lupton, 2 Dec 1891. 'Your most delightful book of tables and constants is I presume on every table ...'. Writing in reply to a letter from Lupton, saying that he hopes to correct his own figures before long, since Lupton had referred him to an article by Professor [George Carey] Foster in Watts' Dictionary [of Chemistry].

Autograph, with signature.

Letter from Matthew Collins of 40 Upper Pitt Street, Liverpool to Augustus De Morgan, 8 Apr 1853. Covering note, enclosing a pamphlet, On Clairaut's theorem ... (1853).

Autograph, with signature. A note in De Morgan's hand states that the content of the pamphlet, published in the Cambridge and Dublin Mathematical Journal, new series vol IX (1854), were plagiarized from a lecture given by Mr James MacCullagh in 1846.

Papers of the De Morgan family, [1756-1928], comprising material relating to the suffragette movement, such as photographs, newpapers, press cuttings and pamphlets; correspondence of Augustus de Morgan, with correspondents including Sir Frederick Richard Pollock, Sir George Biddle Airy, Sir John William Lubbock, John Wrottesley (2nd Baron Wrottesley), John Radford Young, Sir John Frederick William Herschel, John Finlaison, and General Sir John Briggs; correspondence of William Frend de Morgan, mainly with members of his family and Sir Edward Coley Burne Jones; material relating to the de Morgan and Frend families, notably family photographs, drawings, letters, legal documents and memorabilia; letters from Sophia and Mollie de Morgan to Joan Antrobus; manuscript and typescript copies of stories and essays by William and Mary de Morgan; papers relating to Sophia de Morgan's Memoir of her husband Augustus, including letters, reviews and working notes; bundle of letters containing correspondence concerning a petition to the women of America from the women of England about the abolition of slavery; printed material, mainly works by Augustus de Morgan; letters to Francis Baily, [1820-1940]; letters from Thomas Henderson to Thomas Galloway, 1834-1842; 5 watercolours of Scotland by Frances Shakerley, [1920-1930].

Papers of Augustus de Morgan, 1859, comprise a letter to Mrs Bax [grandmother of the composer Sir Arnold Bax], enquiring whether she is comfortably settled at her new address; an obituary of Professor De Morgan is attached to the second sheet.

Papers of Augustus de Morgan, 1833-1870, comprise letters sent and received by De Morgan. Correspondents include: Miss Anne Sheepshanks and [her brother] Rev Richard Sheepshanks, Vice-Admiral W H Smyth, and Professor [Philip] Kelland of the University of Edinburgh.

Copy of the draft of the first work published by Augustus de Morgan, 'The Elements of Arithmetic', 1830.

A collection, compiled in 1723, of mathematical material, principally for the use of navigation.

Paper by Alexander J Ellis 'On clinant geometry, as a means of expressing the general relatings of points on a plane, realising imaginaries, and extending the theories of anharmonic ratios', communicated by Arthur Cayley, Esq. F.R.S. Febr. 1863. Abstract printed in the Proceedings of the Royal Society, vol.12, pp 442-3 Carbon copy of MS, with figures drawn in ink. Text and figures on rectos only. Paper wrappers inscribed 'Prof Augustus De Morgan, with the Author's respects'. Part of A De Morgan's library, given to the University by Lord Overstone in 1871. Former shelf-mark L(P.C.6).

A geometrical exercise book with Frederick's name and the dates 4 May 1795 and 17 May 1796 on the cover. Each page bears a theorem and its accompanying diagram, up to the 21st theorem of the 5th book. The exercises are occasionally relieved by a pencil sketch of a head or half-figure.

Manuscript volume containing an eighteenth century treatise on geometry, entitled 'Geometrie Pratique'. The chapter headings are: 'Livre premier: des logarithmes', 'Livre II: De la trigonometrie rectiligne', 'Livre IV: De la construction des figures', 'Livre V: De la longimetrie', 'Livre VI: De la planimetrie', 'Livre VII: De la stereometrie'.

3 letters from John Thomas Graves of 29 Grosvenor Place, Cheltenham to Augustus De Morgan, 28 Jan, 4 Feb and 4 Jun 1853. Relating to the works of Simon Stevin and other mathematical literature.

Autograph, with signature.

Manual of mathematics, including sections on calculating interest, 'brokage' and the purchase of stock, compiled by James Harrison of Leeds in 1775. At the end of the volume are added medical remedies and recipes in various hands, [1828].

Letter from Leonard Horner of University Chambers to Augustus De Morgan, 25 Feb 1828. Enclosing a letter appointing a Professor of Mathematics in the University of London.

Autograph, with signature.

Manuscript volume containing a translation, [1800], by Charles Hutton of 'Book the 9th of the miscellaneous questions and inventions of Nicholas Tartalea (Niccolò Tartaglia) of Briscia: concerning the sciences of arithmetic, geometry and algebra and almucabala, commonly called the Rule of Coss, or Ars Major; and especially of the discovery for the case of the cube and first power equal to a given number, and its other cases...'. Reginald Rye, Goldsmith's Librarian of the University of London, states that the manuscript is in the handwriting of Charles Hutton.

In Arithmetica diversche questyen met hare solutien: door C.J. Broersz, liefhebber der Reeckenconst ... Tot Haarlem, Bij Gillis Rooman, woonende in de Jacobine-strate, in de vergulden Parsse, Anno 1590. The transcription of the book by Broersz occupies the first 33 leaves, and is signed F.[?] J. Riett, 1612. Ff. 35-88 contain further arithmetical problems, including some in verse form illustrated by pen-and-ink drawings.

Manuscript arithmetic note-book, 1749, signed at the end 'E.Knight, August 1, 1749'. In a copper-plate hand, with many flourished initials and headings.

Manuscript exercise book of elementary geometry, [1748]. On the first leaf is written "Thomas Knight. February 18, 1748".

Letter from James Ludovic Lindsay of 2 Cadogan Square, [London] to R A Rye, [Librarian of the University of London], 9 Jun 1907. Describing how Lord Crawford had used the De Morgan Mathematical Collection, now in in the University Library, to help him in founding the mathematical and physical science section of his own library at Haigh Hall, 'second only, I think, to the Imperial Library of Pulcowa Observatory in Russia [Pulkovo Observatory, near St Petersburg]'. Describing the printing of the 'great catalogue' of his library as 'a very heavy business'. A postscript expresses sympathy for the death of William Brenchley Rye 'a very valued assistant [in the Earl's library] at Haigh'.

Autograph, with signature.

Letter from Baldassarre Boncompagni-Ludovisi, 1858, [To Augustus De Morgan]. Thanking De Morgan for his letter of 14 November 1858, giving information about Francesco Galigai's 'Pratica d'Arithmetica' (1548), and asking for further details. Letter enquires about the library of Dr [Daniel Mitford] Peacock and asks De Morgan to get Count [Guglielmo] Libri to send catalogues of sales he was to hold [in March and August 1859] in England and in Paris. Enquires about further editions of De Morgan's 'Arithmetical Books' (1847) and offers to get one printed in Rome.

Letter from Baldassarre Boncompagni-Ludovisi, 1856 to [To Augustus De Morgan], asking for a copy of 'The Elements of the Mathematical art commonly called Algebra, expounded in two books, by John Kersey. 1717'.

(1) Letter from David Mather Masson of the Garrick Club to Augustus De Morgan, 13 Jun 1867. Discussing Thomas Carlyle's mathematical work.

(2) Letter from Thomas Carlyle of Chelsea to [De Morgan], 19 Jun 1867. Discussing Carlyle's translation of A M Legendre's Eléments de géométrie and the 'the Galbraith legend' [that a Mr Galbraith was the translator of Legendre's work].

Both letters are autograph, with signatures.

Manuscript volume containing mathematical calculations tables, accounts and sketches, with notes in Italian, c1500.

Manuscript volume containing a mathematical treatise, [1682], with diagrams in the text. The chapter headings are: 'Analysis triangulorum rectilineorum', 'geometriae practicae cap. 1m', 'principia geographiae generalia', 'de globe eiusque usibus', 'de projectione astronomica', 'de invenienda locorum longitudine', and 'astronomia'.

Manuscript volume containing writings on mathematics, [1668], and entitled 'The use of the rule and compass in drawings of lines, angles, parallels and geometrical superficial figures comprehended in eight practices, together with notes on decimal arithmetic, logarithms, mensuration, fortification, dialling and other branches of mathematics. The handwriting and watermarks are of the seventeenth century, and the date 1688 appears on the verso of leaf 68, where adjoining a 'Table for the declination of the sunne', is written 'Example for the 22th May 1668'. On leaf 112 appears 'A particular of all my mathematical instruments and the severall prices I paid for them'.

Papers of Augustus De Morgan including letters and notebooks relating to various mathematical subjects and general correspondence 1864-1867.

1-4. Letters to Augustus de Morgan, mostly about mathematical books and the history of the signs + and -.

1. John Bellingham Inglis, 15 Sep 1864
   2-4. John Thomas Graves, 20 and 27 Sep and 8 Oct 1864
   5-7. Items concerning John Dawson of Sedbergh
   5. Thomas Harrison, 18 Apr 1867
   6. Edward Cust, 9 Sep 1867
   7. Short biography of John Dawson, manuscript copy of article in the 'Kendal Times', 24 Nov 1866
   8. MS notes by Augustus de Morgan, mostly concerned with mathematical books and the first use of the signs + and -.

Together with 14 request slips for books in the British Museum, one dated 1854 and the rest 1864.

Papers of Augustus De Morgan including notes and additions made by de Morgan for his 'Arithmetical books'.

(1) Letter from William Frend De Morgan of The Vale, King's Road, Chelsea to H F Heath, Librarian of the University of London, 20 Oct 1900. (2) Letter from William Frend De Morgan of Via Lorenzo Magnifico 25, Florence, Italy to H F Heath, Librarian of the University of London, 4 Nov 1900. Both letters relate to De Morgan's gift of notes and additions made by his father, Augustus De Morgan, for his Arithmetical Books.

Both letters are autograph, with signatures. Filed with a typescript copy of Dr Heath's reply to the first letter.

34 letters from Francis William Newman, 1864-1894. 32 letters addressed to Newman's nephew John Rickards Mozley; 1 letter addressed to Newman's sister Jemima Mozley; 1 letter addressed to J R Mozley's father-in-law Bonamy Price. Topics covered include: domestic and family affairs; Newman's brother John Henry Newman (Cardinal Newman); education (including Augustus De Morgan and University College London); New Testament criticism; religion and morality; classical literature; mathematics; wealth; current affairs (including Irish Home Rule and the American Civil War); William Ewart Gladstone; and John Ruskin.

All items are autograph, with signatures.

Letters and papers relating to Gottfried von Leibnitz's claim to primacy over Sir Isaac Newton in the discovery of calculus. Including correspondence between H Sloman, William Hepworth Dixon (editor of The Athenaeum), W Metcalfe, Augustus De Morgan and a Mr de Fanget, 1861-1863. Many items are autograph and bear signatures.

Letter from Wililam Wallace to Rev George Peacock, Dean of Ely, [1833]. Describing Wallace's part in the introduction of foreign mathematical notation to England and 'the Reformation .... the the Mathematical science in Britain'.

Autograph, with signature. Headed 'First Copy'. Inscribed in another hand: 'Found among Mr Thomas Galloway's papers'.

2 letters to Owen Williams, 22-30 Nov 1806, relating to copper and timber production. Including 3 sheets of tables and calculations.