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

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

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.

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'.

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.

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.

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.

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].

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.

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.

Papers of Thomas Wilson, mid to late 18th century, comprising a volume containing notes by Wilson, of lectures given by John Hunter. Including notes on astronomical and mathematical topics, c 1854.

Papers of Jacob Vale Asbury, 1816-1843, comprising a manuscript volume by Asbury, containing notes of the lectures of John Abernethy given at St Bartholomew's, 25 Jul 1816; notes titled Observations on the Pulse, by Dr Fordyce, 18 Sep 1816; notes titled Lectures on the Principle Operations of Surgery by Sir Everard Home, 1812; notes titled Cases and Original Observations, 1842; tables of statistics on the population of Enfield, and Great Britain; and mathematical calculations on the cubic inches of water in a box.

Scientific and other papers sent to the Royal Society, presented at meetings of Fellows, or commissioned by the Society. They form a complementary series to the Early Letters, both of which were superseded by the Letters and Papers. Many of these items, referred to as the 'Guard Books', are duplicated in the Register Book of the Society. The classification is a simplified form of the 'Philosophical Transactions' abridgment by John Lowthorp. This arrangement was completed in 1741 by Thomas Birch. The majority of the papers in these volumes are manuscript, but a few printed documents occur throughout the series. Some of the papers are earlier in date than the grant on 15 July 1662 of the First Charter to the Society. The Committee of Trades seems to have been associated with the earlier meetings of those philosophers who subsequently became Fellows, and produced a number of practical papers, some of which were written in 1639 and which are mostly found in Volume 3(i). There are still earlier documents, mostly in Volume 25, which may have been included in the gift, in 1667, of the Arundel Library.

Some correspondence, papers, notebooks and publications of Sir James Hopwood Jeans. Early manuscripts in the series relate to Jean's education at Trinity College, Cambridge, in the form of early lecture notebooks, largely on mathematical topics. A collection of letters, 1901-1907, documents his treatment for tuberculosis at Ringwood Sanatorium, where he completed work on the theory of gases; correspondents included G H Hardy and Adam Sedgewick among others. Jean's engagements in popularizing science are represented by proofs and typescript of lectures and essays, especially those written for the BBC, 1934-1935, together with associated letters and press cuttings. The series contains collections of offprints, reprints, and extracts of published works by Jeans and others, notably from the Philosophical Transactions and the Philosophical Magazine.

The correspondence of Sir John William Lubbock, providing information on a wide range of Lubbock's contemporaries, not exclusively in the field of science. The largest collections of scientific letters are from George Biddell Airy (113 letters), John George Children (128 letters), Joshua Alwyn Compton, 2nd Marquis of Northampton (98 letters), G P D de Pontecoulant (67 letters) and William Whewell (87 letters). There are smaller but no less important groups of letters from Charles Babbage, Francis Baily, Francis Beaufort, Charles Darwin, John Couch Adams, J F W Herschel, Baden Powell and W H F Talbot.

A commentary on Newton's 'Principia' by Nicholas Fatio, with an introductory note in English by Dr Johnstone about Fatio, his life, religious beliefs, death and dispersal of his books.

Two manuscripts by Louis Joel Mordell: 1. 'On the geometry of numbers in some non-convex regions' 60 pages, some manuscript corrections and 2. ' Hardy's mathematician, apology' review article 10 pages, photocopy.

A collection of letters to Abraham Sharp between the years 1701-2 and 1719.

Material collected by Thompson, 1825-1915, and removed from books within the S P Thompson Rare Books collection housed within IET Library. It comprises correspondence (1890-1915) from contemporary physicists and mathematicians such as David James Blaikley, Sir William Henry Blagg, Sir Charles Tilston Bright, Hugh Longbourne Callendar, Henry Smith Carhart, Sir John Ambrose Fleming, Sir Richard Tetley Glazebrook, Oliver Heaviside, Gisbert Kapp, Phillip Kelland, Sir Oliver Lodge, Sir William Henry Preece, Albion T. Snell, Sir William Spottiswoode, and William Thompson, Baron Kelvin; and press cuttings, photographs, engravings, autographs and letters (1870-1916) relating to eminent scientists including Sir Cristopher Wren, Sir Isaac Newton, James Watt, William Herschel, Sir John Flamsteed, Alexander Von Humboldt, Charles Darwin, Louis Pasteur, Sir Charles Lyell, William Gilbert, Otto von Guericke, Robert Boyle, Benjamin Franklin, Joseph Priestley, Alessandro Volta, Sir Humphry Davy, Michael Faraday, Sir Charles Wheatstone, James Clerk Maxwell, Josiah Latimer Clark, Werner von Siemens, Alexander Graham Bell, Sebastian Ziani de Ferranti, and many others.

Papers of Bernard Albert Hunn, 1949-[1982], relating to his career and research, including: copy of Hunn's degree certificate from King's College London, 1949; notes on elliptic functions, 1950; correspondence, 1951-1953, relating chiefly to the publication of scientific papers on aeronautics; reports from Hawker Aircraft Ltd design department, 1951-1953; technical papers and notes by Hunn, 1952-1956, relating to aeronautical mathematics; draft monograph by Hunn on 'Inertial guidance', 1964; correspondence, chiefly with James Allason, MP, concerning the British defence industry and world markets, 1964-1965; patent applications for 'improved guiding means for spinning missiles', 1959 and for a 'mind simulator' (an electronic model of the human mind), 1982, with essays and notes on the function of the human mind; photographs of a interlock relay system and of Revenue Systems component parts for a card payment system to be attached to a petrol pump; and memoir concerning Hunn's work in Nigeria, 1974-1978.

Note-books of William Dobinson Halliburton chiefly of lecture notes taken while a student at University College, London. Author's holograph MSS. Produced in London, 1874-1902.

Commonplace books of extracts and notes from works published mainly during the last quarter of the 17th century and early 18th century, relating to science, medicine and mathematics. Written mainly in Latin or Italian, but with some entries in French. Author's holograph MSS. Illustrated by numerous folding and other pen-drawn diagrams and figures, and a few wash-drawings. The numeration of the volumes has been added.

Vol. I In universam scientiam mechanicam institutiones (80 ll. 3 folding pen-and-wash drawings). II Optica. Catoptrica. Dioptrica (56 ll. 4 folding pen-drawings). III Extracts and notes mainly in Latin, but a few in French on medical, scientific, mathematical and philosophical works, mostly published between c 1685 and 1700: with notices of others on Church history and doctrine, Jansenists, etc. There is a long entry towards the end of the volume on the 'Medicina mentis' by Ehrenfried Walter von Tschirnhausen [1651-1708], (352 ll. 1 folding wash-drawing, 8 folding pen-drawings, wash-and pen-drawing in the text). IV A similar collection, but with a preponderance of entries in French, included in which is a long article under the title: 'La vie de demoiselle Antoinette Bourignon [1616-1680], écrite par elle-même [etc.]' Amsterdam. 1683. The date 1705 is found on the verso of the last leaf (312 ll., 5 folding pen-drawings, and a few marginal pen-drawn figures, etc.) V Notes and extracts on geometry, mechanics, optics, physics, etc. on Cartesian principles: in Italian and Latin. At the end is a long entry entitled: 'Fisica generale sopra il lume, ed i colori per il P. Mallebranche (i.e. Nicolas de Malebranche [1638-1715]) dall'Istoria dell'Accademia delle Scienze, 1699' (224 ll. 6 folding pen-drawings). VI Netwon (Sir I.). Optica: in Latin (160 ll. 11 folding pen-drawings and marginal pen-drawn figures, etc.). VII Extracts from Newton's works on astronomy: conics, mechanics, physics, etc.: in Latin (246 ll., 10 folding pen-drawn figures, etc.). VIII Extracts on astronomy, geography, geometry, and chronology: in Latin. Written in 1713 'in hoc anno'. An added note on the first page contains the date 1714 (208 ll. 8 folding pen-drawn figures, and marginal figures, 1 folding Table). IX Sanctorius (S.). Ex commentariis in Avicennam et in Aphoirismos Hippocratis (256 ll.). A note on 'Colica' in Aphorism XXV is dated 1716. X Extracts and notes from 17th cent. medical works, notes of cases, medical receipts, etc.: in Latin (196 ll.). Illustrated with a full-page pen-drawing of a male head. Against this Marmi has written: 'Exhibeo schema communicatum mihi ab excellentissimo D[octore] Schustonio [?] Practico Esslingense ... Elegantissime Burrhus eques Mediolani (i.e. Giuseppe Francesco Borri [1627-1695]) apud Tackium (Johann Tackius [1617-1675]) Phasis p. 160 uti Macrocosmi Compendium homo existimatur, ita homo sive humanus mundus in se quoque habet proprium compendium in vultu et imago nostri corporis est facies'. The illustration shows the facial nerves supposed to correspond with those of other parts of the body. XI A similar volume, mainly in Latin, but with some entries in Italian (318 ll.). There are long extracts and notes on the works of Galen and Hippocrates. A marginal note on the 6th leaf is dated Naples 1714: another entry on 'Aqua Tofana' is dated 1715 apparently at Naples.

Pasted down as end-papers at the beginning of Vol. IV is a small folio sheet containing an engraving of 'Triangulus australis' above a decorated wreath, which includes a small meallion-portrait of Werner XVII Comes de Hapsburgo. It is numbered 132, and is apparently extracted from an unidentified volume of engravings. The identification of the author of these MSS. is based on two entries. The first is in Vol. III is a marginal note on the verso of the 12th leaf of the entry of the 'Medicina mentis' of Tschirnhausen noted above. It begins: 'Mihi Jos. Herm. M[armi]. The expansion of 'Herm' into an Italian Christian name seems doubtful, but it could be 'Hermannus' or 'Herminius' or even 'Hermes' or 'Hermete'. The second entry is however decisive. It is found also in a marginal note on the eating of cucumbers in the summer, in connexion with the onset of bile after drinking in hot weather as observed by Galen. This is definitely signed 'I. H. Marmi'. Produced in Naples?

Papers of James Ware including notes for lectures on the eye and its disorders, notes on anatomy and mathematics, and a partnership indenture, 1760s-1780s.

Papers of Jean-Baptiste Biot, c 1800-1937, including correspondence and a translation of Biot's Memoir on the Circular Zodiac of Denderah.

Papers of George Macdonald dealing predominantly with the later stages of his career, 1938-1977, although there is some material relating to his pre-war activities. They reflect his work as an international figure in the prevention and control of malaria, his involvement with numerous governmental and non-governmental bodies, his relationship with colleagues, his numerous tours on professional business, and his research and writing.

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

Autograph, with signature.

Papers of Hudson comprising 'Angle Generator for use in the study of trigonometry' by W B Bushell, 1873; a letter from H Orfleur concerning surfaces, with photograph of geometrical model attached, 1898; invitation to Hudson from Principal Henry Wace to the Medical Department Prize Distribution, with geometrical drawing on the reverse; mathematical model (quadratic surface: ellipsoid).

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.

Undated mathematical fragments.

Notes on physics and mathematics.

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

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 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.

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.

Mathematical fragments, letters, and papers.

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)

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.

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).

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 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'.

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

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

(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.

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.

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.

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