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 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].

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

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 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.

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.

Undated mathematical fragments.

Thirteen volumes of manuscript notes and calculations about magic squares.

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

Notes on physics and mathematics.

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

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

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'.

'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.

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.

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.

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.

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.

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.

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.

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).

Papers of Thomas Wallace, 1719, comprising a volume written in Latin, containing case notes of patients; lists of symptoms, diseases, and treatments; rules and definitions of arithmetical progression; an article describing the volume, by E Muirhead Little, from the British Medical Journal, 8 Dec 1928; and a letter from the donor, W Reeve Wallace, 27 Mar 1934.

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.

Papers of the Gregory family. Volume One includes writings by Sir Isaac Newton, entitled 'Notae in Newtonii Principia Mathematica Philosophiae Naturalis' and his 'Theory of the Moon', which was incorporated in the Astronomia Physica published by the Savilian Professor of Astronomy at Oxford. Volume Two contains letters and papers of the Gregory family: David Gregory of Kinnairdie; James Gregorie; David Gregorie; and Charles Gregory (Professor of Mathematics at Edinburgh University); also including some papers of Sir Isaac Newton.

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.

Incip. 'Igitur ex quatuor elementis'
Desin 'Et hoc est qod ostendimus. Explicit'
Folios 1-9 [Mundus] igitur ex quatuor elementis isdemque totis in spere modum globatis.... retrogradari facit.
Part of book 8, 'De astronomia' of Martinus Capella, 'De nuptiis.'

Folios 9 verso - 49 verso (Text) Vnitas est esse rei per se discrecio...omnis numerus minor maioris aut est pars aut partes....medios assignare sit possibile.
(Commentary) Aut enim minor numerat maiorem....et hoc est qod ostenimus. Explicit.

Jordanus Nemorariius, 'De Arithmetica' printed several times but with a different commentary. Printed marginalia eg in folio 24, in a hand which occurs also in MS/28.

Fundata duarum Lecturarum in Disciplinis Mathematicis Per Henricum Savile, Collegii Metonensis Custodem. Publicata et Confirmata in Venerabili Domo Convocationis, 11 Aug 1619.

Apollonii Conica methodo nova illustrata et succincte demonstrata per Isaacum Barrow, continet hoc volumen archetypon integrum editionis Londini 1675, in forma quarta, impressa.

Papers of the Gregory family, volume one includes writings by Sir Isaac Newton, friend of David Gregorie, Savilian Professor of Astronomy at Oxford, the volume is entitled 'Notae in Newtonii Principia Mathematica Philosophiae Naturalis' and his 'Theory of the Moon' which was incorporated in the 'Astronomia Physica' published by the Savilian Professor of Astronomy at Oxford; volume two is a volume of letters and papers of the Gregory family, including some papers of Sir Isaac Newton; David Gregorie of Kinnairdie; James Gregorie author of 'Optica Promota'; David Gregorie, Savilian Professor of Geometry at Oxford; James Gregorie Professor of Mathematics at Edinburgh; and Charles Gregory, Professor of Mathematics at Edinburgh University.

Tables prepared by Sir George Everest for the use of the Great Trigonometrical Survey of India.

These are letters and papers of various members of the Gregory family including David Gregorie of Kinnairdie; James Gregory, author of Optical Promota; David Gregorie, Savillian Professor of Geometry at Oxford University; James Gregorie, Professor of Mathematics at Edinburgh University and Charles Gregory.

Latin translation attributed to Abelard of Bath, of Euclid's geometry ending imperfectly near the beginning of book 15 in the propsition 'intra propsitum cubum corpus habens iiij bases triangulas equalium laterum resignare'. Written in England

Mathematical works of Pappus Alexandrinus, stated by JO Halliwell that this was copied from Savilian MS number 9 for William Jones the mathematician.

A mathematical dissertation by Boemke written at Berlin, 1827.

Written in England. Contains the curious characters known as the Boetian contractions, and is a valuable document for the history of arithmetic. The treatise commences on the Roman abacal system, and afterwards proceeds to give an explanation of the Eastern Boetian system with altered characters, and with a complete adoption of the advantages of local position. In Folio 2, recto, line 5, the author says that he will expound 'quaedam de numerorum scientia. regulis uidelicet algorismi' and on Folio 3, verso, he refers to Pithagoras, Nicomachus, Apuleius and Boethius. The text ends on the first line of Folio 34, recto, and is followed by eight lines in a semi-current 13th century hand.

Folio 1, recto ' Prefatio sequentis operis. Vt ait salomon.. punge oculum. et profert lacrimam. punge cor' et profert sensum.....'

Folio 4, verso ' De impari numero..'

Folio 6, verso, line 6, ' Divisio algorismi '. The divisions are given as folows; ' digitus, mediato, multiplicatio, divisio '

Folio 8, recto, title in red in margin, ' Qualiter digitus multiplicat digitum '

Folio 9, recto, line 15 ' Qualiter articulus multiplicatur per articulum '

Folio 9, verso, line 13, heading in red, ' Qualiter digitus multiplicat articulum '

Folio 10, recto, line 10, heading in red, ' Qualiter compositus per compositum multiplicatur '

Folio 10, verso, heading in margin, ' Qualiter compositus multiplicat compositum non eundem habens articulum '

Folio 11, recto, bottom line, heading in red ' Regulo ab uno inequalibus '

Folio 12, recto, line 6, heading in red, ' Regula ab uno in equalibus binario adjecto '

Folio 12, verso, line 8, heading in red ' De duplicatione '

Folio 13, recto, line 5, heading in red, ' De pari adjecto '

Folio 13, verso, line 6, heading in red, ' De impari adjecto '

Folio 14, verso, heading in margin, ' De proposito secundum novenarium dispositum '

Folio 15, recto, line 7-8, heading in red, ' De significationibus et nominibus figarum et locorum '
Transcript extract from line 14 ' Prima itaque omnium est igin. 1. id est unitas. Secunda andras. 2. id est binarius. Tercia ormis. 3. id est ternarius. Quarta arbas. 4. id est quaternarius. Quinta quimas. 5. id est quinarius. Sexta caltis. 6. id est senarius. Septima zemis. 7. id est septenarius. octava celentis. 8. id est octonarius. Nona cemenias. 9. id est novenarius. Singule ataque figure in quocumque loco sint sui ipsius exprimunt significationem. Nunquam enim figura unitatis officium binarii sibi usurpabit, nec binarius ternarii, nec ternarius quaternarii, nec quelibet ceterarum quod alter significare poterit. Ad majorem itaque evidentiam significationes locorum ponamus. primo ita loco posita igin seipsam, id es unitatem, significat. Secundo denarium. Tercio centenarium. Quarto millenarium. Quinto decem milia. Sexto centum milia. Septimo mille milia. Decimo mille mille milia. Undecimo decies milies mille milia. Duodecimo centies milies mille milia. Terciodecimo milies milies mille milia, et sic usque in infinitam singulorum decuplationem locorum extenditur. Similiter autem et andras rimo loco seipsam, id est binarium, significat. Secundo xx. Tercio cc. Quarto duo milia. Quinto xx. Sexto cc. Septima mm. et sic per cetera loca eodem cemate et cetere figure secundum propriam differentiam decuplabutn singulos articulos per loca singula. Est adhucet decima figura cujus nulla significatio est, sed tamen per loca disposita ceterarum significationes auget vel minuit. Dicitur autemzifera, et taliter depingitur 0. Sciendum autem quod omnes figure versus sinistram scribi debent, quia sic vim extendunt. Sed e converso literali ordine legi. '

Folio 17, verso, line 6, heading in red, ' De subtractione'

Folio 18, verso, line 8, heading in red, 'De dupli``catione'.

Papers on mathematics and physics collected by the Reverend Samuel Horsley DD, FRS.

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.

Manuscript volume of 'Philosophiae Naturalis Principia Mathematica', by Isaac Newton. Manuscript written out by Humphrey Newton, Isaac Newton's assistant and amanuensis, and annotated by Newton and Halley. Manuscript from which the First Edition was printed.