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.

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.

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

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'.

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.

Papers of Thomas Muir comprising notebooks: a series of six loosely-bound collections of notes and drafts; 'Articles for Pogendorff VI', notes and first draft completed 1933; 'Oblong Arrays' material for paper 304 1-30, 31-60, 61-93 and 'Dunkel Notes', material for paper 305 1-30, 31-51.

Mathematical and scientific papers of George Boole.

Copy of 'The radix; a new way of looking at logarithms...in five problems by Robert Flower' made in 1877 by Alexander John Ellis with supplementary notes by Ellis including biographical information on Flower.

Correspondence of Dr Brook Taylor, Secretary of the Royal Society on mathematical subjects with Professor Keil, Mr Machin, Bernouilli, the Abbot Conti, the Comte Raymond de Montmort, 1712-1717.