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 They form a complementary series to the Early Letters, both of which were superseded by the Letters and Papers.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.

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

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.

A collection of tracts on fortification and geometry, 17th and 18th centuries: Folio 1 Della Fortificatione; Folio 53 Geometrica Prattica; Folio 83 Della sfera; Folio 104-115 Blank sheets and oddments; Folio 116 Del Misurare da Contano; Folio Il quaduarete Geometrico; Folio Aritmetica.

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).

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

Papers of Professor Andrew Russell Forsyth, [1898-1921], comprising papers and lectures concerning mathematics, notably relating to Abels theorem, Abelian functions, binary forms, quintic equations and other modular functions, Fourier's and other series, algebraic functions, 1909, differential equations of mathematical physics, 1917-1921, elements of theory of functions, 1915-1916, elliptic functions, 1898, 1914-1915, spherical harmonic series, expansion in polynomials, expansion theorems, solid geometry, differential equations of dynamics.

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'.

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.

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).

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

Collection comprising three manuscript notebooks of theoretical problems relating to mechanics compiled by James Clerk Maxwell mainly during his employment at King's College London, including exam questions on aspects of mechanics and geometry, 1860-1865; problems on the collision of elastic spheres and the dynamic relation between other solid bodies; the refraction of light; the relationship between heat and volume in materials; attraction between particles, 1860-1873; notes on the works of leading authorities on mathematics and physics including Arthur Cayley, Franz Neumann and Siméon Poisson, 1867-1873; bibliography of textbooks mainly on mechanics, [1860-1865]; list of scientific instrument suppliers, [1860-1865]; outline of the contents of Maxwell's Treatise on electricity and magnetism (1873).

Of the twelve volumes in this class, two relate to the society of East India Commanders; one, 1780 to 1833, records wagers between members and promises of gifts to the society upon such eventualities as marriage or leaving the service; the other is an account book, 1825 to 1879. The remaining eight volumes are 'Elements of Navigation' by pupils of Christ's Hospital Mathematical School; the earliest is dated 1723 and the latest is c 1845. All are very carefully executed and the subjects include arithmetic, geometry, astronomy, gunnery and navigation; the majority are illustrated with diagrams, maps, pen and ink sketches or watercolours.

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)

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.

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 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.