Mathematics
(Mathematics)  Georgian era arithmetic workbook
£350.00

A substantial early19th century arithmetic workbook with several calligraphic headings featuring animals in the designs, in coloured ink.
The contents of this workbook comprise lessons and exercises in advanced arithmetic, primarily multiplication, division, and the conversion of quantities. The contents are strongly mercantile in flavour, featuring problems such as “In 552 common pounds of silk how many great pounds”; “If I give 1£ 1s 8d for 3 lbs of coffee what must be given for 29 lbs & 1 oz”; and “What is the half years rent of 547 acres of land at 15s 6d per acre per anum”.
The manuscript also features occasional overwriting in a different hand, with some entries dated 1820. These seem to be records of sales of wood and articles fashioned from it.

England, c. 18001820.
84leaf purposemade blank book (200 x 165 mm). Original tan half skiver, waste paper marbled boards. Manuscript equations, notes, and calligraphic illustrations in coloured ink filling all 168 pages. Overwriting in a separate hand, dated 1820, on some pages. Spine rolled, boards worn, occasional smudges and spots to contents. Very good condition.
Bonnycastle, John  A student’s manuscript of mathematical problems from A Treatise on Plane and Spherical Trigonometry.
£500.00

An elegant, substantial early19th century manuscript containing practical mathematical and astronomical problems likely produced by a student of navigation.The majority of the text is from John Bonnycastle's A Treatise on Plane and Spherical Trigonometry, originally published in 1806. Bonnycastle was a respected mathematics teacher who tutored the children of the aristocracy and taught at the Royal Military Academy in Woolwich. A man of “considerable classical and general literary culture”, he was a great friend of Fuseli and also of Leigh Hunt, who included Bonnycastle in his book Lord Byron and Some of His Contemporaries.
“Bonnycastle was a prolific and successful writer of textbooks. Of his chief works, The Scholar's Guide to Arithmetic first appeared in 1780 and ran to an eighteenth edition in 1851… His Introduction to Astronomy (1786), intended as a popular introduction to astronomy rather than as an elementary treatise, was one of the bestselling books on the subject for many years… Besides elementary mathematical books, Bonnycastle was in early life a frequent contributor to the London Magazine. He also wrote the introduction to a translation (by T. O. Churchill) of Bossut's Histoire des mathématiques (1803) and a ‘chronological table of the most eminent mathematicians from the earliest times’ for the end of the book” (ODNB).
This manuscript, titled “Bonnycastle’s Trigonometry”, contains the practical portions of the text, including rules for solving different types of trigonometric problems (“cases”) and practice problems. The practice problems have been completed in full, including large, precise geometrical diagrams made with ruler and compass. Page numbers are given and the problems are dated, the first section having been completed on September 24th, 1813 with additions every few days until the final dated entry on March 31, 1814. The final, undated portion, about a quarter of the manuscript, comprises “Miscellaneous Astronomical Problems” from Andrew Mackay’s The Theory and Practice of Finding the Longitude at Sea or Land (first published in 1793, the second edition in 1801), an important work for which its author “received the thanks of the boards of longitude of England and France” (ODNB).
This manuscript’s focus on mathematical rules and practice problems (at the expense of the more theoretical, textheavy portions), together with the fact that it was updated regularly between September and March, indicates that it was produced by an advanced student working through the book as part of a regular course of study. The script is elegant, clear, and controlled throughout, and pencilled guide rules indicate that the student took great pains to ensure the manuscript was attractive and readable, suggesting that it was evaluated as part of coursework rather than used as a notebook for producing rough calculations (indeed, some rough calculations are included on sheets of scrap paper loosely inserted). Mathematics of this type, focused on spherical trigonometry, astronomy, and navigational problems, would have been of interest primarily to mariners, and it seems reasonable to conclude that the student was attending a naval or military institution, or was perhaps under private tutelage with a naval career in mind. A beautiful example of a student’s efforts at practical mathematics for navigation at a time when Britain was the major power on the seas.
 ...as well as Andrew MacKay’s The Theory and Practice of Finding the Longitude at Sea or Land. 170 page manuscript. Contemporary half speckled sheep, marbled sides. Several contemporary sheets of manuscript with mathematical notations loosely inserted. Corners repaired, a little wear and some discolouration to boards, endpapers tanned, contents with the occasional light spot but overall quite clean. Very good condition.
Boole, Mary Everest  The Mathematical Psychology of Gatry and Boole
£150.00

First edition, first printing.
Author Mary Everest Boole (18321916) was the daughter of a rector who encouraged her interest in mathematics. At eighteen the logician George Boole became her tutor, and she wrote later that it was his book on logic which made her fall in love with him. In 1855 they were married and moved to Cork, where he was teaching. George encouraged Mary “to attend his lectures and improve her knowledge of mathematics. He read his book on differential equations to her, altering it until the language was completely clear to her” (Biographical Dictionary of Women in Science).
Following George’s death, Mary became a matron at Queens College and developed an interested in mathematical education. “Her collected works, published after her death in 1931, reprinted interesting articles on mathematical education that include the idea that a child should construct mathematical table before he or she uses it, and emphasize the need for logical thinking” (BDWS). The present volume is “a detailed analysis of the philosophical writings of the French writer P. Gratry (whom George Boole had admired), comparing them with her husband’s mathematical concepts which she tried (not entirely successfully) to explain using simple geometric concepts. This book also tried to investigate what she termed ‘mathematical psychology’, the importance of logical thinking, and the nature of genius” (BDWS). 
...Translated from the Language of the Higher Calculus and into that of Elementary Geometry.
London: Swan Sonnenschein & Co. Ltd., 1897.
Octavo. Original brown cloth, titles to spine gilt, black coated endpapers. Lightly rubbed at the extremities, spine a little rolled and darkened with some minor wear at the ends, contents slightly toned. A very good copy.
Burr, G. D. [George Dominicus]  Instructions in Practical Surveying, Topographical Plan Drawing, and Sketching Ground Without Instruments
£200.00

Second edition with additions, first published in 1839. An attractively bound prize copy awarded by the Royal Military College at Sandhurst to Henry George White for “attention to, and progress in, military drawing”. With White’s later bookplate giving his rank as Major General.
Author George Dominicus Burr (d. 1855), was for forty years an esteemed professor of military surveying at the Royal Military College, and it is presumably he himself who presented this prize volume. The contents cover practical surveying and military drawing for students with no prior knowledge of the art, “confidently recommending to [them] a practice founded upon long experience, and certain in its results, within the limits we have assigned to it” (introduction).
The recipient, Major General Henry George White (1835  1906) “had a distinguished career in the British Army serving at the Crimean War (185456), in the Indian Mutiny (185859), in Cyprus (187879) and Bechanaland in South Africa in the 1880s” (Irish National Inventory of Architectural Heritage ).

...With Plates and Woodcuts. Second Edition.
London: John Murray, 1847.
Octavo (183 x 115 mm). Contemporary prize binding of green morocco, spine gilt in compartments, title, singleline rules, elaborate crests to boards, acorn and oak leaf roll to turnins, and all edges gilt, marbled endpapers. 5 folding plates on tissue, diagrams within the text. Prize and ownership bookplates to the front endpapers. Binding lightly rubbed with a few mild scuffs and some light wear at the extremities, a little faint spotting to the folding plates. Very good condition.
Glenie, James  The Doctrine of Universal Comparison, or General Proportion [Bound together with] A Geometrical Investigation of Some Curious and Interesting Properties of the Circle
£450.00

A mathematical sammelband containing the first editions of two scarce texts by the soldier and mathematician James Glenie (17501817). The second Glenie volume, A Geometrical Investigation of Some Curious and Interesting Properties of the Circle, is inscribed “From the Author”, and contains a long equation and seven small textual corrections in the same ink, but it is unclear if this is an authorial or secretarial hand.
During his education at St. Andrews Glenie showed aptitude for science and mathematics, but on the outbreak of the American War of Independence he enlisted and was sent to North America, becoming second lieutenant in the engineers in 1776.
“In 1774, while in the army, it seems that Glenie discovered the 'antecedental calculus', and wrote 'a small performance' of it in Latin which was printed in July 1776. He sent a paper on this to the Royal Society, which was read in 1777 and published the following year. At much the same time Glenie wrote papers entitled 'The division of right lines, surfaces and solids' and 'The general mathematical laws which regulate and extend proportion universally', printed in the society's Philosophical Transactions in 1776 and 1777. These publications, with his book, The History of Gunnery with a New Method of Deriving the Theory of Projectiles (1776), secured Glenie's election to the Royal Society on 18 March 1779, while he was still in Quebec... In 1794 Glenie published a new booklet on the antecedental calculus. Newton's approach to the calculus had used the notion of limit unclearly, and also drew upon velocity; Glenie wished to avoid all this, so as an alternative he defined the derivative of a function algebraically by using the binomial theorem in order to express the ratio of the increments of two functions as a power series in the incremental variable h, and then blithely deleting terms containing powers of h above the first. A related work was a letter from Glenie to Francis Maseres, containing 'A demonstration of Sir Isaac Newton's binomial theorem'. This, and other papers by Glenie, were published by Maseres in his Scriptores logarithmici (6 vols., 1791–1807).” (Oxford Dictionary of National Biography).

...[and] Smart, John & Charles Brand. Tables of Interest, Discount, Annuities, &c. First Published in the Year 1724 by John Smart, and now Revised, Enlarged, and Improved by Charles Brand. To Which is Added an Appendix, Containing Some Observations on the General Probability of Life. London: for G. G. J. and J. Robinson [and] T. Longman; T. Cadel; and N Conant, 1789, [1805] [&] 1780.
Quarto (265 x 205 mm). 19th century half calf, buff boards, marbled endpapers, edges of text block speckled blue. Tables and equations. Ownership signature of W. Gordon to each Glenie volume. A Geometrical Investigation lacking the first plate and the full title, and bound in with the half title only. Boards worn and chipped with some loss from the spine, which has been professionally conserved by Bainbridge Conservation, joints cracked but still firm, some offsetting and spotting to contents, particularly the Tables of Interest. Very good condition.
Hartree, Douglas R.  Calculating Machines: Recent & Prospective Developments
£575.00
 First edition, first impression of "the first booklet on electronic computers separately published by a conventional publisher, and also one of the earliest discussions of how these machines could be used in scientific calculations" (Origins of Cyberspace 649). In addition to his significant contributions to ballistics and quantum theory, British mathematician Douglas Hartree (18971958) was a leader in efforts to automate scientific calculations. He was "involved in the development of the digital electronic computer, which emerged from wartime attempts to automate calculation further... In 1946 Hartree's advice was sought in the application of the United States army's ENIAC (electronic numerical integrator and computer) to the production of ballistic tables" (ODNB). This booklet was based on his experience with ENIAC, and describes in detail the machine's operation, its memory capacity, how problems are encoded for it to process, and what types of mathematical questions it can address. It also offers hints of future applications, such as research in fluid dynamics, statistics, number theory, and economics, where the burden of manual calculation was previously too great to allow for indepth analysis.
 Cambridge: Cambridge University Press, 1947. Octavo. Original cream wrappers printed in brown. 2 plates from photographs, equations and charts within the text. Ownership signature to upper cover, title and author's name written in ink on the spine. Wrappers tanned, crease to lower cover also slightly affecting final ten leaves. A very good copy.
Lehmer, Derrick  "Machine Performs Difficult Mathematical Calculations"
£100.00

First edition, staff issue. The present volume collects three years of Carnegie Institution News Service Bulletins (19331935), including articles and scientific papers on a variety of subjects researched by Carnegie staff members around the world (this is the staff edition, as opposed to the press and school editions, which do not include the "Notes on Institution Affairs").
The key article in this volume is "Machine Performs Difficult Mathematical Calculations", an account of the "Congruence Machine" (now known as a Lehmer sieve) developed to determine prime numbers by University of California mathematician Derrick Norman Lehmer (18671938). Determining which numbers are prime is a key problem in mathematics, and Lehmer made his name in 1914 by completing the series of primes up to 10 million. The first Lehmer sieve was constructed by Lehmer and his son Derrick Henry in 1926, using bicycle chains and metal rods that closed an electrical circuit when a solution to a factorization problem was found. In 1932 they completed a more advanced device utilizing gears and light beams, which is detailed in the present article. Lehmer sieves were an important early type of mechanical calculator, and the basic concept is still used for mathematical sieves in modern software.
With the ownership inscription of renowned seismologist Hugo Benioff, known for the innovative seismographs he developed, as well as his work charting the locations of deep earthquakes in the Pacific seabed.
 ...[in] in Carnegie Institution of Washington News Service Bulletin Staff Edition Volume III, Nos. 131. Washington D. C.: Carnegie Institution, 193335. Tall quarto. Original green cloth, titles to upper board gilt. Illustrations throughout. Upper corner bumped, a little dampstain to tail of spine slightly affecting contents, minor rubbing at extremities, margins of contents toned. A very good copy.
Logsdon, Mayme Irwin  Elementary Mathematical Analysis
£195.00

A very attractive set of this uncommon mathematical textbook by the first woman to receive tenure in the University of Chicago mathematics department, Mayme Irwin Logsdon (1881?).
“Mayme Logsdon returned to school after the death of her husband and earned all of her degrees from the University of Chicago. After teaching for four years at Hastings College, she returned to Chicago, where she advanced to associate professor. She remained at that rank for sixteen years without being promoted to professor. In 1946, she took a job as professor at the University of Miami and remained there until retirement [in 1961]. She was a dean of the College of Chicago from 1922 to 1925 and was an International education Board Fellow in Rome from 1924 to 1925. She was a member of the American Association for the Advancement of Science, the Mathematical Society, and the Mathematical Association. Her research interests were algebraic geometry and the problems of mathematics teaching.” (Ogilvie, Biographical Dictionary of Women in Science, p. 800).
Logsdon wrote two textbooks for undergraduates, the present set and A Mathematician Explains (University of Chicago Press, 1936), and she served as the PhD adviser for four students at Chicago.

...with Tables. Volume I [&] Volume II. New York and London: McGrawHill Book Company, Inc., 1932 & 1933.
2 volumes, octavo. Original red cloth, titles to spines gilt, borders to boards blocked in blind. Bookplate of John Hubley Schall, Jr. in volume I. Light rubbing to the extremities, a few small spots to the cloth of volume I. An excellent, fresh set.
Piccard, Sophie  Sur les Ensembles de Distances
£150.00

First edition of this significant work on set theory, text unopened and in the original wrappers.
Author Sophie Piccard (19041990) showed great mathematical ability from an early age. She was born and completed her first undergraduate education in Russia, but fled to Switzerland with her parents in 1925. Piccard then completed a second mathematics degree, and obtained her doctoral dissertation on probability at the University of Lausanne. Following her father’s death, she worked as an actuary and then an administrative secretary, but continued doing research, and in 1936 became assistant in geometry to at professor at the University of Neuchâtel. She succeeded to his position in 1938, and from 1943 held the chair of higher geometry and probability theory, becoming the first female full professor in Switzerland. “Her research interests were set theory and group theory. She published papers in other areas as well: function theory, the theory of relations, probability theory, and actuarial science” (Ogilvie, p. 1020).
“In 1939 Piccard published her book 'Sur les ensembles de distances des ensembles de points d'un espace Euclidean.' If A and B are point sets of a Euclidean space, the distance set of the pair (A,B), denoted by D(A,B), is the set of all numbers d such that there is a pair of points, one in A and the other in B, whose distance is d. Piccard's book made a detailed study of various questions concerning D(A,B). The review of the book in Mathematical Reviews said that 'a few results in the field under investigation are due to Steinhaus, Sierpinski and Ruziewicz, but after chapter I, the results are almost entirely new'" (Biographies of Women Mathematicians, Agnes Scott College website).

...Des Ensembles de Points d'un Espace Euclidien. Neuchâtel: Secrétariat de l’Université, 1939.
Octavo. Original grey wrappers printed in black. Text block unopened. Wrappers tanned along the edges and spine, a little creasing at the edges, small chip at the top of the upper wrapper, contents faintly toned in the margins. An excellent copy.
Tonelli, Giorgio  La Pensée Philosophique de Maupertuis
£50.00

First edition, first impression. A very attractive copy in fresh condition.
This important study analyses the philosophical milieu and influences of Maupertuis, “one of the greatest scientists and original thinkers of the 18th century. His contributions to mathematics (the Principle of Least Action), and his refutation of preformationist theories alone would have justified his preeminence. However, of particular interest was his study and interpretation of pedigrees of genetic traits, the application of the concept of probability to genetic problems, the introducing of experimental breeding as a means of studying the transmission of inherited traits in animals, and his proposed theories of inheritance, all ideas which were far ahead of their time” (Emery, “Pierre Louis Moreau de Maupertuis )16981759)”, Journal of Medical Genetics 25, 1988).

...son Milieu et ses Sources. Édition Posthume par Claudio Cesa. Hildesheim, Zürich & New York: Georg Olms, 1987.
Quarto. Original tan and white boards with text in black and white. Minor bump to the lower corner. Excellent condition.