Mathematics
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
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A mathematical sammelband containing the first editions of two scarce texts by the soldier and mathematician James Glenie (1750-1817). 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).
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...[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.
Lehmer, Derrick | "Machine Performs Difficult Mathematical Calculations"
£100.00
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First edition, staff issue. The present volume collects three years of Carnegie Institution News Service Bulletins (1933-1935), 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 (1867-1938). 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. 1-31. Washington D. C.: Carnegie Institution, 1933-35. 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.