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On the Influence of Signs in Mathematical Reasoning by BABBAGE, Charles

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$85,000.00

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Seller: Jonathan A. Hill, Bookseller, Inc.

Title: On the Influence of Signs in Mathematical Reasoning
Author: BABBAGE, Charles
Seller: Jonathan A. Hill, Bookseller, Inc. (United States)
Description: 1826. 1 p.l., 53 pp. Large 4to, orig. blue wrappers, uncut. London: J. Smith, 1826. A remarkable association copy of this extremely rare offprint, linking two of the greatest scientists of the 19th century, and pre-figuring Babbage’s later work on his difference and analytical engines. This copy bears the following inscription on the title-page in Babbage’s hand: “To M. Gauss from the Author.” Additionally, Babbage has written on the upper wrapper: “M. Gauss. Influence of Signs. 3. Ch. Babbage. On the influence of signs in mathematical reasoning.” Babbage here presents his views on the importance of symbolic notation in mathematical reasoning. He argues that algebraic symbolism enables one to express ideas more briefly and precisely than in ordinary language; it enables one to consider problems in great generality, rather than only in special cases; and it often enables one to consider simultaneously different cases of a problem that would otherwise be treated separately. The use of mathematical symbols is more efficient, and less prone to error, than other forms of reasoning, as he emphasized particularly when discussing the superiority of algebraic analysis over geometrical reasoning: “[T]he power which we possess by the aid of symbols in compressing into a small compass the several steps of a chain of reasoning, whilst it contributes greatly to abridge the time which our enquiries would otherwise occupy, in difficult cases influences the accuracy of our conclusions: for from the distance which is sometimes interposed [in geometrical reasoning] between the beginning and the end of a chain of reasoning, although the separate parts are sufficiently clear, the whole is often obscure” (p. 8). Babbage also emphasizes the importance of choosing the correct notation: it should remind the user of the nature of the quantity itself (so use ‘v’ for velocity, ‘t’ for time, and so on); and related quantities should be denoted by similar symbols (so v, v’, v’’ etc. for the velocities of different bodies in the same problem, for example). Babbage singles out Lagrange’s Mecanique Analitique as a model to be emulated in the correct choice of mathematical symbols. The present paper may be seen as part of a chain of ideas that links not only his mathematical and scientific work, but also his views on politics and industry. While a student at Cambridge, Babbage formed, together with Herschel and Peacock, the “Analytical Society.” This society was principally concerned with a matter of mathematical symbolism: its aim was famously to support “the principles of pure D’ism in opposition to the Dot-age of the University.” Theological overtones apart, this was a plea to replace what Babbage and the other members of the Society viewed as the outdated and inefficient Newtonian fluxional “dot” notation still used in England with the Leibnizian dy/dx notation which was universally employed on the Continent. “For Herschel and Babbage, however, there was more to analysis than a debate about the appropriate mathematical symbols…The key to the success of analytical algebra as they saw it was its efficiency. It was a problem-solving technology that could produce answers quickly and without wasting resources…It was a way of economizing mental labor. As such it could be used to recognize what the most efficient way of proceeding in other enterprises might be too. It could provide the key, for example, to the most profitable way of deploying resources in order to maximize factory production.”–Morus, When Physics became King, p. 36. “Babbage’s ultimate solution to the problem of how to guarantee efficiency, transparency, and accuracy in reasoning was the same as his solution to the same problem in political economy: replace humans with machinery. Babbage was a firm exponent of the division of labor in factory management and equally enthusiastic for mechanization as the ultimate realization of the principle. His primary concern throughout the 1820s and beyond was to work on his projected calculating and analytical engines…The calculating engine would replace the human drudge work for calculating mathematical tables to be used (for example) in actuarial work and in astronomy. The analytical engine would go further — it would replace the human capacity to reason as well.”–ibid., pp. 37-38. When developing his difference engine Babbage again realized the importance of symbolism: in “A Method of Expressing by Signs the Action of Machinery” (Philosophical Transactions: 1826) he developed a special notation, related to Boolean algebra (which was developed later), to accurately describe the working of the engine. Babbage first met Gauss in the course of a European tour he undertook starting at the end of 1827. After travelling through Holland, Belgium, Germany and Italy, Babbage arrived in Berlin in September 1828 to meet Alexander von Humboldt, then regarded as the greatest scientist of the century. At the time, Humboldt was organizing the seventh annual Congress of German scientists. Babbage was present when the Congress opened on 18 September 1828, with Gauss among the several hundred scientists and luminaries present. It was there that Babbage met Gauss. Babbage’s paper was read at a meeting of the Cambridge Philosophical Society on 16 December 1821, but it was not published in its Transactions until more than five years later (Vol. 2, 1827, pp. 325-377). The item offered here is a very rare pre-publication offprint, dated 1826 on the title page. In very fine and fresh condition, entirely uncut. Preserved in a handsome blue morocco-backed box. With the stamps of the “Gauss-Bibliothek” (also on upper wrapper) and the Royal Observatory at Göttingen on title with release stamp date 15 October 1951. ❧ D.S.B., I, pp. 354-56. Dunnington, G.W., Gauss: Titan of Science, 2004. Poggendorff, I, 81.

Catalogue of the very Select and Valuable Library of William Roscoe, Esq. Which will be sold by Auction, by Mr. Winstanley, at his Rooms in Marble Street, Liverpool, on Monday the 19th of August, and Thirteen following Days… by (AUCTION CATALOGUE: ROSCOE, William)

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$1,350.00

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Seller: Jonathan A. Hill, Bookseller, Inc.

Title: Catalogue of the very Select and Valuable Library of William Roscoe, Esq. Which will be sold by Auction, by Mr. Winstanley, at his Rooms in Marble Street, Liverpool, on Monday the 19th of August, and Thirteen following Days…
Author: (AUCTION CATALOGUE: ROSCOE, William)
Seller: Jonathan A. Hill, Bookseller, Inc. (United States)
Description: 3 p.l., 208 pp. 8vo, mid-19th-century blue cloth over boards bound for Sir Thomas Phillipps in the cheapest fashion possible (joints with splits, cloth & title somewhat soiled), uncut. Liverpool: 1816. Roscoe (1753-1831), historian, patron of the arts, abolitionist and M.P., formed a fine library of Italian literature and early printed books illustrating the rise and progress of the art of printing, and several important manuscripts. Following his retirement, he became a partner of a Liverpool bank; after it failed in 1816, Roscoe was obliged to sell his library to satisfy part of the claims. His friends bought a selection of Italian and other books at the sale for 600 pounds, and offered them to him as a gift, which he refused (they were subsequently presented to the Liverpool Athenaeum to form the “Roscoe Collection”). The sale realized 5,013.11.9 pounds; the outstanding item was lot 1810, the famous Italian fourteenth century Bible (170 pounds to Robinson, sold by him to the Earl of Leicester for 200 guineas, who also bought privately Roscoe’s Biblia Pauperum and the 1459 Mainz Psalter). Very good copy from the library of Sir Thomas Phillipps. Bookplate of A.R.A. Hobson. 1813 lots. ❧ De Ricci, pp. 93-94. ODNB.

The Present Age, Vol. I, Nos. 1, 2, III, IV, V and VI (October, 1874-March, 1875) by Whitlock, L. G., editor

3 to 6 days for delivery

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$350.00

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Seller: McBlain Books

Title: The Present Age, Vol. I, Nos. 1, 2, III, IV, V and VI (October, 1874-March, 1875)
Author: Whitlock, L. G., editor
Seller: McBlain Books (United States)
Condition: Good
Description: South Norwalk, CT, 1875. Hardcover. Good. Bound volume containing all six issues. 194p. Original wrappers bound in on all 6 issues. Covers somewhat worn and bowed. Contents reasonably sound although the original wrappers have some chipping and other wear (the wraps on the first issue have been heavily repaired with paper and cellophane tape). Minor worming to last issue. This appears to constitute the entire run as the sixth issue announces suspension of publication and offers to the "goodwill and circulation" for sale. This rare periodical which is not found in OCLC came to us from the library of Reverdy Whitlock, one of the bookselling Whitlocks in the New Haven area who were presumably related in some fashion to the editor. Ownership signature of "Ida Virginia Hale Whitlock" of Bethany on endpaper -- we were told that she married the editor -- who appears to have been the principal author of material in these six issues, including a story ("After Many Days; or, Agnes Ecclethorpe's True Womanhood") that was serialized over these six issues (at pages 1-6; 32-38; 65-70; 97-101; 129-134; and 162-166).

Der Zigeunerbaron [Piano-vocal score] by STRAUSS, Johann, Jr. 1825-1899

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$86.00

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Seller: J & J Lubrano Music Antiquarians LLC

Title: Der Zigeunerbaron [Piano-vocal score]
Author: STRAUSS, Johann, Jr. 1825-1899
Seller: J & J Lubrano Music Antiquarians LLC (United States)
Description: Bruxelles ... London ... Leipzig: Cranz [PN C. 26767], 1886. Large octavo. Full dark red cloth boards with titling gilt to upper, edges blindstamped with floral motif, olive green cloth endpapers with floral motif. 1f. (recto title, verso blank), i-viii (ouverture), 3-88 pp. Handstamp within decorative border to outer lower corner of title ("J.G. Krompholz Berne Magasin de Musique & D'Instruments Pianos & Harmoniums"). Binding slightly worn, rubbed, bumped, and shaken; endpapers browned. Light uniform browning; occasional soiling and foxing. First Edition. Weinmann p. 137. First performed in Vienna at the Theater an der Wien on 24 October 1885, with text by I. Schnitzer after M. Jókai's Saffi. "Certainly Strauss was no judge of librettos and throughout his life he found it both cumbersome and restricting to compose to prescribed texts, though with Der Zigeunerbaron (1885) he showed himself uncharacteristically adept in this. Over the next quarter of a century a further 14 operettas and even a grand opera (Ritter Pásmán, 1892) cemented Strauss's position as the leading light in 'Silver Age' Viennese operetta, though even in the composer's lifetime only three of these found international success: Die Fledermaus (1874), Eine Nacht in Venedig (1883) and Der Zigeunerbaron." Peter Kemp in Grove Music Online.

Hawker Commemorative First Day Cover Signed By Sir Thomas Sopwith

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$85.00

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Seller: Alcuin Books, ABAA-ILAB

Title: Hawker Commemorative First Day Cover Signed By Sir Thomas Sopwith
Seller: Alcuin Books, ABAA-ILAB (United States)
Description: Boldly Signed by Tom Sopwith just after his 91st birthday. A fine first day cover produced in 1979 by Australia's Royal Air Force Museum as part of their test pilot series. It commemorates not only the great Australian aviation pioneer whose exploits as early as 1910 were evidence of how far early aeroplanes could fly but he also became the major aircraft manufacture with Harry Hawker which became famous in World War I.

The Gift of the Face: Portraiture and Time in Edward S. Curtis's "The North American Indian by ZAMIR, Shamoon

4 to 14 days for delivery

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$35.00

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Seller: Lorne Bair Rare Books

Title: The Gift of the Face: Portraiture and Time in Edward S. Curtis's "The North American Indian
Author: ZAMIR, Shamoon
Seller: Lorne Bair Rare Books (United States)
Description: Chapel Hill: University of North Carolina Press, 2014. First Edition. First printing. Octavo. Black cloth hardcover; dustjacket; 334pp; 4 unnumbered leaves of plates. As-new, in fine dustwrapper. From the library of noted poet, translator, and anthropologist Nathaniel Tarn, with his printed bookplate inside front cover.

Notes From A Sea Diary: Hemingway All The Way by ALGREN, Nelson

3 to 14 days for delivery

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$35.00

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Seller: Jeff Hirsch Books, ABAA

Title: Notes From A Sea Diary: Hemingway All The Way
Author: ALGREN, Nelson
Seller: Jeff Hirsch Books, ABAA (United States)
Description: New York: G. P. Putnam's Sons, 1965. First edition and first printing. Hardcover. 254 pages. A lesser known work from the author of "The Man With The Golden Arm." A clean and tight near fine copy in blue cloth boards and in a near fine dust jacket with some very minor wear.

Henrys Stiftstidende Cartoons 1952-1977

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$25.00

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Seller: Weller Book Works ABAA/ILAB

Title: Henrys Stiftstidende Cartoons 1952-1977
Seller: Weller Book Works ABAA/ILAB (United States)
Condition: Very Good
Description: Georg Hemmingsen, 1977. Very Good. . Henrys Stiftstidende Cartoons 1952-1977. Aalborg, Denmark: Georg Hemmingsen, 1977. unpaginatedpp. Folio. Paperback. Inscribed by author. Book condition: Very good. Slight shelf wear. Edges bumped. Inscribed by Henry to previous owner.

Ten Years and William Shakespeare: A Survey of the Publishing Activities of The Limited Editions Club from October 1929 to October 1940

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$20.00

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Seller: Between the Covers- Rare Books, Inc. ABAA

Title: Ten Years and William Shakespeare: A Survey of the Publishing Activities of The Limited Editions Club from October 1929 to October 1940
Seller: Between the Covers- Rare Books, Inc. ABAA (United States)
Condition: Very Good
Description: The Limited Editions Club, 1940. Hardcover. Very Good. First edition. Folio. Black cloth cover lacking the dust jacket as issued. Very good. Hinges starting to crack. Corners rubbed, bent. Spine ends rubbed.

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