Bonnycastle, John | A student’s manuscript of mathematical problems from A Treatise on Plane and Spherical Trigonometry.
An elegant, substantial early-19th 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 best-selling 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, text-heavy 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.
Urey, Harold | Archive of correspondence with astronomer Arthur Beer
An archive of correspondence between astronomer Arthur Beer and Nobel Prize winning chemist Harold Urey regarding the latter’s contribution to Vistas in Astronomy.
Beer (1900-1980) was born in Richenberg, Bohemia (later Czechoslovakia), and educated in Austria and Germany. He worked as an astronomer at Breslau University, where he studied binary stars, and at the German Maritime Observatory. He also wrote newspaper columns and was responsible for developing one of the first scientific radio programmes, Aus Natur und Technik. Beer escaped from Germany in 1934, assisted by Einstein, who wrote him a public letter of recommendation, and spent the rest of his life in the UK. He worked at the Cambridge Solar Physics Observatory and at the Kew Observatory, and became a member of the Royal Astronomical Society. Beer’s most significant contribution to science was as the founding editor of Vistas in Astronomy, a “voluminous and thorough survey of present-day astronomy” in two volumes, conceived as a Festschrift celebrating the 70th birthday of astrophysicist Frederick J. M. Stratton, under whom he had served in Cambridge. The resulting volumes were so impressive that it was continued first as an annual book and then a quarterly journal.
American chemist Harold Urey (1893-1981) did key work on atomic and molecular structures, particularly hydrogen isotopes. This led him to the discovery of deuterium, for which he was awarded the Nobel Prize in 1934. During the Second World War he led the Manhattan Project’s branch at Columbia University, where he applied his knowledge of isotope separation techniques to the problem of isolating of pure uranium 235 on an industrial scale. After the war he worked at the Institute for Nuclear Studies at the University of Chicago. In 1958 Urey moved to the University of California, San Diego, where he did groundbreaking work on the origins of life on Earth, conducting a laboratory simulation of the conditions on the early Earth and proving that they were ideal for the production of cellular building blocks such as amino acids.
The correspondence present here consists of five letters from Urey, mainly on practical issues connected with his contribution to Beer’s book. In the first, on September 10th, 1952, he replies to Beer’s request for submissions, apologising for taking so long to reply as “I have not been able to think of a subkect to write about. I am leaving for Europe on the 14th of September and hope to visit Cambridge about October 15th. If it isn’t too late by that time perhaps we can discuss the question then. In the meantime, I will turn this over in my mind and try to think of something that I might contribute to the book.” On January 8th the following year he writes, “At last the paper for the Stratton volume!... I wish it were a better paper. If you do not wish to publish it I shall not be offended at all. There are quite a few notes and I believe references and notes are more easily read if placed at the bottom of the page. But perhaps your rules are all made long ago.” Later that month Urey sends short note to confirm receipt of the document, and in July he asks that the proofs be mailed to him in Stockholm. The final letter, dated by Beer in pencil as postmarked July 31st, 1953, discusses the terms he has chosen for the index (”I have underlined [in the returned proof, not present here] expressions indicating topics for the index... on the margins I have written additional suggestions” and relates that the illustrations had not arrived yet when he left for the states, but that “I believe the figures can be assumed to be all right”.
Chicago, 1952-53. Including 3 typed letters signed (one with the signature removed for reproduction in Vistas in Astronomy) and 2 autograph letters signed by Urey. Housed in Beer’s tan paper folder with “Urey” in ink on the cover. Just a little creasing to some pieces. Excellent condition.
[Hardouin Brothers] | Zodiac man from a French book of hours
Illuminated zodiac man from a 16th-century French book of hours printed on vellum, probably from the workshop of Germain and Gillet Hardouin.
During the late 15th and early 16th centuries printers often borrowed stylistically from manuscripts, and used vellum and colourful illuminations to increase the cachet of printed books. In France this trade was dominated by the Hardouin brothers, who were active between 1510 and 1550. Gillet was a printer, and unusually, all the illuminations were overseen in-house by his brother Germain, who was registered with the Guild of Illuminators.
The “Homo anatomicus”, bloodletting man, or zodiac man — a type of diagram that codified the relationship between the microcosm of the human body and the divine macrocosm — had its origin in classical thought and was a feature of European and Middle Eastern books of hours, almanacs, and medical texts throughout the Middle Ages and Renaissance. This example depicts man as a corpse surrounded by text explaining the relationship between the signs of the zodiac, the parts of the body, and the four humours. The temperaments associated with the four humours are depicted in the smaller illuminations. Clockwise for the top left they are: the choleric temperament symbolised by a warrior with lion; the sanguine, with a hawk and monkey; melancholy surrounded by stars; and the phlegmatic with a lamb.
Paris: Hardouin, early 16th century.
Single leaf from a French book of hours, printed on vellum and hand illuminated (185 x 115 mm). Professionally mounted, framed and glazed using archival materials. On the recto, a depiction of the “anatomical man” as a skeleton surrounded by information about the humours, the zodiac, and the best times for bleeding, surrounded by an elaborate, uncoloured border. On the verso, the calendar for January with an elaborate border of acanthus leaves and human figures and an illuminated initial. Trimmed closely at the top edge and gutter side, wrinkling and spotting of the vellum. Very good condition.