Was your math homework this beautiful? The elegant problem above is from a 170-page trigonometry manuscript created during the Regency Era by a student who was probably studying for a career in the British navy.
Most of the manuscript is copied from A Treatise on Plane and Spherical Trigonometry, first published in 1806 by the British mathematician John Bonnycastle. 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 close friend of the painter Henry Fuseli and also of the literary critic 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" (ODNB).
This manuscript contains the practical portions of the text, including rules for solving different types of trigonometric problems, and practice problems. The practice exercises have been completed in full, many most with 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 (it excludes most of the theoretical, text-heavy portions of the original book), together with the fact that it was updated regularly between September and March, indicates that it was produced by an 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 show 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. It's a beautiful example of a student’s efforts at practical navigational mathematics at a time when Britain was the major power on the seas.