A NEW APPROACH TO TEACHING PRACTICAL MATHEMATICS
[DONN, Benjamin.]
‘The Mathematicians Pocket Companion. Or a collection of the most valuable Theorems … The whole collected from esteemed authors. By a Teacher of the Mathematics.’
[?Bideford], 1754.
Manuscript on paper, 8vo, pp. [iv], ’171’ (i.e. 172); with tables, diagrams, and drawings throughout; a few marks and stains, withal a very good, clean copy; bound in contemporary calf, gilt double-fillet border to covers, spine gilt in compartments, gilt red morocco lettering-piece, edges sprinkled red; binding worn at edges, splits to joints.
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‘The Mathematicians Pocket Companion. Or a collection of the most valuable Theorems … The whole collected from esteemed authors. By a Teacher of the Mathematics.’
A comprehensive manuscript compendium on mathematics and its practical applications – including architecture, astronomy, book-keeping, dioptrics, hydraulics, mechanics, music, and shipbuilding – most likely compiled by the mathematician and mathematics teacher Benjamin Donn, with examples from his then-unpublished treatise on arithmetic.
The work is a collection of mathematical theorems on a wide-ranging selection of mathematical subjects; as well as the more conventional topics such as arithmetic, trigonometry, geometry, and algebra, the work also includes sections on gunnery, hydraulics, pneumatics, marine architecture, music, and fortifications. Listing basic precepts and providing sample questions or examples to demonstrate concepts, the text is also enhanced with illustrations, from a detailed sketch of a cannon, architectural columns (of various orders), and the solar system, to sample pages for book-keeping systems, sundials, and the eye and its lens.
The information is taken from a range of contemporary works, including Newton’s Opticks and Principia Mathematica (marked ‘(N)’), John Ward’s Young Mathematician’s Guide (marked ‘(W)’), Christian Wolff’s Treatise on algebra (marked ‘(Wol)’), William Salmon’s Palladio Londinensis: or, the London Art of Building ‘(Sal)’, and a manuscript treatise on arithmetic by Donn himself (marked ‘(D)’).
Benjamin Donn (later Donne, 1729–1798), mathematician and cartographer, was a celebrated teacher of mathematics in his hometown of Bideford and later in Bristol, and, from 1796 until his death, master of mechanics to George III. The list of topics covered matches nearly exactly those listed by Donn in an advertisement for his services in 1769, and those sections sourced from ‘manuscript treatise on arithmetic by the author’ marked with the letter ‘D’ and are an equally close match to sections from Donn’s A New Introduction to the Mathematics; being Essays on Vulgar and Decimal Arithmetic, published only four years later in 1758.
Written while Donn was teaching mathematics in Bideford, it seems likely that the text was intended to facilitate his teaching, as an aide-memoire or textbook for his pupils, though whether the present manuscript is in Donn’s own hand or was produced by one of his students from Donn’s original is unclear. The content, notably broad in scope and with a focus on the practical applications of mathematics rather than purely theoretical, aligns with Donn’s teaching style; ‘Donn was one of a number of educational reformers in Bristol at the time who wanted to stop the rote learning of words and substitute the study of things with the aid of toys or experiments, introducing children to the principles behind each subject so that they could accept rationally what they were taught, not merely believe it slavishly. He taught a practical and vocational curriculum, presenting Newtonian experimental science as an integral part of polite learning for both adults and children. His ideas were expounded in his classes and lectures, in letters to the local press, and in his publications such as Mathematical Essays (1764), The Accountant and Geometrician (1765), The Young Shopkeeper’s, Steward’s and Factor’s Companion (1768), and later An Essay on Mathematical Geometry (1796) … the list of subscribers to his Essay on Mathematical Geometry (1796), which includes such figures as Erasmus Darwin, Samuel Taylor Coleridge, and Josiah Wedgwood, shows the regard in which he was held by contemporaries’ (ODNB).
