written by Marilyn Williamson

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John Lodge Cowley (1719-1787?) was a fellow of the Royal Society and Professor of Mathematics at the Royal Military Academy at Woolwich, near London, for a period of several years between 1761 and 1773. Known as "The Shop," the Royal Military Academy was one of the new and practical national academies that began to spring up around 1750 in England and on the Continent. These academies exemplified the shift from private science to public science, and their curricula emphasized applied sciences. Indeed the Royal Military Academy was established to improve the quality of the English military, and mathematics was an important part of the curriculum. Here is a description of the duties of the Professor of Mathematics during the time Cowley taught at "The Shop":

The Professor of Mathematics shall teach the principles of arithmetic, algebra, the elements of geometry, the mensuration of superficies and solids, plane trigonometry, the elements of conic sections, and the theory of perspective, as also geography and the use of the globes.(1)

It is not surprising to find that Cowley was interested in applied mathematics, especially solid geometry, and that his textbooks had practical applications and were widely used, surely at "The Shop," and elsewhere. The titles of his books closely reflect the subjects he taught. (2)

Perhaps the best known of Cowley's textbooks is the one featured in this web site: An Illustration and Mensuration of Solid Geometry in Seven Books. This is the third edition, although the previous two editions bore different titles. The third edition is probably the best known because it was revised, corrected, and augmented by William Jones (1762-1831), a prominent contemporary maker of mathematical instruments. This association of Cowley the mathematics professor, Jones the instrument maker, and the Royal Military Academy ("The Shop") typified the interest in applied sciences which predominated in eighteenth century England.

Euclidean geometry was consistently held in high esteem in England. Robert Simson (1687-1768) published the first edition of his English translation of the Elements of Euclid in 1756, and this translation was highly regarded for its precision and accuracy. Although not the first English translation, Simson's work served as the foundation for most subsequent geometry texts, and it was probably well known to both Cowley and Jones. In his preface to the third edition of Cowley's book, Wiliam Jones alludes to "that dark and groveling method, the rule only." He is referring to the longstanding belief that all geometric constructions had to be effected by a ruler and compasses only, and that all other methods were mechanical and not geometric. Leonardo da Vinci had made advances in construction using other means than the rule and compass, but it was the artist Albrecht Durer who showed that it was possible to construct regular and semi-regular solids out of paper by drawing the bounding polygons all in one piece and then folding the figures along the connected edges. This method is precisely what Cowley demonstrates and Jones augments in An Illustration and Mensuration of Solid Geometry.

There was an immediate application of these constructions to builders and designers of buildings and monuments, to cabinetmakers---in short, to technology. Writing of the second edition of Cowley's book, a nineteenth century bibliographer said:

This work is so constructed, that by means of the schemes traced on paste boards, and all cut out except the part that forms the base of the figure, the form of any of the solids may be at once exhibited by raising up the different parts upon their respective bases. By this contrivance any cabinet-maker can form out of wood, on any given scale, the figures of the 5 regular solids, and most of the compound mathematical bodies. (3)

These are practical applications indeed. Given the practical nature of Cowley's work, it is surprising to find a copy extant in such excellent condition as the Georgia Tech copy. Even in Jones's time the earlier editions of the book were no longer in print, and by1806 copies of any edition could scarcely be found. The third edition was expensive for its time at 18 shillings, and this high price was probably due to the exacting nature of the cutting of the figures.

Cowley's textbooks on geometry are typical of the English view of Euclidean geometry. According to historian of mathematics Florian Cajori, "England has been the home of conservatism in geometric teaching." (4) He mentions that the first Latin translation of Elements was brought out by the Englishman Billingsley in 1570. However, the study of geometry fell into decline during the seventeenth century, despite a strong attempt by Sir Henry Savile (1549-1622) to bring it into the curriculum at Oxford. Savile had presented a series of lectures on Greek geometry, and he endowed a professorship of geometry, remarking that "geometry was almost totally abandoned and unknown in England" at that time. (5) Possibly Savile was more influential than he may have thought, since many English editions of Euclid appeared during the 1700's, culminating in Simson's important edition.

Cowley's work reflects the English allegiance to Euclidean geometry, but stresses the more practical aspects of it, very much in keeping with the rise of applied mathematics.

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