## The theory of perspective demonstrated; in a method entirely new. By which the several planes, lines, and points, made use of in this art, are shewn in the true positions in which they are to be considered.

London: sold by J. Bennett, Mathematical instrument-Maker to their Royal Highnesses William Duke of Gloucester, Prince Henry, and Prince Frederick, 1765.

First edition, very rare and an exceptional copy bound in contemporary red morocco. John Lodge Cowley (1719-97) was Professor of Mathematics at the Royal Military Academy at Woolwich near London from 1761 to 1773. Most of his publications were on geometry, and here he attempts “to explain and facilitate the doctrine of planes as applicable to perspective” (Preface). Cowley’s *Theory* was designed as a geometrical primer with engraved diagrams that could be removed from the book to form solids, thus demonstrating the doctrines of the 11th, 12th, and 15th books of Euclid. The present work amends his *Appendix to the Elements to Euclid* (1758), and forms a new and more comprehensive attempt to explain the doctrines of planes as applicable to perspective; it is among the most elaborate and most unusual of all eighteenth-century works on geometry and perspective. Included are the eleven engraved plates, of which ten, printed on vellum, are cut-out to form regular and irregular solids, prisms, pyramids, cones, etc., each accompanied by Cowley’s analytic text. Plate IX incorporates strands of coloured cotton thread to illustrate the various projected lines from a single vanishing point. Cowley’s mathematical textbooks were extremely popular in their day, widely disseminated and well used, and are rarely found complete. As early as 1806 this work was recorded as ‘scarce’ by Adam Clarke in *The Bibliographical Miscellany* (cf. Sotheran). Two issues of this first edition were published, the present one by Bennett in 1765, and a second with a cancel title in the following year by T. Payne. The only other complete copy we can trace at auction is the De Vitry copy of the second issue, sold at Sotheby’s, 10 April, 2002.

“John Lodge Cowley was the author of a textbook entitled *The theory of perspective demonstrated; in a method entirely new*, presumably intended for use in military academies … Cowley began his book on perspective by presenting the history of the literature on the subject, and in this connection he praised [John Joshua] Kirby fulsomely. Kirby, on his part, spoke of ‘my ingenious and worthy friend Mr Cowley.’ Incidentally, it is interesting to notice that Cowley ascribed a distance point construction to [Baldassarre] Peruzzi, and claimed that [Giacomo Barozzi da] Vignola had copied Peruzzi. In Cowley’s opinion, the two most important perspectivists before [Brook] Taylor were Peruzzi and Guidobaldo [dal Monte].

“Cowley’s work is unique in the literature on perspective because his main concern is not to present perspective constructions, but to make his readers familiar with three-dimensional geometry. To this end he designed pop-up diagrams that fold out from the page and can be shaped in a given three-dimensional form. This is presumably the technique to which he referred in his title when claiming that the theory is demonstrated in an ‘entirely new’ way, because his proving style is the same as Euclid’s. Cowley’s figures, thirteen in total, are well meant, but folding them into the right shape tests not only one’s intelligence, but one’s patience and dexterity as well.

“In the first part of his book Cowley taught three-dimensional geometry. In the second he introduced all the concepts belonging to perspective, including those relating to a directing plane. In accordance with the British tradition, he thought that most of these concepts originated with Taylor. The largest part of his theory consists of theorems about relations between the fundamental concepts. He carefully included all details, such as the result that the point of intersection of two lines is mapped upon the point of intersection of the images of two lines (p. 254).

“In the third and last part of the book, Cowley presented a few examples of constructing the perspective images of plane figures. In this connection he also discussed inverse perspective – once again more from the theoretical point of view than with the purpose of solving problems. Finally, he treated stereographic and parallel projections” (Andersen, pp. 570-571).

John Lodge Cowley was an English cartographer, geologist and mathematician. He was a professor of mathematics at the Royal Military Academy, Woolwich, London, between 1761 and 1773, was elected a Fellow of the Royal Society in April, 1768, and was also Cartographer Royal to King George. He specialised in maps that depicted the counties of the United Kingdom from which arose his most famous work, *Counties of England*. Another of his publications was *A new and easy introduction to the study of geography*, which was structured as a series of questions and answers with decorative maps added later. Cowley collaborated with Robert Dodsley for several years in the creation of his maps. Among his works are remembered the superb engravings representing the constellations drawn on glass globes created by Thomas Heath. Cowley also published a number of introductory works on solid geometry with fold-up figures to aid learners: *Geometry Made Easy* (1752), *An Appendix to Euclid’s Elements* (1758) and the present work. *An illustration and mensuration of solid geometry *(1758) anticipated the work of Oliver Byrne, who nearly 100 years later, sought to provide a highly visual way to study Euclid using coloured diagrams. Cowley taught geometry to subscribers of the St. Martin's Lane Academy, a drawing school established by William Hogarth and John Ellys. Cowley had a daughter called Mrs Johnstone who inherited her father’s passion for science and over the years instructed many members of the British nobility in the use of globes and maps.

Cowley dedicated the present work to the military hero John Manners, Marquis of Granby (two portraits of whom were painted by Sir Joshua Reynolds).

ESTC T178295. Vagnetti EIVb47. Lowndes II, 540. Not in Norman, Sotheran *Bibliotheca Chemico-Mathematica*, Honeyman, Wheeler Gift, or Cajori. Andersen, *The Geometry of an Art*, 2008.

Two vols., 4to (252 x 205mm), pp. [viii], xi, [1], 117, [1], with 11 engraved plates, plates 1-9 and 11 with folding parts and printed on both vellum and card, both versions of plate 9 retaining original coloured cotton threads (occasional light spotting, some mostly marginal light soiling). Contemporary English red morocco, covers with gilt tooled foliate border enclosing central gilt decoration, spines richly gilt in compartments, black morocco lettering pieces, all edges gilt (extremities lightly rubbed).

Item #5413

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Price:
$42,500.00
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