Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram is based on illustrations from Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Spherical Trigonometry). It illustrates Propositions 14 and 16 on Spherical Trigonometry. Cunn describes Proposition 14 as ‘In any spherical triangle G H D, the poles of the sides, being joined by great circles, do constitute another triangle X M N, which is the supplement of the triangle G H D; viz. the sides N X, X M, and N M, shall be supplements of the arcs that are the measures of the angles D, G, H, to be the semicircles; and the arcs that are the measures of the angles M, X, N, will be the supplements of the sides G H, G D, and H D, to semicircles’.1 Proposition 16 is described as ‘The three angles of a spherical triangle greater than two right angles, and less than six’.2 There are sketches of both Propositions in Turner’s lecture notes.3
Blank, save for an inscription by an unknown hand in pencil ‘22’ bottom left.
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