Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Spherical Trigonometry, Propositions 14 and 16


In Tate Britain

Prints and Drawings Room

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Joseph Mallord William Turner 1775–1851
Graphite on paper
Support: 489 x 694 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 39

Catalogue entry

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
Cunn 1759, pp.289–9.
Ibid., p.300.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 X folios 3 verso, 13 verso, 21.
Technical notes:
Peter Bower states that the sheet is Super Royal size Whatman paper made by Finch and Thomas Robert Hollingworth, at Turkey Mill, Maidstone, Kent.1
Notes in Tate catalogue files.
Blank, save for an inscription by an unknown hand in pencil ‘22’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

Read full Catalogue entry

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