Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Plane Trigonometry, Proposition 10


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Joseph Mallord William Turner 1775–1851
Graphite and watercolour on paper
Support: 490 × 692 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 133

Catalogue entry

Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram is based on an illustration from Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Plane Trigonometry). It illustrates Proposition 7 on Plane Trigonometry, which Cunn defines as ‘Theorem. Let the arcs A B, B C, C D, D E, E F, & be equal; and let the subtenses of the arcs A B, A C, A D, A E, & be drawn; then will A B: A C::A C : A B + A D: : A D : A C + A E : : A E : A D + A F : : A F : A E + A G’.1 There are sketches of the Proposition in Turner’s lecture notes.2
Cunn 1759, pp.285–8.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 X folios 19, 27.
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 ‘127’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

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