J.M.W. Turner: Sketchbooks, Drawings and Watercolours

ISBN 978-1-84976-386-8

Joseph Mallord William Turner Lecture Diagram: 'Euclid's Elements of Geometry', Plane Trigonometry, Propositions 1, 2, 3, and 4 c.1817-28

Joseph Mallord William Turner 1775–1851
Lecture Diagram: ‘Euclid’s Elements of Geometry’, Plane Trigonometry, Propositions 1, 2, 3, and 4 circa 1817–28
Turner Bequest CXCV 41
Pencil and watercolour on white wove paper, 489 x 695 mm
Watermarked ‘J WHATMAN | TURKEY MILLS | 1817’
Inscribed by Turner in black watercolour with various initial letters within diagram
Inscribed by John Ruskin in red ink ‘41’ bottom right
Accepted by the nation as part of the Turner Bequest 1856
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 Propositions 1, 2, 3 and 4 on Plane Trigonometry. The left figure represents Proposition 1, which is described as: ‘Theorem. The two sides of any right-angled triangle being given, the other side is also given’.1 The right diagram illustrates three Propositions: Proposition 2, ‘Problem. The sine DE of the arc BD, and the radius CD, being given, to find the cosine DF’, Proposition 3, ‘Problem. The sine DE of any arc DB being given, to find DM or BM, the sine of half the arc’ and Proposition 4, ‘Problem. The sine BM of the arc BL being given, to find the sine of a double that arc’.2 There are sketches of the Propositions in Turner’s lecture notes.3
Cunn 1759, p.279.
Ibid., pp.279–80.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 X folios 11, 24 and verso.
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 ‘24’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

How to cite

Andrea Fredericksen, ‘Lecture Diagram: ‘Euclid’s Elements of Geometry’, Plane Trigonometry, Propositions 1, 2, 3, and 4 c.1817–28 by Joseph Mallord William Turner’, catalogue entry, June 2004, revised by David Blayney Brown, January 2012, in David Blayney Brown (ed.), J.M.W. Turner: Sketchbooks, Drawings and Watercolours, Tate Research Publication, December 2012, https://www.tate.org.uk/art/research-publications/jmw-turner/joseph-mallord-william-turner-lecture-diagram-euclids-elements-of-geometry-plane-r1136726, accessed 19 September 2021.