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
A.J. Finberg, A Complete Inventory of the Drawings of the Turner Bequest, London 1909, vol.I, p.583, CXCV 41, as ‘Two Figures’.
Maurice William Davies, ‘J.M.W. Turner’s Approach to Perspective in His Royal Academy Lectures of 1811’, unpublished Ph.D thesis, Courtauld Institute of Art, London 1994, p.279.
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
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
Blank, save for an inscription by an unknown hand in pencil ‘24’ bottom left.
Supported by The Samuel H. Kress Foundation
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.