Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Book 4, Propositions 10, 15, and 16


In Tate Britain

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Joseph Mallord William Turner 1775–1851
Graphite and watercolour on paper
Support: 677 × 1010 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 32

Catalogue entry

Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram of figures within circles is based on illustrations from Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Book 4). The top centre diagram shows Proposition 10: ‘Problem. To make an isosceles triangle, having each of the angles at the base double to the other angle’.1 The centre right diagram represents Proposition 15: ‘Problem. To inscribe an equilateral and equiangular hexagon in a given circle’.2 The bottom centre diagram represents Proposition 16: ‘Problem. To describe an equilateral and equiangular quindecagon in a given circle’.3 The centre left diagram is again based on Proposition 15, which is also referred to on another sheet from this series (Tate D16992; Turner Bequest CXCV 23). There are pencil sketches of each figure in Turner’s lecture notes.4
Cunn 1759, pp.109–10.
Ibid., pp.115–17.
Ibid., p.117.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 V folios 23, 26, 27.
Technical notes:
Peter Bower states that the sheet is Double Elephant size Whatman paper made by William Balston and 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 ‘18’ 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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