Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Book 12, Propositions 13 and 14


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Joseph Mallord William Turner 1775–1851
Graphite and watercolour on paper
Support: 490 x 695 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 45

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 (Book 12, Plate 2). The left figure illustrates Proposition 13: ‘Theorem. If a cylinder be divided by a plane parallel to the opposite planes; then, as one cylinder is to the other cylinder, so is the axis to the axis’.1 The right represents Proposition 14: ‘Theorem. Cones and cylinders, being upon equal bases, are to one another as their attitudes’.2 There are pencil sketches of the figures in Turner’s lecture notes.3
Cunn 1759, pp.265–6.
Ibid., pp.266–7.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 V folio 33 and verso and W folio 8.
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.
A pencil sketch illustrating Proposition 13 from Book 12 of Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Book 12, Plate 2); inscribed by an unknown hand in pencil ‘51’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

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