Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Book 1, Propositions 1 and 4


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Joseph Mallord William Turner 1775–1851
Graphite and watercolour on paper
Support: 580 x 870 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 26

Catalogue entry

Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram of various geometrical figures is based on an illustration in Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, book 1, plate 1, Propositions 1 and 4). The left figure illustrates Proposition 1, ‘Problem: To describe an equilateral triangle upon a given finite right line’, while the right describes Proposition 4:
Theorem: If there are two triangles that have two sides of the one equal to two sides of the other, each to each, and the angle contained by those equal sides in one triangle equal to the angle contained by the correspondent sides in the other triangle; then the base of one of the triangles shall be equal to the base of the other, the whole triangle equal to the whole triangle, and the remaining angles of one equal to the remaining angles of the other, each to each, which subtend the equal sides.1
There are sketches of both Propositions in Turner’s lecture notes.2
Cunn 1759, pp.5, 7–8.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 V folios 10, 17, 18.
Technical notes:
Peter Bower states that the sheet is Colombier size Whatman paper made by William Balston, at Springfield Mill, Maidstone, Kent.1
Notes in Tate catalogue files.
Blank, save for an inscription by an unknown hand in pencil ‘5’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

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