Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Book 4, Proposition 5


View this artwork by appointment, at Tate Britain's Prints and Drawings Rooms

Joseph Mallord William Turner 1775–1851
Graphite and watercolour on paper
Support: 584 x 874 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 33

Display caption

This illustrated a lecture about basic principles of geometry. Turner copied it from Euclid's 'Elements of Geometry' but made a mistake in the title - it shows triangles inside circles, not circles inside triangles. A copy of Euclid with Turner's annotations (no.153) is displayed in a showcase.

Gallery label, September 1992

Catalogue entry

Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram of two triangles within circles – inexplicably inscribed ‘Circles within a Triangle’ – completes Proposition 5 from Book 4 of Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Book 4). See Tate D17004; Turner Bequest CXCV 34 for the initial portion. Cunn defines the proposition as ‘Problem: To describe a circle about a given triangle’.1 There are sketches of both figures in Turner’s lecture notes.2
Cunn 1759, pp.105–6.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 V folio 21 verso.
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 ‘13’ 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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