Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Book 4, Propositions 6, 7, and 8


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

Joseph Mallord William Turner 1775–1851
Crayon and watercolour on paper
Support: 584 x 872 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 30

Catalogue entry

Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, these three diagrams of a square within a circle and circles within squares are based on an illustration representing Propositions 6, 7, and 8 from Book 4 of Samuel Cunn’s Euclid’s Elements of Geometry (London 1759). Beginning from the left, the first figure shows Proposition 6: ‘Problem. To inscribe a square in a given circle’. The next represents Proposition 7: ‘Problem. To describe a square about a given circle’. The last illustrates Proposition 8: ‘Problem. To describe a circle in a given square’.1 There are pencil sketches of each in Turner’s lecture notes.2
Cunn 1759, pp.106–8.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 V folios 21 verso–22 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 ‘16’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

Read full Catalogue entry