Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Spherical Trigonometry, Proposition 22


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

Graphite and watercolour on paper
Support: 489 x 694 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 38

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 (London 1759, Spherical Trigonometry). It illustrates Proposition 22 on Spherical Trigonometry: ‘In any spherical triangle A B C, if the angles at the base B and C be of the same affection, then the perpendicular falls within the triangle; and if they be of a different affection, the perpendicular falls without the triangle’.1 There is a sketch of the left diagram in Turner’s lecture notes.2
Cunn 1759, p.302.
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 X folio 21; see also 5 verso.
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.
Blank, save for an inscription by an unknown hand in pencil ‘21’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

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