Joseph Mallord William Turner

Lecture Diagram: ‘Euclid’s Elements of Geometry’, Book 5, Propositions 1 and 2


In Tate Britain

Prints and Drawings Room

View by appointment
Joseph Mallord William Turner 1775–1851
Graphite and watercolour on paper
Support: 585 × 868 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 27

Catalogue entry

Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram of upright lines of various lengths intersected is based on an illustration from Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Book V). The left portion represents Proposition 1: ‘Theorem. If there be any number of magnitudes equimultiples of a like number of magnitudes, each of each; whatsoever multiple any one of the former magnitudes is of its correspondent one, the same multiple are all the former magnitudes of all the latter’.1 The right represents Proposition 2: ‘Theorem. If the first be the same multiple of the second, as the third is of the fourth; and if the fifth be the same multiple of the second, as the sixth is of the fourth; then shall be the first, added to the fifth, be the same multiple of the second, as the third, added to the sixth, is of the fourth’.2
Cunn 1759, p.123.
Ibid., p.124.
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 ‘7’ 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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