Lecture Diagram 30: Perspective Method for a Cube (after Samuel Marolois and Jean-François Niceron)

c.1810

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Artist: Joseph Mallord William Turner 1775–1851
Part of: I. Numbered Perspective Diagrams
Medium: Graphite and watercolour on paper
Dimensions: Support: 672 x 998 mm
Collection: Tate
Acquisition: Accepted by the nation as part of the Turner Bequest 1856
Reference: D17044
Turner Bequest CXCV 74

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Diagram 30 combines methods by Samuel Marolois, a mathematician and fortification designer, and Jean-François Niceron, a geometrical theorist.

For Marolois's technique, Turner directs his students to place the eye (E) at the center line (C) where it cuts the horizon line (H). Then draw the plan of the object (P) to be put into perspective. Where perpendicular lines meet the base line (B), mark vanishing lines to the eye. Now draw transfer lines from the plan to the base line and connect to a point (V) at the side. The places at which all these lines intersect form the bottom of the cube.

Gallery label, August 2004

Catalogue entry

Diagram 30 for Turner’s Lecture 3 as Professor of Perspective at the Royal Academy illustrates a perspective projection of a cube proposed by the French mathematician and designer or fortifications, Samuel Marolois (1572–1627). For his understanding of Marolois’s method, Turner relied on John Joshua Kirby’s Dr Brook Taylor’s Method of Perspective made Easy, both in Theory and in Practice (1768 ed., II, pl.XIX, fig.2);1 Turner owned a copy, which passed to him from his friend Henry Scott Trimmer, a descendant of Kirby (private collection). Turner also attributes the diagram to Jean-François Niceron (1613–1646), a geometrical theorist. According to Maurice Davies, Turner initially copied three diagrams from Niceron’s Thaumaturgus Opticus (1646, tab.3, fig. V; tab.6, fig.VIII; and tab.41, fig.LXXXVI) on a single sheet of paper.2 One of these diagrams (1646, tab.6, fig.VIII) ultimately informed his brief description in Lecture 3.3 Turner revised his description of Marolois’s and Niceron’s methods in a later version of the lecture.4

Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 A folio 18, F folio 3 and M folio 3 verso.

Davies 1994, p.92; Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 BB folio 22 recto.

Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 F folio 4 and M folio 5.

Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 AA folio 11.

Technical notes:

Peter Bower states that the sheet is Double Elephant size Whatman paper made by William Balston, at Springfield Mill, Maidstone, Kent. The largest group within the perspective drawings, this batch of paper shows a ‘grid-like series of shadows that can be seen within the sheet in transmitted light. This appears to have been caused by a trial method of supporting the woven wire mould cover on the mould’. Because this is the only batch he has seen with such a feature, Bower believes that ‘it may have been tried on one pair of moulds and for some reason never tried again’. He also writes that it is ‘not the best Whatman paper by any means; the weight of this group is also very variable and the moulds have not been kept clean during use’.1

Notes in Tate catalogue files.

Verso:

Blank, save for an inscription by an unknown hand in pencil ‘76’ bottom left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

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  - Niceron, Jean-François(1)
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  - mathematics(54)
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Joseph Mallord William Turner

Lecture Diagram 30: Perspective Method for a Cube (after Samuel Marolois and Jean-François Niceron)

c.1810

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