Joseph Mallord William Turner

Diagram of the Geometry of a Parabola, after John Hamilton


In Tate Britain

Prints and Drawings Room

View by appointment
Joseph Mallord William Turner 1775–1851
Pen and ink on paper
Support: 88 × 115 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CVIII 17 a

Catalogue entry

To the right of the diagram, Turner has noted: ‘Ap the given | diameter Bb is | its double ordinate | in S [?make] O [?equal] | the diameter of A | S thro A the longest | L M DD equal | to B.b.’; points on the diagram itself are marked ‘Tangent’, ‘<Diameter>’, ‘Diameter’ and ‘Ord’.
Maurice Davies has identified the notes and diagrams running from folio 15 verso to folio 18 verso (D40670, D07381–D07386) as from John Hamilton, Stereography, or, a Compleat Body of Perspective, in All Its Branches, London 1738.1 Turner could have consulted the copy at the British Museum (since transferred to the British Library).
The present, simplified sketch, from plate 23 figure 73, was used as the basis of one of two versions of Turner’s perspective lecture diagram 22, headed ‘Hamilton’ and showing the geometry of a parabola, as noted by Davies2 and Andrea Fredericksen (see entry for Tate D17036; Turner Bequest CXCV 66). Turner has not transcribed Hamilton’s complex explanation on pages 112–13. The abbreviated and rather inadequate notes here, from page 143 (Book III, Section III, Prop. XVII, Prob. XIV: ‘To describe a Parabola, method I’), refer instead to plate 29 figure 84 no.1, which he copied on folio 18 recto opposite (D07385).

Matthew Imms
June 2008

Davies 1994, p.288.
Ibid., p.255.

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