J.M.W. Turner: Sketchbooks, Drawings and Watercolours

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).