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

The elaborated triangular shape in this diagram is annotated in ink ‘equal’ up an inclined line bisecting it, and ‘dimini<...>shed’ down its near-vertical left-hand side.

Maurice Davies has suggested the source of this diagram is possibly Heinrich Lautensack, Des Circkels unt Richtscheyts, auch der Perspectiva, Frankfurt 1564, ‘pp 3 or 4’.1 However, those two similar diagrams, respectively plates 7 (folio 3 verso) and 8 (4 recto) show lines radiating down from the top left to horizontal, measured lines with numbers and letters.

Turner’s sketch seems rather to be taken from plate 47, a double-page diagram tipped in between folios 29 and 30, showing two parallel, vertical features at the far left, the first of which is marked with horizontal divisions diminishing as they near the top, and the second with equal divisions throughout. From these features, independent cones of vision (divided mid-way by oblique lines like the one marked ‘equal’ in Turner’s sketch) converge on the eyes of two small figures standing at the centre and to the right of the diagram. The intention seems to be to show how equal divisions of a vertical surface will seem to diminish the higher they are above the observer, though Lautensack’s imprecisely engraved diagram is not exact enough to demonstrate this measurably.

There are other dagrams from the book, which Turner probably consulted at the British Museum (since transferred to the British Library, London), on folios 68 verso and 69 recto (D07468, D07469).