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

ISBN 978-1-84976-386-8
J.M.W. Turner > 1802-18 Academician and professor > Perspective lectures c.1809-28 > Perspective Sketchbook > Artwork

Joseph Mallord William Turner Inscription by Turner: Notes on Geometric Proportion, from John Hamilton c.1809

Joseph Mallord William Turner, ‘Inscription by Turner: Notes on Geometric Proportion, from John Hamilton’ c.1809
Joseph Mallord William Turner 1775–1851
Folio 16 Verso:
Inscription by Turner: Notes on Geometric Proportion, from John Hamilton circa 1809
D07382
Turner Bequest CVIII 16a
Pen and ink on white wove paper, 88 x 115 mm
Inscribed by Turner in ink (see main catalogue entry)
 
Accepted by the nation as part of the Turner Bequest 1856
The whole page is taken up with the following notes:
from the proportions of Harmonic <Sections> division | used by M. de la Hire
– Harmonic lines divided by way of Lemmas | short ways. If a line AB be so divided into 3 parts | by the Points CD as that the whole line AB has the same | proportion to the extreme part AC as the other | extreme DB to the middle CD or the Rectangle | of the whole line <D>AB its middle CD be equal | to the Rectangle between the parts AC and DB thus | the line AB is said to be Harmonically divided
Maurice Davies has identified the whole sequence of notes and diagrams running from folio 15 verso to folio 18 verso (D40670, D07381, this page and D07383–D07386) as taken 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, London).
The first lines here continue directly from those on the recto of this leaf (D07381), from the third, unpaginated page of Hamilton’s preface. ‘M. de la Hire’ is Philippe de la Hire, author of a 1672 geometrical treatise in Latin and French that Turner could also have read at the British Museum.
The subsequent explanation of harmonic division is carefully taken from ‘Def. I’ and an introductory passage immediately preceding it on Hamilton’s page 92 (within Book III, Section I: ‘Of the Properties of Harmonical Lines’). The notes relate to the diagrams on folio 17 recto opposite (D07383) based on Hamilton’s plate 18 figures 55 and 56.
1
Davies 1994, p.288.
Technical notes:
There is a small hole towards the centre of the sheet, due to a fault or damage whereby a small area of the surface has become partly detached.

Matthew Imms
June 2008

How to cite

Matthew Imms, ‘Inscription by Turner: Notes on Geometric Proportion, from John Hamilton c.1809 by Joseph Mallord William Turner’, catalogue entry, June 2008, in David Blayney Brown (ed.), J.M.W. Turner: Sketchbooks, Drawings and Watercolours, Tate Research Publication, December 2012, https://www.tate.org.uk/art/research-publications/jmw-turner/joseph-mallord-william-turner-inscription-by-turner-notes-on-geometric-proportion-from-r1136578, accessed 25 April 2024.