It should be mentioned that in German usage the golden ration (Goldener Schnitt) refers more to the proportions of the spaces separated by the cutting line than

It should be mentioned that in German usage the golden ration (Goldener Schnitt) refers more to the proportions of the spaces separated by the cutting line than to the proportions of the surrounding rectangle. Its common application is basically a finer form of the rule of thirds. It shouldn't go unmentioned that William Hogarth already proposed a similar system, based on a serpentine line [0] (and, more important, in its three dimensional form, on a spiral) in his "The Analysis of Beauty. Written with a view of fixing the fluctating Ideas of Taste." [1] in 1753. Sidenote: While Hogarth observes this as an important regulating idea in the work of Michelangelo, he explicitly complains the lack of any notion thereof in Leonardo's contemporary "Trattato della Pittura". [0] Hogarth, The Painter and his Pug (see bottom left) http://www.tate.org.uk/art/artworks/hogarth-the-painter-and-his-pug-n00112 http://www.tate.org.uk/art/artworks/hogarth-the-painter-and-... [1] http://en.wikipedia.org/wiki/The_Analysis_of_Beauty http://en.wikipedia.org/wiki/The_Analysis_of_Beauty