In the introduction to his book, 'Geometry in Pictorial Composition,' Brian Thomas began with the following words...
"In studying old paintings of many periods it is continually noticeable that features in a composition which strike the spectator as harmoniously related can be found to have also a geometrical relationship.
Many people, including a number of living painters, believe that any geometry that may be detected occurred unconsciously, as part of the artists' natural instinct for design. It must be admitted in support of this view that artists accustomed to observing effects of perspective and parallax in the course of their day-to-day study of nature might well have become saturated with a sense of mathematical coordination. On the other hand, it is hard to believe that highly analytical observers would have consistently achieved harmony by geometrical means without noticing the fact and regularizing its use, particularly as many painters were also architects experienced in applying stock proportions when designing.
At the other extreme, certain modern theorists have analysed old compositions and have propounded geometrical frameworks of fantastic complexity. It is inconceivable that such constructions could have been in general use as practical aids for busy craftsmen, many of whom were not intellectuals. Had such procedures been general, some reference to them must inevitably have appeared in contemporary literature. Theorizing about composition is unfortunately the kind of subject which attracts ingenious but complicated minds. It is noteworthy that when these analysis are themselves analysed a simpler more probable construction can invariably be produced."