Hero's use of the term is in fact a derived one. The original, older (and usual) meaning in Greek mathematics is not in applied maths but in number theory: a gnomon is an *indicator* (there's the link with the shadow-indicator of a dial), from _gignoskein_, to appear: it is someting which causes something else to become manifest.
The most usual types of gnomon were the odd numbers drawn as L's, by adding which you can generate the series of squares (shown here by capital O's, building on the preexisting squares, shown with lowercase o's): oO OO ooO ooO OOO oooO oooO oooO OOOO etc.; Hero's use of the term is a physical extension: a template-like device whereby something can expand according to a certain rule (shells along a spiral; but speaking of spirals, he would surely have used it for the way in which DNA sequences are generated). Bill Thayer LacusCurtius http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman
