structure be built up of successive parts, similar and similarly situated, we can always trace through corôÙreôÙsponôÙding points a series of logarithmic spirals (Figs. 258, 259, etc.);
- (2) it is charôÙacôÙterôÙisôÙtic of the growth of the horn, of the shell, and of all other organic forms in which a logarithmic spiral can be recognised, that each successive increment of growth is a gnomon to the entire pre-existing structure.
- And conversely (3) it follows obviously, that in the logarithmic spiral outline of the shell or of the horn we can always inscribe an endless variety of other gnomonic figures, having no necessary relation, save as a {514} mathôÙeôÙmatôÙiôÙcal accident, to the nature or mode of development of the actual structure10.
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