CHAPTER VI¶
On Its Worthy Commendation
This our proportion, Most Exalted Duke, is worthy of as great prerogative and excellence as could ever be uttered regarding its infinite power; inasmuch as without knowledge of it very many things most worthy of admiration could never come to light either in philosophy or in any other science.
This gift is assuredly granted to it by the invariable nature of higher principles, as the great philosopher Campanus, our most famous mathematician, declares in his commentary upon the tenth proposition of the Fourteenth Book ([XIV.10])—especially when we behold that it is this very proportion which attunes so great a diversity of solids, whether in magnitude, in multitude of faces (basi), or in figures and forms, to one another with a certain irrational symphony (con certa irrationale simphonia fra loro accordi), as will be understood in the course of our treatise when we set forth the stupendous effects of a line divided according to it, which ought truly to be called not natural, but divine. Of these effects, the first in their enumeration is the following.