Abstract

"TAKE A LINE cut in two unequal sections, one for the kind that is seen, the other for the kind that is thought, and go on and cut each section in the same ratio". In order to follow this request, not only must one know geometry, which treats linear magnitudes; one must also know the relations between geometry and the art which treats kinds. The problem of the first cut in the line is the problem of determining what ratio of two parts of a line is the same as the ratio of the two kinds: visible and thinkable. In order to solve this problem, a procedure seems to be needed for deciding when a ratio of magnitudes, a geometric ratio, is the same as a ratio of kinds, or at least what ratio of magnitudes is the same as the ratio of visible to thinkable.