Abstract

The directions for constructing the figure are to take a line cut into two unequal parts, and cut each part in the same ratio. The proportions of the lengths of segments to one another will then represent the "relative clarity" of each of four kinds of knowledge, and Book vi. closes with a summary of these proportions. If we letter the four segments from top to bottom a, b, c, and d, their relation is a:b :: c:d. From the context, it is quite clear that these four segments are unequal. However, if any line is cut in a ratio m/n, and its segments subdivided in that same ratio, two of the resulting segments will be equal, and their ratio 1:1. However, this is the construction explicitly given in the directions.