Extreme and mean ratio
idea · 1 work · 3 mentions · 10 anchored passages
cut in extreme and mean ratio · extreme and mean ratio
in the texts
Elements
A division of a straight line such that the whole line is to the greater segment as the greater segment is to the lesser.
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
[But if a rational line be cut in extreme and mean ratio, each of the segments is an irrational apotome.
therefore, when NO is cut in extreme and mean ratio, UV is the greater segment.