Continued proportion
idea · 1 work · 2 mentions · 20 anchored passages
numbers in continued proportion · continued proportion · continuously proportional
in the texts
Elements
A sequence of numbers each pair of which stands in the same ratio, the central organizing structure of Book VIII's number theory
If there be as many numbers as we please in continued proportion, and each by multiplying itself make some number, the products will be proportional;
If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the numbers are the least of those which have the same ratio with them.
From this it is manifest that, if three numbers in continued proportion be the least of those which have the same ratio with them, the extremes of them are squares, and, if four numbers, cubes.