Similar polygons can be divided into equal numbers of similar triangles corresponding (in proportion) to the wholes, and one polygon has to the (other) polygon a squared ratio with respect to (that) a corresponding side (has) to a corresponding side.
The ratio of the areas of two similar rectilinear figures is proportional to the squared ratio of the lengths of corresponding sides.^{1}
Euclid formulates this proposition generally for all similar rectilinear figures but proves it for pentagonal figures only (editor's note). ↩