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. * Let $ABCDE$ and $FGHKL$ be similar polygons, and let $AB$ correspond to $FG$. * I say that polygons $ABCDE$ and $FGHKL$ can be divided into equal numbers of similar triangles corresponding (in proportion) to the wholes, and (that) polygon $ABCDE$ has a squared ratio to polygon $FGHKL$ with respect to that $AB$ (has) to $FG$.
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). ↩