gnomon (idea)

The geometric interpretation, according to Euclid

And in any parallelogrammic area let any one whatever of the parallelograms about its diameter with the two complements be called a gnomon.

The space included between the boundary lines of two similar parallelograms, the one within the other, with an angle in common; as, the gnomon bcdefg of the parallelograms ac and af. The parallelogram bf is the complement of the parallelogram df.

• Make a parallelogram.
• Take any point on either diagonal of the parallelogram.
• Make a smaller parallelogram, using this point and either corner of the original parallelogram which is an endpoint of the diagonal, with edges parallel to the edges of the original.
• Subtract the smaller from the larger, and the L-shaped figure remaining is a gnomon.