Similar polygons inscribed in circles are to one another as the squares on their diameters. Proposition 2 .
Circles are to one another as the squares on their diameters.
Lemma for XII.2. Proposition 3 . Any pyramid with a triangular base is divided into two pyramids equal and similar to one another, similar to the whole, and having triangular bases, and into two equal prisms, and the two prisms are greater than half of the whole pyramid. Proposition 4 . If there are two pyramids of the same height with triangular bases, and each of them is divided into two pyramids equal and similar to one another and similar to the whole, and into two equal prisms, then the base of the one pyramid is to the base of the other pyramid as all the prisms in the one pyramid are to all the prisms, being equal in multitude, in the other pyramid.