There is proof of this theorem in it that blew my mind some years ago [1]. Someday I want to finish reading the rest of the book.

> Starting with a given convex quadrilateral, construct a square, external to the quadrilateral, on each side. Van Aubel's theorem states that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another.

https://en.wikipedia.org/wiki/Van_Aubel%27s_theorem