What Borromini Might Have Known About Ovals. Ruler and Compass Constructions

This paper is about drawing ovals using a given number of certain parameters. New constructions are displayed, including the case when the symmetry axes are not given. Many of these constructions make use of a recent conjecture by Ragazzo, for which a Euclidean proof is found, thus suggesting it might have been known at the time Borromini chose the ovals for the dome of San Carlo alle Quattro Fontane. A geometric proof of the same conjecture—as well as constructions—in the more general case of eggs and polycentric curves is the subject of the first part of this same research (Mazzotti, a Euclidean approach to eggs and polycentric curves, 2014).