The model illustrates some statements of Apollonius (Book I°, 52-58) applied to the case of ellipse: An ellipse (or hyperbola) is the section curve of infinite conic right surfaces (with a circle like base). The locus of the vertices of these surfaces is a hyperbola (or an ellipse) lying in a plane perpendicular to the plane of the first curve.The vertices of the first curve are the foci of the second curve and vice versa.