The Kansas University Quarterly, Vol. I, No. 2, October 1892

Delve into a fascinating slice of late‑19th‑century mathematics, where a lively classroom of Kansas University scholars unravels the hidden relationships between conic sections and their inverted counterparts. The paper opens with a clear invitation to readers unfamiliar with geometric inversion, pointing them toward essential background before guiding them through a step‑by‑step transformation that turns ellipses, hyperbolas and parabolas into elegant unicursal cubic curves.

Through deft algebraic manipulation and vivid geometric insight, the author shows how a simple inversion creates nodal or cuspidal cubics, each bearing distinctive points of inflection and symmetry. The discussion weaves together concrete examples—such as projecting pencils of rays and circles—to illustrate broader theorems, while also hinting at the rich tapestry of projective properties awaiting further exploration. Listeners will appreciate the blend of rigor and curiosity that characterizes this historic contribution to modern geometry.