In sophomore mathematics (May 2013) at St. John's College, I read Apollonius' Conics, exploring the aspects of conic surfaces and their intersections with flat planes. I wrote this paper partially in response to Apollonius and partially in response to Blaise Pascal's explorations in projective geometry. In this paper I explore what sections are created if two conic surfaces are themselves made to intersect. I created all of the diagrams myself. Here is the original pdf.