When one considers the prodigious prolificity of theorems established by Apollonius and others upon the cone and the conic sections, it may be surprising to observe that certain aspects still remain unexplored. Although Apollonius (3rd century B. C.), a master of the synthetic method in geometry, established 387 propositions on the cone during his forty-year life time, his results have been extended by many others even down to modern times. In the latter part of this paper the author wishes to contribute one new development on the cone, but first proposes to invite the reader's attention to some earlier aspects of the cone's illustrious career. The discovery of the conic sections is attributed to Menaechmus in the 4th century B. C. He employed conics to solve the famous Delian problem -the Duplication of the Cube. Apollonius investigated the non-focal properties of the conic, its conjugate diameters, asymptotes, and the harmonic property of the pole and polar for the case in which the pole lies outside the curve. Not until the 17th century were any further major advances made on conics. The latter theorem of Apollonius was then generalized by the genius of Desargues. Among the lost works attributed to Euclid were four Books on Conics, the last one however not being completed by him. It seems that Apollonius took over the completion of these and added four more of his own. He defined the basic cone as one having an oblique axis and set on a circular base. This was called a scalene cone. He proved that all sections parallel to the base are also circular; and that there is another parallel set of circular sections, "sub-contrary" to these. In the latter part of this paper the author will invoke modern analytic geometry methods to determine the dihedral angle between these two sub-contrary sets of circular sections. Apollonius derived the equivalent of the focus-directrix properties of the sections of this general cone, obtaining results equivalent to the modern analytic definitions of the conics. However, he made no reference to a directrix nor did he evince any knowledge thereof. Neither did he utilize a focus for the parabola. He showed that the conic has the same property with reference to any diameter as it has with reference to its axis (a special diameter). He expressed the fundamental property of each conic by equations between areas of associated rectangles. These relations were equivalent to the Cartesian equation of the conic. However, it remained for Pappas to state the modern locus definition for the conics. The latter first introduced the concept of eccentricity. Apollonius assigned the appropriate names to the sections, parabola (equivalent), ellipse (falls short) and hyperbola (exceeds). Straight lines and circles were then known as "plane loci", whereas conics were spoken of as "solid loci".