Sections of n-dimensional spherical cones

Many proofs have been given for the proposition: "The intersection of a right circular cone and a plane is a second degree curve (conic)". Among the first mathematicians to have proved it was Apollonius, during the period 262-200 B.C.. In fact the first book in conic sections M8S juritten by Apollonius. In this thesis, first, we supply a vector proof of this proposition, thereby simplifying procedures in the proof. Then we generalize the theorem for sections of a spherical cone in an n-dimensional Euclidean space.