Apollonius of Perga Treatise on Conic Sections

angle Apollonius applied Archimedes asymptotes axes axis base bisected Book centre chord circle complete cone conic conjugate constant construction contained corresponding curve described determined diameter direction draw drawn ellipse equal equation Euclid expression extremity fact fall figure fixed follows further geometrical given gives greater Hence hyperbola increases intersection Join length less locus manner means meet method moves normal opposite branch ordinate original Pappus parabola parallel parallelogram parameter particular passing perpendicular plane position possible problem produced proof Prop proportion Proposition proved quadrilateral ratio rectangle reference relation respectively result right angles segment separate side similar similarly solution square straight line Suppose taken tangent touch treatise triangles whence προς υπό