Treatise on Conic Sections

apex Apollonius Archimedes Archytas Aristaeus asymptotes axes axial triangle bisected Book central conic centre circle cone conic sections conjugate diameters conjugate hyperbola construction corresponding draw drawn parallel ellipse equal equation Euclid Eutocius figure follows four-line locus geometrical given hyperbola Hence intersection Join latus rectum M₂H meet the curve Menaechmus middle point moves further normal opposite branch ordinates P₁ Pappus parabola parallelogram parameter perpendicular plane problem Proclus produced proof Prop Proposition proved quadrilateral ratio rectangle reference respectively right angles right cone segment side similar triangles Similarly solution square Suppose tangent at Q theorems treatise vertex whence ἄρα δὲ ἐπὶ καὶ πρὸς τὸ ἀπὸ τὰ τῇ τὴν τῆς τοῦ τῶν ὑπὸ ὡς