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angle CEF asymptotes axis bisected circle common quadrilateral compounding conic section conjugate opposite sections constant ratio cutting the section differs from triangle drawn parallel drawn through H ellipse Eucl Eutocius ex aequali figure on AC H parallel hyperbola joined and produced joining the points KRXL let AC let some point Let the common lines touching opposite meeting the tangents midpoint opposite sections meet parabola parallel to AC perpendicular pllg point H point of meeting points of contact Proposition rectangle contained remainder quadr remainder rect right angle say that sq shown similar triangles sq.AE straight line drawn straight line joining straight lines cut straight lines touching things supposed three-line locus touch the section touching opposite sections Translator's Note trgl upright diameter upright side vertex