Treatise On Conic Sections
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Also OA < OP, because it is a property of hyperholas that ATe procedure is used for finding /*', the other extremity of the diameter through Ρ : the lengths A A', PP' are then in each case double of the line adjacent to the axis [in one case of the whole surface, and in the other of a segment of which Ρ is tlie 'vertex']. This term for AA', PP' was, no doubt, only used in order to avoid mention of the cone of (12 Hi THE EARLIER HISTORY OV CONICS. which the hyperbola is a section, as the introduction of this cone might have complicated matters (seeing that the enveloping cone also appears); for it is obvious that A A' appeared first as the distance along the principal diameter of the hyperbola intercepted between the vertex and the point where it meets the surface of the opposite half of the double cone, and the notion of the asymptotes came later in the order of things. 2. If from a point on a hyperbola two straight lines are drawn in any directions to meet the asymptotes, and from another point two other straight lines are similarly drawn parallel respectively to the former, the rectangles contained by each pair will be equal*.
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To quickly assess the difficulty of the text, read a short excerpt:
Also OA < OP, because it is a property of hyperholas that ATe procedure is used for finding /*', the other extremity of the diameter through Ρ : the lengths A A', PP' are then in each case double of the line adjacent to the axis [in one case of the whole surface, and in the other of a segment of which Ρ is tlie 'vertex']. This term for AA', PP' was, no doubt, only used in order to avoid mention of the cone of (12 Hi THE EARLIER HISTORY OV CONICS. which the hyperbola is a section, as the introduction of this cone might have complicated matters (seeing that the enveloping cone also appears); for it is obvious that A A' appeared first as the distance along the principal diameter of the hyperbola intercepted between the vertex and the point where it meets the surface of the opposite half of the double cone, and the notion of the asymptotes came later in the order of things. 2. If from a point on a hyperbola two straight lines are drawn in any directions to meet the asymptotes, and from another point two other straight lines are similarly drawn parallel respectively to the former, the rectangles contained by each pair will be equal*.
What to read after Treatise On Conic Sections?
You can find similar books in the "Read Also" column, or choose other free books by Of Perga Apollonius to read online
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