A Geometrical System of Conic Sections
Excerpt from book: DEFINITIONS. 1. AN Hyperbola is the locus of a point whose distance from a given point exceeds its distance from another given point by a constant difference. 2. Each of the given points is a Focus of the hyperbola. 3. Two hyperbolas so described that the remoter focus of each is the nearer focus of the other, and the constant difference the same, are Opposite Hyperbolas. 4. The Transverse Axis of the hyperbola is the straight line drawn through the foci and limited by the opposite hyperbolas. 5. The Centre is the middle point of the transverse. 6. A Diameter of an hyperbola is the straight line drawn through the centre, limited by the opposite hyperbolas. 7. The Conjugate Axis is a straight line drawn through the centre perpendicular to the transverse, and limited by the circumference of a circle described about a vertex of the transverse at the distance of a focus from the centre. 8. When two opposite hyperbolas are described,and two other having the conjugate axis of the former for their transverse and the transverse of the same for their conjugate axis, these are called Conjugate to the former: and the four are called Conjugate Hyperbolas. 9. A diameter Conjugate to the diameter of an hyperbola is the diameter of the conjugate hyperbolas parallel to a tangent at its vertex. 10. An External Ordinate to a diameter is a straight line parallel to a tangent at its vertex, and limited by the diameter and conjugate hyperbola. 11. The Parameter to a diameter of the hyperbola is a third proportional to the diameter and its conjugate. 12. An Asymptote of the hyperbola is a straight line drawn through the centre, to which the hyper oola (followed in one direction) continually approaches and nearer than any assigned distance, but never meets it. Oth...
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 PDF  50 pages
 Geometrical system
 General Books LLC
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