The Geometry of Conics, Part 1 |
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Page 1
... Vertex . Let the axis meet the directrix in X. The vertex A is the centre of the straight line SX , since from the definition the distance of A from S must be equal to its perpendicular distance AX from the directrix . 2. From the ...
... Vertex . Let the axis meet the directrix in X. The vertex A is the centre of the straight line SX , since from the definition the distance of A from S must be equal to its perpendicular distance AX from the directrix . 2. From the ...
Page 10
... vertex meet the directrix on the diameters through the ends of the chord . 33. Find the locus of the centre of a circle which passes through a given point and touches a given straight line . 34. A point moves in such a way that its ...
... vertex meet the directrix on the diameters through the ends of the chord . 33. Find the locus of the centre of a circle which passes through a given point and touches a given straight line . 34. A point moves in such a way that its ...
Page 12
... of that diameter . In particular The tangent at the vertex is parallel to the principal ordi- nates , or perpendicular to the axis . 18. To take another example : -In Art . 14 ( 12 ) TANGENT-PROPERTIES OF THE PARABOLA.
... of that diameter . In particular The tangent at the vertex is parallel to the principal ordi- nates , or perpendicular to the axis . 18. To take another example : -In Art . 14 ( 12 ) TANGENT-PROPERTIES OF THE PARABOLA.
Page 19
Charles Taylor. If P , Q lie on opposite sides of the vertex , then in the preceding figure produce TS to t . Then < PSt = 1⁄2 PSQ [ 29 . = PTQ . [ 30 . Hence by Euc . I. 32 , < STP + SPT = STQ + STP . Therefore < SPT = STQ . And △ TSP ...
Charles Taylor. If P , Q lie on opposite sides of the vertex , then in the preceding figure produce TS to t . Then < PSt = 1⁄2 PSQ [ 29 . = PTQ . [ 30 . Hence by Euc . I. 32 , < STP + SPT = STQ + STP . Therefore < SPT = STQ . And △ TSP ...
Page 21
... Vertex , Ordinate , Latus Rectum , Diameter , Tangent , Normal , Subtangent , Subnormal . So too is Art . 21 . EXAMPLES . 48. Shew how to draw a tangent to a parabola from a point on the tangent at the vertex . 49. If a leaf of a book ...
... Vertex , Ordinate , Latus Rectum , Diameter , Tangent , Normal , Subtangent , Subnormal . So too is Art . 21 . EXAMPLES . 48. Shew how to draw a tangent to a parabola from a point on the tangent at the vertex . 49. If a leaf of a book ...
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Common terms and phrases
abscissa auxiliary circle bisects the angle Bishop of Carlisle CA² Cambridge CB² CD² centre CN² concyclic Conic Sections conjugate diameters conjugate radii constant ratio CP² CS² CV² draw drawn ellipse equally inclined Fellow of Trinity fixed point focal chord focal perpendicular focal radii focus Geometry Hence intersect J. W. DONALDSON late Fellow latus rectum locus meet the asymptotes meet the curve meet the directrix meets the axis middle point minor axis normal parabola parallel chords parallelogram Pembroke College PN² point Q principal ordinate PROP QV² radius rectangular hyperbola right angles right-angled triangles Second Edition Shew shewn sides SP² St John's College straight line joining subtends a right supplementary angles tangent Third Edition Treatise Trinity College vertex
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