The Geometry of Conics, Part 1 |
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... described by a particle moving in a vacuum under the influence of gravity . A practical construction is given in Example 11 . THE HYPERBOLA is most simply drawn by the analogous construction of Example 213 . THE CONE . The three curves ...
... described by a particle moving in a vacuum under the influence of gravity . A practical construction is given in Example 11 . THE HYPERBOLA is most simply drawn by the analogous construction of Example 213 . THE CONE . The three curves ...
Page 1
... described in a plane by a point which moves in such a way that its distance from a certain fixed point , called the Focus , is always equal to its perpendicular distance from a certain fixed straight line , called the Directrix . 1 ...
... described in a plane by a point which moves in such a way that its distance from a certain fixed point , called the Focus , is always equal to its perpendicular distance from a certain fixed straight line , called the Directrix . 1 ...
Page 3
... described with the help of Prop . I. To find successive points , on the curve , we may proceed as follows . Measure off an abscissa AN of any length , for example , of length 34S . Then by the propo- sition , PN24AS . 3AS . Therefore PN ...
... described with the help of Prop . I. To find successive points , on the curve , we may proceed as follows . Measure off an abscissa AN of any length , for example , of length 34S . Then by the propo- sition , PN24AS . 3AS . Therefore PN ...
Page 9
... described touching any two diameters of a parabola and the focal radii to their extremities . 19. The locus of the centre V of a focal chord is another parabola . Prove this by shewing that if VL be the ordinate of V , then VL2 = 2AS ...
... described touching any two diameters of a parabola and the focal radii to their extremities . 19. The locus of the centre V of a focal chord is another parabola . Prove this by shewing that if VL be the ordinate of V , then VL2 = 2AS ...
Page 10
... the point de- scribes a parabola . 35. Find the locus of the centre of a circle which touches a given circle and a given straight line , 36. Circles being described on the segments of a focal 10 CHORD - PROPERTIES OF THE PARABOLA .
... the point de- scribes a parabola . 35. Find the locus of the centre of a circle which touches a given circle and a given straight line , 36. Circles being described on the segments of a focal 10 CHORD - PROPERTIES OF THE PARABOLA .
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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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