The Geometry of Conics, Part 1 |
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Page 3
... measuring off abscissæ of different lengths and using Prop . I. to find the lengths of the corresponding ordinates , we may determine successively any number of points on the parabola . In this construction the ordinates may be measured ...
... measuring off abscissæ of different lengths and using Prop . I. to find the lengths of the corresponding ordinates , we may determine successively any number of points on the parabola . In this construction the ordinates may be measured ...
Page 6
... measured parallel to the chords bisected by PV , then QV , PV are the ordinate and abscissa of Qreferred to the diameter through P. The ordinates of all points on the curve referred to any fixed diameter are parallel . [ 6 . * Or thus ...
... measured parallel to the chords bisected by PV , then QV , PV are the ordinate and abscissa of Qreferred to the diameter through P. The ordinates of all points on the curve referred to any fixed diameter are parallel . [ 6 . * Or thus ...
Page 17
... measured on a tangent subtends equal angles at the focus and at the point in which the diameter through the point of contact meets the directrix . 30. PROP . XI . The acute angle between any T. 2 TANGENT - PROPERTIES OF THE PARABOLA . 17.
... measured on a tangent subtends equal angles at the focus and at the point in which the diameter through the point of contact meets the directrix . 30. PROP . XI . The acute angle between any T. 2 TANGENT - PROPERTIES OF THE PARABOLA . 17.
Page 23
... measured from the curve to the axis . 82. A diameter meeting a chord and the tangent at an end of it is cut by the curve in the ratio in which it cuts the chord . 83. Draw a chord which shall be cut in a given ratio by a given diameter ...
... measured from the curve to the axis . 82. A diameter meeting a chord and the tangent at an end of it is cut by the curve in the ratio in which it cuts the chord . 83. Draw a chord which shall be cut in a given ratio by a given diameter ...
Page 25
... measured parallel to any fixed straight line which meets the directrix . When this fixed straight line meets the directrix perpendicularly we come back to the original definition . T45 . As a particular case of the above let P , Q be ...
... measured parallel to any fixed straight line which meets the directrix . When this fixed straight line meets the directrix perpendicularly we come back to the original definition . T45 . As a particular case of the above let P , Q be ...
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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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