The Geometry of Conics, Part 1 |
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Page 20
... Normal at any point of a curve is the straight line drawn through that point at right angles to the tangent . The Subtangent is the portion of the axis intercepted between the tangent and the principal ordinate . The Subnormal is the ...
... Normal at any point of a curve is the straight line drawn through that point at right angles to the tangent . The Subtangent is the portion of the axis intercepted between the tangent and the principal ordinate . The Subnormal is the ...
Page 21
... 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 be folded so that one corner moves along an opposite side ...
... 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 be folded so that one corner moves along an opposite side ...
Page 22
... normal from the point in which it meets the axis envelopes an equal parabola . 62. Normals at the extremities of a ... normal at any point is equal to twice the focal per- pendicular upon the tangent , and is also a mean proportional ...
... normal from the point in which it meets the axis envelopes an equal parabola . 62. Normals at the extremities of a ... normal at any point is equal to twice the focal per- pendicular upon the tangent , and is also a mean proportional ...
Page 23
... normal at the other . 72. The locus of the foot of the focal perpendicular on the normal is a parabola . 73. If the tangents at P , Q intersect in R , the circle through P touching QR in R passes through S. 74. If from the foot of the ...
... normal at the other . 72. The locus of the foot of the focal perpendicular on the normal is a parabola . 73. If the tangents at P , Q intersect in R , the circle through P touching QR in R passes through S. 74. If from the foot of the ...
Page 43
... normal at P meet DD ' in F. Then PF . CD parallelogram PD = СА . СВ . 101. In Art . 86 it is shewn that the rectangles contained by the segments of any two intersecting chords are to one another as the rectangles contained by the ...
... normal at P meet DD ' in F. Then PF . CD parallelogram PD = СА . СВ . 101. In Art . 86 it is shewn that the rectangles contained by the segments of any two intersecting chords are to one another as the rectangles contained by the ...
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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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