An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 113
... directrix will be a conic , having the same focus and directrix as the given conics , and of which 4ll ' 79 the latus - rectum is 乙で· 7 ± 7 ' ' + Again , take the ordinary definition of an ellipse , that it is the locus of a point ...
... directrix will be a conic , having the same focus and directrix as the given conics , and of which 4ll ' 79 the latus - rectum is 乙で· 7 ± 7 ' ' + Again , take the ordinary definition of an ellipse , that it is the locus of a point ...
Page 116
... of the point of intersection of the variable tangents is a straight line . If the fixed point be a focus , the locus will be the correspond- ing directrix . 5. Chords are drawn to a conic , subtending a 116 MODERN GEOMETRY . EXAMPLES.
... of the point of intersection of the variable tangents is a straight line . If the fixed point be a focus , the locus will be the correspond- ing directrix . 5. Chords are drawn to a conic , subtending a 116 MODERN GEOMETRY . EXAMPLES.
Page 118
... directrix in common with the given parabola . " Reciprocate this , with respect to any point whatever , and we get " If a chord be drawn to a conic , sub- tending a constant angle at a given point in the curve , it always touches a ...
... directrix in common with the given parabola . " Reciprocate this , with respect to any point whatever , and we get " If a chord be drawn to a conic , sub- tending a constant angle at a given point in the curve , it always touches a ...
Page 133
... directrix ? What is its eccen- tricity , and what its latus - rectum ? 5. Prove that the equation p = a + c cos represents a circle ; and determine the radius of the circle . 6. Prove that the evolute of the ellipse a2¿2 + b2n3 = 1 is ...
... directrix ? What is its eccen- tricity , and what its latus - rectum ? 5. Prove that the equation p = a + c cos represents a circle ; and determine the radius of the circle . 6. Prove that the evolute of the ellipse a2¿2 + b2n3 = 1 is ...
Page 142
... directrix is the polar of the focus , hence , if two conics have the same focus and directrix , they project into two conics having a common chord of contact for their common tangents , that is , having double contact with one another ...
... directrix is the polar of the focus , hence , if two conics have the same focus and directrix , they project into two conics having a common chord of contact for their common tangents , that is , having double contact with one another ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα