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" B 3 = 0 , an equation also containing nine constants. A, C, E are (Art. 42) tangents at points of inflexion, which lie on a right line B, and we have the theorem proved already, Art. 49, the line joining two points of inflexion must pass through a third.... "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 136
by George Salmon - 1852 - 316 pages
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Proceedings of the Royal Irish Academy, Volume 3

Royal Irish Academy - Science - 1847 - 678 pages
...such an ellipsoid is a surface such, that the square of the distance of any point from a fixed point is in a constant ratio to the product of its distances from two fixed planes. Or, more generally, if a surface be such, that the product of the distances of a...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 334 pages
...A, C, E are evidently the three asymptotes, and we have the theorems, " The asymptotes, if all reed, meet the curve again in three finite points, which...of its connexion with points of inflexion. (5.) aA2 + 6B2 + cC2 - 3dAEC = 0, an equation involving nine constants, three expressed, and six implied, and...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1852 - 329 pages
...distance from the line F. In equation (2) let BDF coincide, and the equation becomes (4) ACE - B 3 = 0 , an equation also containing nine constants. A,...account of its connexion with points of inflexion. (5.) aA? + SB 3 + cC 3 - 3dABC = 0, an equation involving nine constants, three expressed, and six implied,...
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A Treatise on Conic Sections: Containing an Account of Some of the Most ...

George Salmon - 1855 - 376 pages
...circle be infinitely small-, the locus of a point, the square of whose distance from a fixed point is in a constant ratio to the product of its distances from two fixed lines, is a conic section; and the fixed lines maybe considered as chords of imaginary intersection...
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An Elementary Treatise on Conic Sections and Algebraic Geometry ...

George Hale Puckle - Conic sections - 1887 - 404 pages
...triangle. 40. Find the, locus of a point (i) such that the square of the tangent from it to a fixed circle is in a constant ratio to the product of its distances from two fixed lines ; and (ii) such that the tangent from it to a fixed circle is in a constant ratio to...
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An Elementary Treatise on Conic Sections and Algebraic Geometry: With ...

George Hale Puckle - Conic sections - 1887 - 396 pages
...triangle. 40. Find the. locus of a point (i) such that the square of the tangent from it to a fixed circle is in a constant ratio to the product of its distances from two fixed lines ; and (ii) such that the tangent from it to a fixed circle is in a constant ratio to...
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Notes on Analytical Geometry: An Appendix

Alfred Clement Jones - Geometry - 1903 - 212 pages
...parabola. 120. A point moves so that the product of the lengths of the tangents from it to an ellipse is in a constant ratio to the product of its distances from the foci. Show that it lies on a similar ellipse. 121. PP' is a double ordinate of an ellipse and the normal...
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The Calculus of Extension

Henry George Forder, Robert William Genese - 516 pages
...The metric interpretation of this is that L moves so that the product of its distances from a and b' is in a constant ratio to the product of its distances from b and a ' . It is clear that the development dual to the above can be carried out in detail. In particular...
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