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" PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant. "
London graduation mathematics, questions in arithmetic and algebra set from ... - Page xli
by Thomas Kimber - 1880
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An Elementary Treatise on Conic Sections

Charles Smith - Conic sections - 1883 - 452 pages
...we have also S'P=e.NZ' = e(CZ'-CN) = a-ex; An ellipse is sometimes defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant. To find the equation of the curve from this definition. Let the constant sum be 2a, and...
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Mathematical Questions with Their Solutions: From the ..., Volumes 40-42

1884 - 434 pages
...chosen outside the line in which the point-series lie 89 7771. (The late Professor Clifford, FRS) — Find the locus of a point P which moves so that the length of the resultant of the translations PA, PB, PC is constant— the points A, B, C being fixed...
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Mathematical Questions and Solutions, Volume 42

Mathematics - 1885 - 150 pages
...solutions. The converse follows at once by reciprocation. 7771. (By the late Professor CLIFFORD, FRS)— Find the locus of a point P which moves so that the length of the resultant of the translations PA, PB, PC is constant — the points A, B, C being fixed....
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Analytical Geometry (the Straight Line and Circle).

Arthur Le Sueur - Circle - 1886 - 120 pages
...diameter bisecting chords perpendicular to it. THE ELLIPSE. DEF. — An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points ((he foci) is constant. Equation to an ellipse. S, S' the foci. 2« the given constant. C the middle...
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Elements of Dynamic: An Introduction to the Study of Motion and Rest in ...

William Kingdon Clifford - Dynamics - 1887 - 140 pages
...DEFINE a rigid body, and a movement of translation. Explain how translations are compounded together. Find the locus of a point P which moves so that the length of the resultant of the translations PA, PB, PC is constant — the points A, B, C being fixed....
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1892 - 468 pages
...706. Given two points and the focus, to find the directrix. THE ELLIPSE. 838. The locus of a point which moves so that the sum of its distances from two fixed points is constant is called an ellipse. The fixed points are called the foci, and the straight lines which...
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An Elementary Treatise on Analytical Geometry: With Numerous Examples

W. J. Johnston - Geometry, Analytic - 1893 - 462 pages
...a + ex Also S'P = ePM'=e(CX'-CN) = .-. S'P = a - ex We infer that SP + S'P =23 Thus the ellipse is the locus of a point P which moves so that the sum of its distances from two fixed points S, S' = a constant 2 a. (Compare § i04.) This gives a method of describing the ellipse mechanically....
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An Elementary Treatise on Modern Pure Geometry

Robert Lachlan - Geometry - 1893 - 312 pages
...- sin Л 0(7. Hence we have the required result. 37. If A, B, C, D бе any four points in a plane, the locus of a point P, which moves so that the sum of the areas (PAB), (PCD) is constant, is a straight line. JD Let the straight lines AB, CD meet in the...
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Examinations Papers

1895 - 800 pages
...the focal distances of any point on an ellipse is constant. Find the equation of the locus of a point which moves so that the sum of its distances from two fixed points is constant. 5. Find from the definition the differential coefficient of sin ./;, and deduce the differential...
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Elements of Geometry

George Cunningham Edwards - Geometry - 1895 - 328 pages
...— This is the problem of the lights not confined to a plane. 88. Find the locus of a point in space which moves so that the sum of its distances from two fixed points always remains the same. 89. Find the locus of the centre of a sphere which is tangent to a given plane,...
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