| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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.... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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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