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" Show that the locus of a point such that the sum of the squares of its distances from two fixed points is constant, is a circle. "
Euclid simplified. Compiled from the most important French works, approved ... - Page 168
by John Reynell Morell - 1875 - 16 pages
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The Edinburgh Review: Or Critical Journal, Volume 92

1850 - 638 pages
...which we have, therefore, to resolve the geometrical problem (a very elementary one) — ' to find a point such that ' the sum of the squares of its distances from a certain number ' of given points shall be a minimum,' — a problem which is, in effect, identical...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...to a given line. The same, except the difference of the sides equal to a given line. 35. To find a point such that the sum of the squares of its distances from two given points shall be equal to a given square. D PROBLEMS. PROBLEM I.* To bisect a given line AB. FROM...
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Mathematical Questions and Solutions

Mathematics - 1864 - 96 pages
...is the focus. Prove that the tangents at the vertices of the parabolas thus described intersect in a point, such that the sum of the squares of its distances from the four given points is equal to the square of the diameter of the circle 34 1435. Show how to find...
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Mathematical Questions with Their Solutions, from the "Educational Times"...

1864 - 104 pages
...is the focus. Prove that the tangents at the vertices of the paraholas thus descrihee intersect in a point, such that the sum of the squares of its distances from the four given points is equal to the square of the diameter of the circle. Solution hy the PROPOSER....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...seen from a point is the angle contained by the two tangents from that point. 186. Find the locus of a point, such that the sum of the squares of its distances from the vertices of a given triangle is equal to the square of a given line. (Ex. 166.) 187. From any point...
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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - Geometry - 1872 - 102 pages
...intersecting each other at right angles, so as to inclose a rectangle. 870. Prob.—Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points. drawn through the extremities...
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A Treatise on Special Or Elementary Geometry: In Four Parts ..., Part 3

Edward Olney - Geometry - 1872 - 96 pages
...intersecting each other at right angles, so as to inclose a rectangle. 870. Prob. — Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points. OF LOCI. drawn through...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...intersecting each other at right angles, so as to inclose a rectangle. 870. Prob. — Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points. OF LOCI. drawn through...
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An Elementary Treatise on the Differential Calculus: Containing the Theory ...

Benjamin Williamson - Calculus, Differential - 1872 - 370 pages
...find no difficulty in giving the geometrical interpretation of the preceding result. i49. To find a point such that the sum of the squares of its distances from n given points shall be a Minimum. — Let («, b, с), (а, b', с), &с., be the co-ordinates of...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...seen from a point is the angle contained by the two tangents from that point. 186. Find the locus of a point, such that the sum of the squares of its distances from the vertices of a given triangle is equal to the square of a given line. (Ex. 166.) 187. From any point...
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