...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...

...equal 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 the two centers A and B, with any equal...

...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....

...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...

...of ratios can be compounded into a single ratio. 17. Find a point in a given line, such that the sum of its distances from two given points shall be equal to a given line. 1 8. State Euclid's twelfth axiom, Book I., and the use which he makes of it. Show that the following...

...whose distances from two given straight lines is equal to a given constant k. 174. Find the locus of a point such that the sum of the squares of its distances from two given points is equal to a given constant, k2. (III. 62.) 175. Find the locus of a point such that the difference...

...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...

...whose distances from two given straight lines is equal to a given constant k. 174. Find the locus of a point such that the sum of the squares of its distances from two given points is equal to a given constant, k3. (III. 62.) 175. Find the locus of a point such that the difference...

...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...

...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...