...determined by the resolution of the cubic equation л ' - (a1 + Cl + JD1) ,r - 2 CD a = 0, where ). To find a point within a triangle, from which, if lines be drawn to the angular points, their sum is the least possible. Let А ПС be the triangle (Fig. 102), P the point quired: let liC=a, AC—b,...

...в' — ф' : the point P, therefore, is situated in the concourse of the diagonals AC and BD*. (10). To find a point within a triangle, from which if lines be drawn to the angular points, the sum of their squares is the least possible. Making use of the same construction and notation as...

...= 2а, the given length ; whence x = у = ж = a, and ellipsoid becomes a sphere. Ex. 15. Find that point within a triangle, from which if lines be drawn to the angular points, the sum of their squares shall be a minimum. Let ABC be a triangle, and P a point within it, a, b,...

...2x+2y + 2z=6a, the given length ; whence x=y=z=a, and ellipsoid becomes a sphere. Ex. 15. Find that point within a triangle, from which if lines be drawn to the angular points, the sum of their squares shall be a minimum. Let А В С be a triangle, and P a point within it, a,...

...of the sphere, the parallelo2a pipedon is a cube having — ^ for its edge. .yo We find 9. Determine a point within a triangle, from which, if lines be drawn to the vertices of the angles, the sum of their squares shall be a maximum. C The point is the intersection...

...!• Proceeding as in the last example, we find a 6 _ EXAMPLES. 8. Find the point in the surface of a triangle from which, if lines be drawn to the angular points, the sum of their squares shall be a minimum. Let ABC be the triangle, and let P be the required point....

...Differential and Integral Calculus, 1841, Chap. VII, p. 124, ex. 22, I find the following celebrated problem: "To find a point within a triangle from which if lines...angular points their sum may be the least possible." The author remarks that "the direct solution of this problem is long and complicated, etc." Required a...

...Differential and Integral Calculus, 1841, Chap. VII, p. 124, ex. 22, I find the following celebrated problem: "To find a point within a triangle from which if lines be drawn to the angular points then- sum may be the least possible." The author remarks that "the direct solution of this problem...

...MORLEY, RE MORITZ, O. DUNKEL and RC ARCHIBALD. Solutions, remarks, and historical notes for the problem : To find a point within a triangle from which if lines be drawn to their angular points their sum may be the least possible (p. 38 — 41). K1, Via £. J. MATHKSON. Continuity...