 | George Peacock - 1820 - 542 стор.
...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,... | |
 | George Peacock - 1820 - 552 стор.
...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... | |
 | Thomas Grainger Hall - 1846 - 480 стор.
...= 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,... | |
 | Thomas Grainger Hall - 1863 - 408 стор.
...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,... | |
 | Horatio Nelson Robinson - 1867 - 498 стор.
...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... | |
 | James Gregory Clark - 1875 - 448 стор.
...!• 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.... | |
 | 1919 - 556 стор.
...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... | |
 | 1920 - 522 стор.
...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... | |
 | 1926 - 976 стор.
...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... | |
| |
To find a point within a triangle from which if lines be drawn to the angular points their sum may be the least possible. 