 | George Peacock - Calculus - 1820 - 552 pages
...point is the centre of gravity of the triangle. (17). To find a point within a quadrilateral figure from which, if lines be drawn to the angular points, the sum of their squares is the least possible. Making use of the same notation and construction as in Ex. 15., we shall find + \(a -x + \ c* + x*... | |
 | George Peacock - Calculus - 1820 - 542 pages
...by the resolution of the cubic equation i3 - (a1 + C1 + D1) г — 2 CD a = 0, where and£>=v/ (1+). To find a point within a triangle, from which, if lines be drawn to the angular points, their sum is the least possible. Let ARC be the triangle (Fig. 102), P the point required: let KC —... | |
 | Oxford univ, exam. papers, 2nd publ. exam - 1831 - 70 pages
...Prove that ea-.n , and from it deduce Taylor's theorem. 5. Find a point within a triangular pyramid, from which, if lines be drawn to the angular points, the sum of the squares is the least possible. 6. Integrate the following differential equations : tly+y*dx+ —... | |
 | Thomas Grainger Hall - Calculus - 1846 - 480 pages
...= 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, c, the sides of the triangle.... | |
 | Ramchundra - Algebra - 1850 - 222 pages
...The same may easily be solved without impossible roots. PROB. (8.) TO FIND THAT POINT WITHIN A GIVEN TRIANGLE, FROM WHICH IF LINES BE DRAWN TO THE ANGULAR POINTS, THE BUM OF THEIR SQUARES SHALL BE A MINIMUM. (Fig. 65.) Let ABC be the given triangle, and let BD = a,... | |
 | James Haddon - Differential calculus - 1851 - 180 pages
...the parallelopipedon, _ ab с Sabe </Ъ У~ Vs' ""v/s' V"~ 3* (20.) To find a point P within a given triangle, from which, if lines be drawn to the angular points, the sum of their squares shall be a minimum. If А, В, С be the angles, а, Ь, с the sides of the triangle ; then C7>=4(2a2+262-c2)i.... | |
 | Rāmachandra (son of Sundara Lāla.) - Maxima and minima - 1859 - 250 pages
...The same may easily be solved without impossible roots. PROB. (8.) TO FIND THAT POINT WITHIN A GIVEN TRIANGLE, FROM WHICH IF LINES BE DRAWN TO THE ANGULAR POINTS, THE SUM OF THEIR SQUARES SHALL BE A MINIMUM. (Fig. 65.) Let ABC be the given triangle, and let BD — a, AC = b, AD = c, AE... | |
 | Thomas Grainger Hall - 1863 - 408 pages
...2x+2y + 2z=6a, the given length ; whence a:=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 AB С be a triangle, and Pa point within it, a, A, i; the sides of the triangle.... | |
 | Horatio Nelson Robinson - Calculus, Integral - 1867 - 498 pages
...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 - Calculus - 1875 - 448 pages
...!• 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. Designate the sides by... | |
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TRIANGLE, FROM WHICH IF LINES BE DRAWN TO THE ANGULAR POINTS, THE SUM OF THEIR SQUARES SHALL BE A MINIMUM. 