 | 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...points, the sum of their squares is the least possible. Making use of the same construction and notation as in Ex. 14., we have и=лг* +у* + (a - x)* +у*... | |
 | 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,... | |
 | Oxford univ, exam. papers, 2nd publ. exam - 1831 - 70 стор.
...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 - 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, c, the sides of the triangle.... | |
 | Ramchundra - 1850 - 222 стор.
...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 - 1851 - 180 стор.
...parallelopipedon, ^_ а _ b с 8abc ""~ ~7Í у~^ъ *~~7ъ U'"~W (20.) To find a point P within a given triangle, fr-om 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, a, b, с the sides of the triangle ; 3 The point is... | |
 | Rāmachandra (son of Sundara Lāla.) - 1859 - 250 стор.
...The same may easily be solved without impossible roots. PROB. (16.) 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. 69.) This Problem is a more elegant solution of Prob. (8.) Let AB C be the... | |
 | 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, b, c, the sides of the... | |
 | 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. Designate the sides by... | |
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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. 