 | Oxford univ, exam. papers, 2nd publ. exam - 1831 - 70 pages
...table of sines, cosines, &c. •I. 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+ —... | |
 | Duncan Farquharson Gregory - Calculus - 1841 - 566 pages
...contact bisect the sides of the triangle. Bérard, Ib. p. 284. (20) 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. The centre of gravity of the triangle is the point which possesses this property. (21) Among all triangular... | |
 | Thomas Grainger Hall - Calculus - 1846 - 480 pages
...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.... | |
 | D. F. Gregory - Calculus - 1846 - 572 pages
...the triangle. Bérard, Ib. p. 284. о 3 (20) To find a point within a triangle from which if lines he drawn to the angular points the sum of their squares is the least possible. The centre of gravity of the triangle is the point which possesses this property. (21) Among all triangular... | |
 | Ramchundra - Algebra - 1850 - 222 pages
...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 ABC be the... | |
 | James Haddon - Differential calculus - 1851 - 198 pages
...x=—=> y=—=iz=—=i M= — — • v/3 </3 v/3 3* i (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 A, B, G be the angles, a, I, c the sides of the triangle ; then CrP=|(2a2+2i2-c2)*.... | |
 | Rāmachandra (son of Sundara Lāla.) - Maxima and minima - 1859 - 250 pages
...solved without impossible roots. PROB. (14.) TO FIND A POINT P WITHIN A QUADRILATERAL FIGURE ABCD, FROM WHICH IF LINES BE DRAWN TO THE ANGULAR POINTS, THE SUM OF THEIR SQUARES SHALL BE THE LEAST POSSIBLE. (Fig. 68.) Let AD = b, AB = а, BC — с. From the points D, C and P... | |
 | Thomas Grainger Hall - 1863 - 408 pages
...С ^— oocsin A , . _ :U1< "P~ oocsinCr Ex. 17. Find a point P within a quadrilateral figure ABCD, from which if lines be drawn to the angular points, the sum of their squares shall be the least possible. AB=a; BC=b; AD=c; AN=x; NP=y; x2+yí + y'2 + (a—x)í + (ísinB-y)í... | |
 | 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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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. 