 | Edinburgh encyclopaedia - 1830 - 828 pages
...have u = у, z = я /, * = e, and ç y = sin. u ; conjequently и =: :-fc sin. z (sin. z) — t ¡on of a point, the sum of the squares of whose distances from four given pointe in space shall be the least possible. Let one of the pointe be the origin of the... | |
 | Cork city, univ. coll - 1851 - 208 pages
...respectively. Find the ratio of their areas. 6. Explain what is meant by the locus of a point. Determine the locus of a point, the sum of the squares of whose distances from two given points is constant. What is the limiting case of this problem. 7- The base and hypothenuse... | |
 | Peter Guthrie Tait - 1867 - 364 pages
...? 6. Find the equation of the plane which contains the two parallel lines Fa(p-/3) = 0, FaCp-fr) = 0. 7. Find the equation of the plane which contains...the equation of the plane which bisects, at right angles, the shortest distance between two given lines. Find the locus of a point in this plane which... | |
 | Philip Kelland - 1873 - 248 pages
...planea consequently all pass through the same straight line. Ex. 7. To find the locus of a point, tlie sum of the squares of whose distances from a number of given points has a given value. Let p denote the sought point ; a, ß, ... the given ones ; then (pa)2+(p-/3)2+&c.... | |
 | 1874 - 124 pages
...solid angles, faces, and edges of any polyhedron (Euler's theorem) 26 4128. (AB Evans, MA) — Find the locus of a point the sum of the squares of whose distances from the vertices of a given triangle is constant 28 4135. (JJ Walker, MA) — A vertical circle may be... | |
 | W. J. C. Miller - Mathematics - 1874 - 118 pages
...found in Chauvenet's Elementary (jeumrtry, pp. 230, 236.] 4128. (Proposed by AB EVANS, MA) — Find the locus of a point the sum of the squares of whose distances from the vertices of a given triangle is constant. I. Solution by H. MURPHY. Let the vertices be A, B, C.... | |
 | George Albert Wentworth - 1879 - 196 pages
...their squares is equal to three times the sum of the squares of the sides of the triangle. Ex. 285. The locus of a point, the sum of the squares of whose distances from two fixed points is constant, is the circumference of a circle. Ex. 286. Convert a parallelogram into... | |
 | George Bruce Halsted - Measurement - 1881 - 258 pages
...20. 14. Prove ii + 42 + 42 "^ i (^2 + ^2 + c-2). 15. In any right-angled triangle prove Ja-==. 15 16. The locus of a point, the sum of the squares of whose distances from two fixed points is constant, is a circumference whose center is the midpoint of the straight line... | |
 | Philip Kelland, Peter Guthrie Tait - Quaternions - 1882 - 296 pages
...That if b = 0, c = 0, the question is satisfied by p = aa, whatever be a, therefore &c. Ex. 5. Find the locus of a point, the sum of the squares of whose...distances from a number of given planes is constant. Let iS81pI = C'1, 8S^a = Ca, (fee. be the equations of the given planes, p the vector to the point... | |
 | Philip Kelland, Peter Guthrie Tait - Quaternions - 1882 - 288 pages
...if 6 = 0, c = 0, the question is satisfied by p = aa, whatever be a, therefore &c. Ex. 5. Find tJif locus of a, point, the sum of the squares of whose...distances from a number of given planes is constant. Let S&,p1 = Ci, *S82pa = (7,, &c. be the equations of the given planes, p the vector to the point under... | |
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Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute " lines" for "planes 
