Mathematical Problems on the First and Second Divisions of the Schedule of Subjects for the Cambridge Mathematical Tripos ExaminationMacmillan and Company, 1878 - 480 páginas |
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Página viii
... Equation Conicoids referred to their axes Tetrahedral Co - ordinates Focal Curves : Reciprocal Polars 2174-2179 . VI . General Functional and Differential Equations 2180-2187 . VII . Envelopes PROBLEMS STATICS . Composition and ...
... Equation Conicoids referred to their axes Tetrahedral Co - ordinates Focal Curves : Reciprocal Polars 2174-2179 . VI . General Functional and Differential Equations 2180-2187 . VII . Envelopes PROBLEMS STATICS . Composition and ...
Página 18
... equation ax2 + 2hx + b = 0 be possible and different , the roots of the equation --- ( a + b ) ( ax2 + 2hx + b ) = 2 ( ab − h2 ) ( x2 + 1 ) will be impossible : and vice versâ . 130. Prove that the equations x + y + z = a + b + c , x y ...
... equation ax2 + 2hx + b = 0 be possible and different , the roots of the equation --- ( a + b ) ( ax2 + 2hx + b ) = 2 ( ab − h2 ) ( x2 + 1 ) will be impossible : and vice versâ . 130. Prove that the equations x + y + z = a + b + c , x y ...
Página 19
... equations ( 1 ) -8x - 108 = 0 , ( 2 ) x1 - 10x3- 3456 = 0 . 133. Prove that the equation b2 x2 + 3ax2 + 3bx + 0 a 19 can be solved directly , and that the complete cubic x3 + 3px2 + 3qx + r = 0 can be reduced to this form by the ...
... equations ( 1 ) -8x - 108 = 0 , ( 2 ) x1 - 10x3- 3456 = 0 . 133. Prove that the equation b2 x2 + 3ax2 + 3bx + 0 a 19 can be solved directly , and that the complete cubic x3 + 3px2 + 3qx + r = 0 can be reduced to this form by the ...
Página 20
... equations if a ( a− 1 ) = 1 . [ This may also be proved from Statical considerations . ] 110. The six equations a2 = ( cy + bz ) ( by + cz ) ( by + cz ) ( bc + yz ) bc + yz 2 — ( az + cx ) ( cz + ax ) - y2 = cy + bz ( cz + ax ) ( ca + ...
... equations if a ( a− 1 ) = 1 . [ This may also be proved from Statical considerations . ] 110. The six equations a2 = ( cy + bz ) ( by + cz ) ( by + cz ) ( bc + yz ) bc + yz 2 — ( az + cx ) ( cz + ax ) - y2 = cy + bz ( cz + ax ) ( ca + ...
Página 26
... equation a2 + b2 + c2 + 2abc = 1 , then will a2 , b3 , c2 be all less than 1 , or all greater than 1 . 167. If x , y ... equation be equal to c + 172. Having given the equations yz a2 + x2 200 a2 + y2 2 = = C1 c ' + a2y ' 29 c1 + a2x2 ...
... equation a2 + b2 + c2 + 2abc = 1 , then will a2 , b3 , c2 be all less than 1 , or all greater than 1 . 167. If x , y ... equation be equal to c + 172. Having given the equations yz a2 + x2 200 a2 + y2 2 = = C1 c ' + a2y ' 29 c1 + a2x2 ...
Otras ediciones - Ver todas
Mathematical Problems on the First and Second Divisions of the Schedule of ... Joseph Wolstenholme Sin vista previa disponible - 2012 |
Mathematical Problems: On the First and Second Divisions of the Schedule of ... Joseph Wolstenholme Sin vista previa disponible - 2017 |
Términos y frases comunes
angular points angular velocity asymptotes ax² axes bisected cardioid centre of perpendiculars chord circumscribed circle co-ordinates common point common tangents confocal conicoid conjugate diameters constant continued fraction cos² curve described diagonals directrix envelope equal excentric angles fixed circle fixed point fixed straight line foci focus four points given circle given conic given ellipse given point given the equations inscribed latus rectum length locus major axis meet minor axis normal parabola parallel particle passes plane point of intersection points of contact polar pole prove radical axis radius of curvature ratio rectangle rectangular hyperbola respectively right angles roots self-conjugate sin² sin³ straight line joining subtends a right tangents drawn tetrahedron triangle ABC velocity vertex vertical
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