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 124
... excentricity of the conic will be the ratio LL ' : SS ' . 746. Three points A , B , C are taken on a conic such that CA , CB are equally inclined to the tangent at ( ' : prove that the normal at C will pass through the pole of AB . 747 ...
... excentricity of the conic will be the ratio LL ' : SS ' . 746. Three points A , B , C are taken on a conic such that CA , CB are equally inclined to the tangent at ( ' : prove that the normal at C will pass through the pole of AB . 747 ...
Página 125
... excentricity , and a tangent : prove that the directrix will touch a fixed conic having the same focus and excentricity , and the minor axis of this envelope will lie along the given tangent . 749. A conic described with its foci at the ...
... excentricity , and a tangent : prove that the directrix will touch a fixed conic having the same focus and excentricity , and the minor axis of this envelope will lie along the given tangent . 749. A conic described with its foci at the ...
Página 127
... excentricity e ' not less than that of the given conic it will intercept on the minor axis a segment subtending at the given focus a constant angle = 2 cos ̄1 ( - ) . ] 773. With a focus S of a given conic as focus and any tangent as ...
... excentricity e ' not less than that of the given conic it will intercept on the minor axis a segment subtending at the given focus a constant angle = 2 cos ̄1 ( - ) . ] 773. With a focus S of a given conic as focus and any tangent as ...
Página 130
... excentricity equal to the ratio of the focal distances of the common point . 804. Given a point and the directrices ; prove that the locus of each focus is a circle , and the envelope of the conic is a conic having the given point for ...
... excentricity equal to the ratio of the focal distances of the common point . 804. Given a point and the directrices ; prove that the locus of each focus is a circle , and the envelope of the conic is a conic having the given point for ...
Página 131
... excentricity and whose auxiliary circle is the given circle . 809. The tangent to a conic at P meets the axes in T , t and the central radius at right angles to CP in Q : prove that the ratio of QT to Qt is constant . 810. Through a ...
... excentricity and whose auxiliary circle is the given circle . 809. The tangent to a conic at P meets the axes in T , t and the central radius at right angles to CP in Q : prove that the ratio of QT to Qt is constant . 810. Through a ...
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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