Mathematical Problems on the First and Second Divisions of the Schedule of Subjects for the Cambridge Mathematical Tripos ExaminationMacmillan and Company, 1878 - 480 sider |
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Side xii
... direction . 19. Through the ends of a fixed chord of a given circle are drawn two other chords parallel to each other : prove that the straight line joining the other ends of these chords will touch a fixed circle . 20. Two circles with ...
... direction . 19. Through the ends of a fixed chord of a given circle are drawn two other chords parallel to each other : prove that the straight line joining the other ends of these chords will touch a fixed circle . 20. Two circles with ...
Side 2
... directions intersecting in a point R , and the angles POQ , PRQ are equal and on the same side of PQ ( or supplementary and on opposite sides ) : prove that R lies on a fixed circle . 37. From the point of intersection of the diagonals ...
... directions intersecting in a point R , and the angles POQ , PRQ are equal and on the same side of PQ ( or supplementary and on opposite sides ) : prove that R lies on a fixed circle . 37. From the point of intersection of the diagonals ...
Side 3
... direction ; ( 3 ) the circle ABC is given in magnitude ; and ( 4 ) the centre of the circle ABC lies on a fixed equal circle . 47. Any three points are taken on a given circle and from the middle point of the arc intercepted between two ...
... direction ; ( 3 ) the circle ABC is given in magnitude ; and ( 4 ) the centre of the circle ABC lies on a fixed equal circle . 47. Any three points are taken on a given circle and from the middle point of the arc intercepted between two ...
Side 4
... direction . 64. ABC is a triangle and O the centre of its circumscribed circle ; A'B'C ' another triangle whose sides are parallel to OA , OB , OC ; and through A ' , B ' , C ' are drawn straight lines respectively parallel to the ...
... direction . 64. ABC is a triangle and O the centre of its circumscribed circle ; A'B'C ' another triangle whose sides are parallel to OA , OB , OC ; and through A ' , B ' , C ' are drawn straight lines respectively parallel to the ...
Side 5
... direction and terminated by the two sides : prove that the rectangle under the segments of this straight line is constant . 72. In the hexagon AB'CA'BC ' the three sides AB ' , CA ' , BC " are parallel , as are also the three BA ' , CB ...
... direction and terminated by the two sides : prove that the rectangle under the segments of this straight line is constant . 72. In the hexagon AB'CA'BC ' the three sides AB ' , CA ' , BC " are parallel , as are also the three BA ' , CB ...
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Vanlige uttrykk og setninger
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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