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 xi
... bisected in D , E , and CD , BE intersect in F : prove that the triangle BFC is equal in area to the quadrangle ADFE ... bisect the right angle . 8. Through the vertex of an equilateral triangle is drawn a straight line terminated by the ...
... bisected in D , E , and CD , BE intersect in F : prove that the triangle BFC is equal in area to the quadrangle ADFE ... bisect the right angle . 8. Through the vertex of an equilateral triangle is drawn a straight line terminated by the ...
Side xii
... bisected by either CA or CB . 15. AB is the diameter of a circle , P a point on the circle , PM perpendicular on AB ; on AM , MB as diameters are described two circles meeting AP , BP in Q , R respectively : prove that QR will touch ...
... bisected by either CA or CB . 15. AB is the diameter of a circle , P a point on the circle , PM perpendicular on AB ; on AM , MB as diameters are described two circles meeting AP , BP in Q , R respectively : prove that QR will touch ...
Side 1
... bisect the angles at E , F , G respectively will be in the same directions . 32. Through one point of intersection of two circles is drawn a straight line at right angles to their common chord and terminated by the circles , and through ...
... bisect the angles at E , F , G respectively will be in the same directions . 32. Through one point of intersection of two circles is drawn a straight line at right angles to their common chord and terminated by the circles , and through ...
Side 2
... bisected by a straight line which meets a chord PQ of the circle in R : prove that the angles ROP , OQR are equal ... bisect the chord drawn through O parallel to PR . 39. Two chords AB , AC of a circle are drawn and the perpendicu- lar ...
... bisected by a straight line which meets a chord PQ of the circle in R : prove that the angles ROP , OQR are equal ... bisect the chord drawn through O parallel to PR . 39. Two chords AB , AC of a circle are drawn and the perpendicu- lar ...
Side 3
... bisected in D , and on DA is taken a point P such that the rectangle DP , DA is equal to the rectangle BD , DC : prove that the angles BPC , BAC are together equal to two right angles . 53. If the circle inscribed in a circle ABC touch ...
... bisected in D , and on DA is taken a point P such that the rectangle DP , DA is equal to the rectangle BD , DC : prove that the angles BPC , BAC are together equal to two right angles . 53. If the circle inscribed in a circle ABC touch ...
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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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