The Principles of the Solution of the Senate-house 'riders,' Exemplified by the Solution of Those Proposed in the Earlier Parts of the Examinations of the Years 1848-1851 |
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Page 11
... plane , the other is at right angles to the same plane . ( XI . 8. ) ( B ) . From a point E draw EC , ED perpendicular to two planes CAB , DAB , which intersect in AB , and from D draw DF perpendicular to the plane CAB , meeting it in F ...
... plane , the other is at right angles to the same plane . ( XI . 8. ) ( B ) . From a point E draw EC , ED perpendicular to two planes CAB , DAB , which intersect in AB , and from D draw DF perpendicular to the plane CAB , meeting it in F ...
Page 12
... plane CAB ; and therefore / AGH is a right angle . Similarly , a line GH ' drawn parallel to ED will lie in the plane of ECD , and will be at right angles to the plane DAB . Therefore △ AGH ' is a right angle . Hence AB will be at ...
... plane CAB ; and therefore / AGH is a right angle . Similarly , a line GH ' drawn parallel to ED will lie in the plane of ECD , and will be at right angles to the plane DAB . Therefore △ AGH ' is a right angle . Hence AB will be at ...
Page 18
... plane parallel to a line in its surface , and perpendicular to the plane containing that line and the axis , is a parabola . ( B ) . The foci of all parabolic sections which can be cut from a given right cone lie upon the surface of ...
... plane parallel to a line in its surface , and perpendicular to the plane containing that line and the axis , is a parabola . ( B ) . The foci of all parabolic sections which can be cut from a given right cone lie upon the surface of ...
Page 19
... plane PAR is parallel to the axis of the cone , and that angle will be equal to the vertical angle of the cone . 1851 . ( A ) . In the parabola , at any point P , the chord of cur- vature parallel to the axis and that through the focus ...
... plane PAR is parallel to the axis of the cone , and that angle will be equal to the vertical angle of the cone . 1851 . ( A ) . In the parabola , at any point P , the chord of cur- vature parallel to the axis and that through the focus ...
Page 30
... plane , no three of which are in the same straight line , with the exception of p , which are in the same straight line ; find the number of lines which result from joining them . If no three of the points were in the same straight line ...
... plane , no three of which are in the same straight line , with the exception of p , which are in the same straight line ; find the number of lines which result from joining them . If no three of the points were in the same straight line ...
Other editions - View all
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson No preview available - 2018 |
The Principles of the Solution of the Senate-House 'Riders: Exemplified by ... Francis J. Jameson No preview available - 2015 |
Common terms and phrases
AC² AN.NM Arithmetic arithmetical progression axis bisects body C₁ Cambridge centre of gravity chord CHURCHILL BABINGTON circle cloth cone Conic Sections conjugate hyperbola constant curvature curve cycloid describe diameter direction directrix distance drawn Edition ellipse equations equilibrium Fellow of St fluid focus geometrical given point Hence horizontal hyperbola inches inclined inscribed John's College joining latus-rectum least common multiple Lemma length locus meet mirror move number of seconds oscillation parabola parallel parallelogram particle perpendicular plane polygon pressure prop proportional proposition prove pullies quadrilateral quantity radius ratio rays rectangle refraction right angles sewed shew sides specific gravity spherical square straight line string surface tan² tangent triangle ABC Trinity College tube V₁ vary vertex vertical W₁ weight
Popular passages
Page 4 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 6 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Page 11 - AB is a diameter, and P any point in the circumference of a circle; AP and BP are joined and produced if necessary ; if from any point C of AB, a perpendicular be drawn to AB meeting AP and .BP in points D and E respectively, and the circumference of the circle in a point F, shew that CD is a third proportional of CE and CF.
Page 9 - IF the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Page 4 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.