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 58
... spaces ( in feet ) through which a body would fall from rest in t 1 , t , and t + 1 seconds respectively . Then , by ( 4 ) , S 1g ( t − 1 ) 2 , s ' & gt2 , s " = 1g ( t + 1 ) " , we have 1g ( 2t − 1 ) = s ' s = 144 · 9 .... ( 1 ) ...
... spaces ( in feet ) through which a body would fall from rest in t 1 , t , and t + 1 seconds respectively . Then , by ( 4 ) , S 1g ( t − 1 ) 2 , s ' & gt2 , s " = 1g ( t + 1 ) " , we have 1g ( 2t − 1 ) = s ' s = 144 · 9 .... ( 1 ) ...
Page 59
... space passed over in t " , we have , by ( A ) , s = ut + 1 ft2 . Hence , space described in the first second , ( s , ) So = 1 7 , by hypothesis . $ 3 ( 3u + 1ƒ.32 ) — ( 2u + 1⁄2ƒ.22 ) , = utf + 11 , by hypothesis . We now have two ...
... space passed over in t " , we have , by ( A ) , s = ut + 1 ft2 . Hence , space described in the first second , ( s , ) So = 1 7 , by hypothesis . $ 3 ( 3u + 1ƒ.32 ) — ( 2u + 1⁄2ƒ.22 ) , = utf + 11 , by hypothesis . We now have two ...
Page 66
... space moved over varies as the square of the time of motion . ( B ) . If a body fall down an inclined plane , and another be projected from the starting - point horizontally along the plane ; find the distance between the two bodies ...
... space moved over varies as the square of the time of motion . ( B ) . If a body fall down an inclined plane , and another be projected from the starting - point horizontally along the plane ; find the distance between the two bodies ...
Page 67
... space ( s ) in the time t ; and let V be the velocity of projection of the second body . The distance between the bodies at the time t Vt . But , by ( A ) , sg.sin a.t " , a being the inclination of the plane to the horizon . Therefore ...
... space ( s ) in the time t ; and let V be the velocity of projection of the second body . The distance between the bodies at the time t Vt . But , by ( A ) , sg.sin a.t " , a being the inclination of the plane to the horizon . Therefore ...
Page 78
... space it occupies . If the temperature vary , what relation exists between the pressure , the volume , and the temperature ? ( B ) . A given quantity of air under the pressure of m pounds to the square inch , occupies n cubic inches ...
... space it occupies . If the temperature vary , what relation exists between the pressure , the volume , and the temperature ? ( B ) . A given quantity of air under the pressure of m pounds to the square inch , occupies n cubic inches ...
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.