Solutions of the problems and riders proposed in the Senate-house examination for 1854, by the moderators and examiners |
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Page 11
... axes of a rigid body , and shew that for every point in space there exists a system of such axes . Shew that in general there is only one point for which the principal axes are parallel to those drawn through a given point ; but that ...
... axes of a rigid body , and shew that for every point in space there exists a system of such axes . Shew that in general there is only one point for which the principal axes are parallel to those drawn through a given point ; but that ...
Page 23
... axes , is z = x cota + y cotß = px + qy ; therefore the volume of the part between OBDA and OFGE SS ρα = [ " [ [ z dy dx = [ " [ " ( px + qy ) dy dx a2b ab2 = P +9 2 = ab 2 2 ( ap + bq ) . And since this is always the smaller part , the ...
... axes , is z = x cota + y cotß = px + qy ; therefore the volume of the part between OBDA and OFGE SS ρα = [ " [ [ z dy dx = [ " [ " ( px + qy ) dy dx a2b ab2 = P +9 2 = ab 2 2 ( ap + bq ) . And since this is always the smaller part , the ...
Page 24
... axes are a , b , the greatest value of ጥ r ' is equal to 3 / a 26 ( 0-0 ) a dx ' dy We know that · ( 1 ) , dy ' da and therefore , by differentiation , d'x'.dy ' - d'y'.dx ' dy ' dx d'y - dy d'x dx2 1 Hence = ' 2 ( dx'd'y ' - dy'd'x ...
... axes are a , b , the greatest value of ጥ r ' is equal to 3 / a 26 ( 0-0 ) a dx ' dy We know that · ( 1 ) , dy ' da and therefore , by differentiation , d'x'.dy ' - d'y'.dx ' dy ' dx d'y - dy d'x dx2 1 Hence = ' 2 ( dx'd'y ' - dy'd'x ...
Page 29
... axes are half the semi - latus - rectum , and half the minor axis of the given ellipse ; therefore the locus of G is an ellipse whose semi - axes are one- fourth of the semi - axis minor , and one - fourth of the semi - latus- rectum of ...
... axes are half the semi - latus - rectum , and half the minor axis of the given ellipse ; therefore the locus of G is an ellipse whose semi - axes are one- fourth of the semi - axis minor , and one - fourth of the semi - latus- rectum of ...
Page 31
... axes 4a , 46. The latter belongs to the case when the triangle is constantly zero . 11. The radii vectores of any series of points in the path of a particle , moving about a centre of force , being in arith- metical progression , the ...
... axes 4a , 46. The latter belongs to the case when the triangle is constantly zero . 11. The radii vectores of any series of points in the path of a particle , moving about a centre of force , being in arith- metical progression , the ...
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Solutions of the Problems and Riders Proposed in the Senate-House ... Exam Papers Cambridge Univ No preview available - 2016 |
Common terms and phrases
angular velocity asymptote axes Cambridge catenary centre of force centre of gravity chord circle cloth conic section constant cos² cose cosẞ cota cotß Crown 8vo curvature curve cylinder denoting described diameter direction distance dx dy dy dx ecliptic elastic ellipse equal equation equilibrium Fellow of St fixed point fluid geometrical progression given Hence horizontal hyperbola inclined plane intersection lamina latus rectum length locus longitude M.A. Fellow major axis middle point motion orbit parabola parallel particle passing perpendicular position pressure projection prove radius refraction right angles ring shew sides Similarly sine sino sinẞ straight line string Supposing surface tana tangent tanß triangle Trinity College tube V₁ vertical
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