Solutions of the problems and riders proposed in the Senate-house examination for 1854, by the moderators and examiners |
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Page 5
... diameters , in I , J , respectively . Prove that IS , JH , BC , pro- duced indefinitely , intersect each other in a single point . Let IY , JZ , fig . ( 4 ) , produced if necessary , intersect the major axis in Y ' , Z ' , respectively ...
... diameters , in I , J , respectively . Prove that IS , JH , BC , pro- duced indefinitely , intersect each other in a single point . Let IY , JZ , fig . ( 4 ) , produced if necessary , intersect the major axis in Y ' , Z ' , respectively ...
Page 19
... diameters . If S , S ' , be the interior foci of the two branches , prove that S'P ' - SP AC- BC . = Draw PN , P'N ... diameter is described a circle cutting the parabola again in two points ; if these points be joined , shew that the ...
... diameters . If S , S ' , be the interior foci of the two branches , prove that S'P ' - SP AC- BC . = Draw PN , P'N ... diameter is described a circle cutting the parabola again in two points ; if these points be joined , shew that the ...
Page 20
... diameter , is 2 2 2 2 2 ( x − x , + x ; ) 2 + ( y − 1 , + 3 , ) 2 = ( ~ , — * , ) * + ( Y › = ' ' ) " , - or x2 - 2 - 2 2 2 2 = 0 . ( x + x2 ) x + y2 - ( y1 + Y2 ) y + x ̧X1⁄2 + Y1Y1⁄2 Combining this with the equation to the parabola ...
... diameter , is 2 2 2 2 2 ( x − x , + x ; ) 2 + ( y − 1 , + 3 , ) 2 = ( ~ , — * , ) * + ( Y › = ' ' ) " , - or x2 - 2 - 2 2 2 2 = 0 . ( x + x2 ) x + y2 - ( y1 + Y2 ) y + x ̧X1⁄2 + Y1Y1⁄2 Combining this with the equation to the parabola ...
Page 74
... , ) shall be at the opposite end of the diameter through B ' . Hence B'C ' produced will pass through B " , and B'C'B " will be a 1 semicircle . Let A , be the middle point 74 [ Jan. 18 , SENATE - HOUSE PROBLEMS AND RIDERS .
... , ) shall be at the opposite end of the diameter through B ' . Hence B'C ' produced will pass through B " , and B'C'B " will be a 1 semicircle . Let A , be the middle point 74 [ Jan. 18 , SENATE - HOUSE PROBLEMS AND RIDERS .
Page 94
... diameter of the plate , its intrinsic brightness and breadth being given , prove that the illumination varies as the diameter of the plate . Let the length of the lamina , c = 7 = its breadth , a = the radius of the plate . Let u = the ...
... diameter of the plate , its intrinsic brightness and breadth being given , prove that the illumination varies as the diameter of the plate . Let the length of the lamina , c = 7 = its breadth , a = the radius of the plate . Let u = the ...
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Solutions of the Problems and Riders Proposed in the Senate-House ... Exam Papers Cambridge Univ No preview available - 2016 |
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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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