Solutions of the Cambridge Senate-house Problems and Riders for the Year 1875Sir George Greenhill Macmillan and Company, 1876 - 236 páginas |
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Página 50
... curvature , prove by Newton's method that the ratio OP + 0Q- arc PQ : arc PQ - chord PQ tends to the limit 2 : 1 as the arc PQ is indefinitely diminished . Let the involute PB ( fig . 37 ) of the arc PQ be drawn meeting OQ in B , and PN ...
... curvature , prove by Newton's method that the ratio OP + 0Q- arc PQ : arc PQ - chord PQ tends to the limit 2 : 1 as the arc PQ is indefinitely diminished . Let the involute PB ( fig . 37 ) of the arc PQ be drawn meeting OQ in B , and PN ...
Página 85
... curvature of the path on the surface . Let S be the surface ( fig . 54 ) , M the particle of mass m projected in the direction MT with velocity v , and let F be the resultant impressed force represented by MF . If N be the normal ...
... curvature of the path on the surface . Let S be the surface ( fig . 54 ) , M the particle of mass m projected in the direction MT with velocity v , and let F be the resultant impressed force represented by MF . If N be the normal ...
Página 86
... curvature of the normal section made through MT ; then MI is equal to the algebraical sum of MN and the projection of MF on MN . The osculating plane being then determined , if a line be drawn through I at right angles to the plane IMT ...
... curvature of the normal section made through MT ; then MI is equal to the algebraical sum of MN and the projection of MF on MN . The osculating plane being then determined , if a line be drawn through I at right angles to the plane IMT ...
Página 107
... curvature . If ( x'y ' ' ) be the coordinates of P , ( xyz ) of Q , ( aßy ) the direction cosines of the normal at P , p the length of the perpendicular on the tangent plane at P , COS & = px ' a " , cosß = Py ' Z cosy = = c2 pz ' ; and ...
... curvature . If ( x'y ' ' ) be the coordinates of P , ( xyz ) of Q , ( aßy ) the direction cosines of the normal at P , p the length of the perpendicular on the tangent plane at P , COS & = px ' a " , cosß = Py ' Z cosy = = c2 pz ' ; and ...
Página 112
... curvatures of the sphere and cylinder are equal , and the sphere is acted upon during the motion solely by a force tending to and equal to μ times the distance of its centre from the nearest point of the central axis of the cylinder ...
... curvatures of the sphere and cylinder are equal , and the sphere is acted upon during the motion solely by a force tending to and equal to μ times the distance of its centre from the nearest point of the central axis of the cylinder ...
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Solutions of the Cambridge Senate-House Problems and Riders for the Year 1875 George Greenhill Sin vista previa disponible - 2016 |
Términos y frases comunes
apse line Arabic numbers axes axis Cambridge centre of inertia circle coefficient conic section coordinates cos² cose cosec Crown 8vo curvature curve density diameter differential equation distance dx dy dz dx² Edition electricity ELEMENTARY TREATISE ellipse ellipsoid equal equations of motion equilibrium Extra fcap Fellow of St fixed fluid force given GREEK harmonic Hence hyperbola hypocycloid integral intersect J. P. MAHAFFY John's College late Fellow LATIN length lines of curvature liquid lunar precession magnets middle points normal numerous Illustrations orbit Owens College parabola parallel particle perpendicular plane polar pressure prism Professor prove radius ratio refracting right angles Roman numbers School shew sin sin sin sin² sphere straight line surface tangent triangle ABC Trinity College velocity vertical
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