Cambridge Senate-house Problems and Riders for the Year 1860: With SolutionsMacmillan, 1860 - 198 σελίδες |
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Σελίδα 33
... curvature is ρ will be m - ρ The pressure will there- fore vary as the curvature . For divide the arc into small elements 8 , s ... 8 , and let s , Sn , v12 ... v2 be the velocities acquired at the end of those arcs ; let F , F ... F be ...
... curvature is ρ will be m - ρ The pressure will there- fore vary as the curvature . For divide the arc into small elements 8 , s ... 8 , and let s , Sn , v12 ... v2 be the velocities acquired at the end of those arcs ; let F , F ... F be ...
Σελίδα 55
... curvature is proportional to the re- ciprocal of the radius of curvature at the corresponding point of the reciprocal polar . Let PY be the tangent to one curve , QZ the tangent to the corresponding point of the reciprocal polar . See ...
... curvature is proportional to the re- ciprocal of the radius of curvature at the corresponding point of the reciprocal polar . Let PY be the tangent to one curve , QZ the tangent to the corresponding point of the reciprocal polar . See ...
Σελίδα 59
... curvature , and c is an arbitrary constant . If the curve be an equiangular spiral with the centre of force in the pole , and if one end of the string rest freely on the spiral at a distance a from the pole , then the pressure is equal ...
... curvature , and c is an arbitrary constant . If the curve be an equiangular spiral with the centre of force in the pole , and if one end of the string rest freely on the spiral at a distance a from the pole , then the pressure is equal ...
Σελίδα 61
... curvature . The law of attraction being as the distance , the attraction of the whole arc on any particle is the same as if the whole mass was collected at its centre of gravity . Take this point for origin , and let T be the tension at ...
... curvature . The law of attraction being as the distance , the attraction of the whole arc on any particle is the same as if the whole mass was collected at its centre of gravity . Take this point for origin , and let T be the tension at ...
Σελίδα 107
... curvature at any point P of an ellipse which is common to the ellipse and circle , and if it be produced to cut the ellipse in Q and the tangent in T , prove that CPCQ , and that each is a mean proportional between CN and CT . If two ...
... curvature at any point P of an ellipse which is common to the ellipse and circle , and if it be produced to cut the ellipse in Q and the tangent in T , prove that CPCQ , and that each is a mean proportional between CN and CT . If two ...
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acceleration angular velocity Arabic numbers asymptotes attraction axes axis bisects Cambridge centre of force centre of gravity chord circle circular cloth co-ordinates CO.'S PUBLICATIONS cone conic conic section cos² Crown 8vo curvature cylinder described diameter differential equation direction directrix distance drawn dt dt ellipse ellipsoid equal angles equiangular spiral equilibrium extremity Fcap fixed point fluid foci given point Hence horizontal hyperbola inclined intersection latus rectum length locus MACMILLAN & CO.'S motion normal osculating plane parabola parallel particle perpendicular point of contact position pressure PROBLEMS AND RIDERS prove ratio respectively right angles Roman numbers SENIOR MODERATOR shew sides sin² singular solution sphere spherical straight line string subtend surface tangent tension triangle Trinity College uniform vertex vertical Vis Viva weight
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