Solutions of the Cambridge Senate-house Problems and Riders for the Year 1875Sir George Greenhill |
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Page 7
... curve of section from a certain point bears a constant ratio to the distance from a certain straight line . If any sphere be inscribed in the cone , the length of the tangent line drawn from any point on the curve of section to the ...
... curve of section from a certain point bears a constant ratio to the distance from a certain straight line . If any sphere be inscribed in the cone , the length of the tangent line drawn from any point on the curve of section to the ...
Page 22
... curve under the action of gravity . A circle is drawn to touch at their middle points the chord and arc of oscillation of a particle which is moving on a vertical circle under the action of gravity . Prove that a point on the first ...
... curve under the action of gravity . A circle is drawn to touch at their middle points the chord and arc of oscillation of a particle which is moving on a vertical circle under the action of gravity . Prove that a point on the first ...
Page 49
... curve of given length which on a given chord encloses a maximum area is an arc of a circle . Let AD , BC ( fig . 36 ) intersect in O. Keeping AB fixed displace C to C and D to D ' ; O is the instantaneous centre of CD . The area being a ...
... curve of given length which on a given chord encloses a maximum area is an arc of a circle . Let AD , BC ( fig . 36 ) intersect in O. Keeping AB fixed displace C to C and D to D ' ; O is the instantaneous centre of CD . The area being a ...
Page 50
... curve and the radius drawn to it from a point in the plane which is either fixed or moves uniformly in a straight line describes areas about the point proportional to the time . Prove that the body is acted on by a force tending to the ...
... curve and the radius drawn to it from a point in the plane which is either fixed or moves uniformly in a straight line describes areas about the point proportional to the time . Prove that the body is acted on by a force tending to the ...
Page 71
... curve in a certain direction , prove that the area of the curve is expressed by faxdy or - fydx or 1 fr2 d0 . are Interpret these expressions when the perimeter cuts itself . Prove that the areas of the two loops of the curve r2 - 2ar ...
... curve in a certain direction , prove that the area of the curve is expressed by faxdy or - fydx or 1 fr2 d0 . are Interpret these expressions when the perimeter cuts itself . Prove that the areas of the two loops of the curve r2 - 2ar ...
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Solutions of the Cambridge Senate-House Problems and Riders for the Year 1875 George Greenhill No preview available - 2016 |
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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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