Cambridge Senate-house Problems and Riders for the Year 1860: With SolutionsMacmillan, 1860 - 198 páginas |
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Página 24
... conic , they subtend equal angles at either focus . One of these tan- gents in this problem becomes an asymptote , the other is TP . Therefore if SR be drawn parallel to QT , the angles TSQ , TSR are equal , and therefore the angles QST ...
... conic , they subtend equal angles at either focus . One of these tan- gents in this problem becomes an asymptote , the other is TP . Therefore if SR be drawn parallel to QT , the angles TSQ , TSR are equal , and therefore the angles QST ...
Página 34
... Conics , Prop . IX . , q lies on a rectangular hyperbola whose asymptotes are parallel and per- pendicular to BA . And since the position and magnitude of this hyperbola is independent of μ , all the coloured rings will lie on the ...
... Conics , Prop . IX . , q lies on a rectangular hyperbola whose asymptotes are parallel and per- pendicular to BA . And since the position and magnitude of this hyperbola is independent of μ , all the coloured rings will lie on the ...
Página 53
... two tangents drawn from any point T to touch a conic in P and Q , and if S and H be the foci , then ST2 - HT2 SP . SQ HP . HQ ' The construction of the figure being indicated by the ques- ( 53 ) TUESDAY, Jan. 17. 9 to 12. ...
... two tangents drawn from any point T to touch a conic in P and Q , and if S and H be the foci , then ST2 - HT2 SP . SQ HP . HQ ' The construction of the figure being indicated by the ques- ( 53 ) TUESDAY, Jan. 17. 9 to 12. ...
Página 54
... conic become a parabola , these expressions become each equal to unity . iii . A polygon is inscribed in an ellipse so that each side subtends the same angle at one of the foci . Prove that , if the alternate sides be produced to meet ...
... conic become a parabola , these expressions become each equal to unity . iii . A polygon is inscribed in an ellipse so that each side subtends the same angle at one of the foci . Prove that , if the alternate sides be produced to meet ...
Página 55
... conic section having the same focus as the ellipse , but latus rectum and eccentricity each altered in the ratio of 1 sec ß cos 28 . Hence the directrix is the same as before . Also since 0 = a + 2B , it follows that the line joining ...
... conic section having the same focus as the ellipse , but latus rectum and eccentricity each altered in the ratio of 1 sec ß cos 28 . Hence the directrix is the same as before . Also since 0 = a + 2B , it follows that the line joining ...
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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 cone conic conic section constant 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 focus given point Hence horizontal hyperbola inclined intersection latus rectum length locus MACMILLAN & CO.'S meridian motion normal parabola parallel particle perpendicular point of contact position pressure prove ratio respectively right angles Roman numbers SENIOR MODERATOR shew sides sin² singular solution smooth sphere spherical straight line string subtend surface tangent tension triangle Trinity College uniform vertex vertical Vis Viva weight аф
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