Cambridge Senate-house Problems and Riders for the Year 1860: With SolutionsMacmillan, 1860 - 198 páginas |
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Página 3
... meet in G , join QP and pro- duce it to any point R. Then the angle between the tangents is equal to the angle PGQ which is = RPG - RQG = ( RPS — RQS ) + ( SPG − SQG ) . - - Now SPG = SQG , being the halves of equal angles , and the ...
... meet in G , join QP and pro- duce it to any point R. Then the angle between the tangents is equal to the angle PGQ which is = RPG - RQG = ( RPS — RQS ) + ( SPG − SQG ) . - - Now SPG = SQG , being the halves of equal angles , and the ...
Página 7
... meets the window . Hence since this line meets the window in points which move in the direction of the carriage's motion , the direction of the carriage must be continually varying , and the carriage must be on a curve concave to the ...
... meets the window . Hence since this line meets the window in points which move in the direction of the carriage's motion , the direction of the carriage must be continually varying , and the carriage must be on a curve concave to the ...
Página 8
... meet this line at distances ВА ' 2 BA 2 and from B , it follows that 00 ' = 1 ( BA - BA ' ) cosec B. Now BA and BA ' are the values of p determined from the equation c2 - 2ac cos B + a2 = b2 ; .. BA − BA ' = 2 √ ( b2 — a2 sin3 B ) ...
... meet this line at distances ВА ' 2 BA 2 and from B , it follows that 00 ' = 1 ( BA - BA ' ) cosec B. Now BA and BA ' are the values of p determined from the equation c2 - 2ac cos B + a2 = b2 ; .. BA − BA ' = 2 √ ( b2 — a2 sin3 B ) ...
Página 22
... meets the outermost circle be R. Again , with centre Q and radius equal to that of the largest circle describe a circle , and let one of the points in which it meets the innermost circle be S. Then if R and S be taken properly RP and PS ...
... meets the outermost circle be R. Again , with centre Q and radius equal to that of the largest circle describe a circle , and let one of the points in which it meets the innermost circle be S. Then if R and S be taken properly RP and PS ...
Página 23
... . Hence the diameter which bisects chords parallel to EF meets the ellipse in P , and therefore the tangent at P is parallel to EF . 4. If the tangent at any point P of an 9-12 . ] 23 SENATE - HOUSE PROBLEMS AND RIDERS .
... . Hence the diameter which bisects chords parallel to EF meets the ellipse in P , and therefore the tangent at P is parallel to EF . 4. If the tangent at any point P of an 9-12 . ] 23 SENATE - HOUSE PROBLEMS AND RIDERS .
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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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