Weekly problem papers, with notes. [With] Solutions1885 |
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Page x
... touches the chord . ' 6 , first line , for ' conjugate ' read ' ' any twò . ' 5 , at the end add and if KM and QN intersect in R ' , shew that QR ' QN . ' LXI . دو ور دو دو دو LXXIII . 99 دو 99 29 LXXIV . LXXXVII . 99 1 , for 7 read 5 ...
... touches the chord . ' 6 , first line , for ' conjugate ' read ' ' any twò . ' 5 , at the end add and if KM and QN intersect in R ' , shew that QR ' QN . ' LXI . دو ور دو دو دو LXXIII . 99 دو 99 29 LXXIV . LXXXVII . 99 1 , for 7 read 5 ...
Page 22
... bisect the angle between them , so that LOA = L'OA = a . Then if P be any point on 04 , P is the centre of one of the circles which touch OL and OL , and its radius = OP sin a . If B be the fixed point , the polar of 22 SOLUTIONS OF.
... bisect the angle between them , so that LOA = L'OA = a . Then if P be any point on 04 , P is the centre of one of the circles which touch OL and OL , and its radius = OP sin a . If B be the fixed point , the polar of 22 SOLUTIONS OF.
Page 23
... touch OA in O and pass through B. Let BE be the diameter through B , so that E is a fixed point . Join PE cutting the circle in Q. Then BQE is a right angle . Let RY , per- pendicular to PB , meet PE in Y , and draw YS parallel to PB ...
... touch OA in O and pass through B. Let BE be the diameter through B , so that E is a fixed point . Join PE cutting the circle in Q. Then BQE is a right angle . Let RY , per- pendicular to PB , meet PE in Y , and draw YS parallel to PB ...
Page 36
... the lengths of the tangents from these points to the sphere . Let the sphere touch the edges AD , BC in P , Q. Then P is the C. of G. of the weights at A , D ; Q the C. of G. of those at B , C ... the C. of G. of 36 SOLUTIONS OF.
... the lengths of the tangents from these points to the sphere . Let the sphere touch the edges AD , BC in P , Q. Then P is the C. of G. of the weights at A , D ; Q the C. of G. of those at B , C ... the C. of G. of 36 SOLUTIONS OF.
Page 39
... touch OP in R , and let the other focal sphere touch OP ' in R ' . Then OP + OP ' = OR + RPOR ′ – K'P ' - = OR + SP + OR ' P'S ' = OR + OR ' , since SPS'P ' is a parallelogram , = const . 7. Tripos 1875. Tuesday morning . No. 1 . П B C ...
... touch OP in R , and let the other focal sphere touch OP ' in R ' . Then OP + OP ' = OR + RPOR ′ – K'P ' - = OR + SP + OR ' P'S ' = OR + OR ' , since SPS'P ' is a parallelogram , = const . 7. Tripos 1875. Tuesday morning . No. 1 . П B C ...
Common terms and phrases
a+b+c ABCD axis bisects the angle Cambridge centre chord circle round circle will go circum-circle Clifton College coef College conic const coordinates cos² cosec Crown 8vo denote diameter directrix draw Edition ellipse envelope equal equation Fcap fixed point geometrical given expression hyperbola inscribed circle intersect Join Let ABC Let the tangent locus Mathematics meet middle point Monday afternoon morning nine-point circle nth term orthocentre PAPER parabola parallel perpendicular plane Professor quadrilateral radical axis radius right angles shew shewn sides Similarly sin² sin³ straight line tan² tangent Todh triangle Trinity College Tripos velocity vertex vertical
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