Weekly problem papers, with notes. [With] Solutions1885 |
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Page 8
... resultant must act along the tangent . 7. Let the diameter through Q ' meet the tangent at P in T. Join RQ cutting the curve in L and the diameter at P in M. Then Now Similarly RL . RQ ' = RM 2 . RM : RQ ' :: RP : RT :: 1 : 3 .. RM = RQ ...
... resultant must act along the tangent . 7. Let the diameter through Q ' meet the tangent at P in T. Join RQ cutting the curve in L and the diameter at P in M. Then Now Similarly RL . RQ ' = RM 2 . RM : RQ ' :: RP : RT :: 1 : 3 .. RM = RQ ...
Page 32
... resultant of the two forces at B must be a force P parallel to the force at 4 ... the forces at B must each make an angle 60 ° with the resultant , and .. must make an angle 120 ° with each other . 6. We will first prove the following ...
... resultant of the two forces at B must be a force P parallel to the force at 4 ... the forces at B must each make an angle 60 ° with the resultant , and .. must make an angle 120 ° with each other . 6. We will first prove the following ...
Page 44
... resultant of the forces along DB and DC cut BC in E. Let them be replaced by this resultant . Then the resultant of this force and the force along DA will cut the plane ABC in a point in AE , and is .. neither wholly in , nor parallel ...
... resultant of the forces along DB and DC cut BC in E. Let them be replaced by this resultant . Then the resultant of this force and the force along DA will cut the plane ABC in a point in AE , and is .. neither wholly in , nor parallel ...
Page 49
... resultant = 2 √81 +1323 , = AB√351 . 7. Let PG be the normal , Q its middle point , PN , QM the ordinates of P and Q. Then MN = AN ; NG = AS . , SM = .. QM2 = † PN2 = AS . AN = AS . SM . ..the locus of Q is a parabola , vertex S , and ...
... resultant = 2 √81 +1323 , = AB√351 . 7. Let PG be the normal , Q its middle point , PN , QM the ordinates of P and Q. Then MN = AN ; NG = AS . , SM = .. QM2 = † PN2 = AS . AN = AS . SM . ..the locus of Q is a parabola , vertex S , and ...
Page 129
... resultant of PB , PC is represented by 2PD ; and PA .. resultant of PA , PB , PC : = twice resultant of PD , PD ' = = 20P . = 7. Let ( h , k ) be the point from which the tangents are drawn . Then by Paper XXXV . , No. 7 , ( +1 ) ...
... resultant of PB , PC is represented by 2PD ; and PA .. resultant of PA , PB , PC : = twice resultant of PD , PD ' = = 20P . = 7. Let ( h , k ) be the point from which the tangents are drawn . Then by Paper XXXV . , No. 7 , ( +1 ) ...
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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