A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 192
... co - ordinates , of the given line , and let △ DAX = α , then cot a - 2 5 2 and therefore cos α = √29 2 ΙΟ Now AD = x cos a = 5 × = √29 √29 18. Let y = 2x be the equation to AP , y x + 4 3 y = Ax + B ......... ... OL 10 BB Q BP , PQ ...
... co - ordinates , of the given line , and let △ DAX = α , then cot a - 2 5 2 and therefore cos α = √29 2 ΙΟ Now AD = x cos a = 5 × = √29 √29 18. Let y = 2x be the equation to AP , y x + 4 3 y = Ax + B ......... ... OL 10 BB Q BP , PQ ...
Page 196
... ordinates AL , BM , CN from the angular points A , B , C of the triangle , whose abscissæ , a , a ' , a " are in ... co - ordinates , when the equation to the circle is x2 + y2 — 3x + 4y = 0 , is a point in the circumference . Now when y ...
... ordinates AL , BM , CN from the angular points A , B , C of the triangle , whose abscissæ , a , a ' , a " are in ... co - ordinates , when the equation to the circle is x2 + y2 — 3x + 4y = 0 , is a point in the circumference . Now when y ...
Page 198
... co - ordinates of the centre of the circle being h , k , the square of the distance of the centre of the circle from the line x cos y sin a = a will be equal to ( h cos a + k sin a − a ) 2 — ( h cos a + k sin a − a ) 3 . cos2 a + sin2 ...
... co - ordinates of the centre of the circle being h , k , the square of the distance of the centre of the circle from the line x cos y sin a = a will be equal to ( h cos a + k sin a − a ) 2 — ( h cos a + k sin a − a ) 3 . cos2 a + sin2 ...
Page 207
... co - ordinates of Q ; ( x , y ) those of P ; and therefore PQ and Qp are a2 " - 4a2 y those of p , then the equations to y - y ' = y " — y ' = - " .. ( 1 ) , x ' y'y ' and y - 3 " — — 25 ′ ( 402 + 1 ) ) " ) ( x — . . . ......... ( 2 ...
... co - ordinates of Q ; ( x , y ) those of P ; and therefore PQ and Qp are a2 " - 4a2 y those of p , then the equations to y - y ' = y " — y ' = - " .. ( 1 ) , x ' y'y ' and y - 3 " — — 25 ′ ( 402 + 1 ) ) " ) ( x — . . . ......... ( 2 ...
Page 208
... co - ordinates of the point R ; then the equation to the line REF is y = −k , and when this line meets the parabola k2 = lx , whence x === = 7 EF ; .. RE = h - Τ ; .. EF : RE = k2 = ī The equation 72 k2 208 PARABOLA .
... co - ordinates of the point R ; then the equation to the line REF is y = −k , and when this line meets the parabola k2 = lx , whence x === = 7 EF ; .. RE = h - Τ ; .. EF : RE = k2 = ī The equation 72 k2 208 PARABOLA .
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A Companion to Wrigley's Collection of Examples: Being Illustrations of ... John Thompson Platts,Alfred Wrigley No preview available - 2016 |
Common terms and phrases
a+b+c a²+b² a²b³ AB² ABCD AC² angle ABC axis BC² beam centre of gravity chord circle co-ordinates coefficient cos² cos³ cosec² curve diameter draw ellipse equal equilateral Eucl Hence hyperbola Join latus rectum Let ABC middle point MULTINOMIAL THEOREMS parabola parallel perpendicular plane point of contact point of intersection r₁ radius required locus right angle roots S₁ sec² segment sides Similarly sin² sin³ square straight line tan² tangent term transformed equation triangle ABC values vertical weight whence X₁