A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 97
... parallel to AC , and FE parallel to BC . Then AB is trisected in the points D , E. For since AC is parallel to FD , and FA meets them , therefore the alternate angles FAC , AFD are equal ; but the angle FAD is equal to the angle FAC ...
... parallel to AC , and FE parallel to BC . Then AB is trisected in the points D , E. For since AC is parallel to FD , and FA meets them , therefore the alternate angles FAC , AFD are equal ; but the angle FAD is equal to the angle FAC ...
Page 100
... parallel to PD ; join PE ; PE bisects the tri- angle ABC . Since AE is parallel to PD , the triangle APD is equal to the triangle EPD ; to each of these equals add B P the triangle PDC ; .. CPE = CAD = half the triangle ABC . 40. Draw ...
... parallel to PD ; join PE ; PE bisects the tri- angle ABC . Since AE is parallel to PD , the triangle APD is equal to the triangle EPD ; to each of these equals add B P the triangle PDC ; .. CPE = CAD = half the triangle ABC . 40. Draw ...
Page 102
... parallel to AB , touching the inner circle , and let EF be any other tangent to the inner circle . From O , the centre of the outer circle , draw OH perpendicular to CD , and OL perpendicular to EF , cutting the circle in G. Then OH is ...
... parallel to AB , touching the inner circle , and let EF be any other tangent to the inner circle . From O , the centre of the outer circle , draw OH perpendicular to CD , and OL perpendicular to EF , cutting the circle in G. Then OH is ...
Page 103
... parallel to CD ; and AC is parallel to ED ; therefore the figure ACED is a parallelogram ; and there- fore AC - ED . F E B 60. Let AB , CD cut one another at right angles in E ; the sum of the squares of AE , EB , CE , ED will be equal ...
... parallel to CD ; and AC is parallel to ED ; therefore the figure ACED is a parallelogram ; and there- fore AC - ED . F E B 60. Let AB , CD cut one another at right angles in E ; the sum of the squares of AE , EB , CE , ED will be equal ...
Page 106
... parallel to OD , cutting OAE in E. E is the cen- tre of the circle required . Since ( Eucl . 1. 29 ) the angle ODA ... parallel to CB ; O is the centre of the circle required . Through O draw OE parallel to DC ; therefore CO is a ...
... parallel to OD , cutting OAE in E. E is the cen- tre of the circle required . Since ( Eucl . 1. 29 ) the angle ODA ... parallel to CB ; O is the centre of the circle required . Through O draw OE parallel to DC ; therefore CO is a ...
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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 a²b² AB² AC² axis BC² beam bisects centre of gravity chord circle co-ordinates coefficient cos² cos³ cosec curve diameter draw ellipse equal Eucl Hence hyperbola Join latus rectum Let ABC middle point MULTINOMIAL THEOREMS parabola parallel perpendicular plane point of contact r₁ radius required locus right angle roots S₁ S₂ sec² segment sides Similarly sin² sin³ square Taking the moments tan¹ tan² tangent term transformed equation triangle ABC values velocity vertical weight whence X₁ ΙΟ