A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 96
... join BE . = Now , in the triangles ADC , BDE , we have AD = DE ( by construction ) ; BDBC ( by hypothesis ) ; and △ BDE = 2 ADC ( Euc . 1. 15 ) . Therefore ( Euc . I. 4 ) BE AC , = and angle BED = angle DAC ; but angle DAC = angle BAD ...
... join BE . = Now , in the triangles ADC , BDE , we have AD = DE ( by construction ) ; BDBC ( by hypothesis ) ; and △ BDE = 2 ADC ( Euc . 1. 15 ) . Therefore ( Euc . I. 4 ) BE AC , = and angle BED = angle DAC ; but angle DAC = angle BAD ...
Page 97
... join BE cutting CD in G. Join also AG . Then AG and BG make equal angles with CD . For since AF is equal to FE , and FG is common to the two triangles AGF , EGF , and the included angles AFG , EFG are equal ; C D F G E therefore the ...
... join BE cutting CD in G. Join also AG . Then AG and BG make equal angles with CD . For since AF is equal to FE , and FG is common to the two triangles AGF , EGF , and the included angles AFG , EFG are equal ; C D F G E therefore the ...
Page 98
... Join GD , GA , GB , GC . Since AF FC and FG is common to the triangles AFG , CFG , and the angles at Fare right angles , therefore AG is equal to GC . Similarly it may be shewn that GC is equal to GB , and therefore AG is equal to GB ...
... Join GD , GA , GB , GC . Since AF FC and FG is common to the triangles AFG , CFG , and the angles at Fare right angles , therefore AG is equal to GC . Similarly it may be shewn that GC is equal to GB , and therefore AG is equal to GB ...
Page 100
... join AD , PD ; and from A draw AE 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 the triangle PDC ; .. CPE = CAD ...
... join AD , PD ; and from A draw AE 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 the triangle PDC ; .. CPE = CAD ...
Page 101
... join DO , FO ; the angle DOF is a right angle . = Join CO . Then since CF - FB , A CO OB ; and the angles at C and B being right angles , are equal , there- fore CFO LOFB , and CFB is bisected by FO . = Similarly it may be shewn that ...
... join DO , FO ; the angle DOF is a right angle . = Join CO . Then since CF - FB , A CO OB ; and the angles at C and B being right angles , are equal , there- fore CFO LOFB , and CFB is bisected by FO . = Similarly it may be shewn that ...
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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