A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 101
... tangents at A , B ; also DF a tan- gent at any point C : and let O be the centre ; join DO , FO ; the angle DOF is a right angle . = Join CO . Then since CF - FB , A CO OB ; and ... tangent to the MISCELLANEOUS THEOREMS AND PROBLEMS . 101.
... tangents at A , B ; also DF a tan- gent at any point C : and let O be the centre ; join DO , FO ; the angle DOF is a right angle . = Join CO . Then since CF - FB , A CO OB ; and ... tangent to the MISCELLANEOUS THEOREMS AND PROBLEMS . 101.
Page 102
... tangent to the two circles . Draw CD 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 ...
... tangent to the two circles . Draw CD 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 ...
Page 104
... tangent to the circle at P. Then ( Eucl . III . 31 ) the angle CDB is a right angle ; and ( Eucl . II . 13 ) BC2 is less than AB + AC2 by 2AB.AD ; i . e . ( Eucl . III . 36 ) by 2AP2 . = B D 68. Let CFH , CGE be the circles touching 104 ...
... tangent to the circle at P. Then ( Eucl . III . 31 ) the angle CDB is a right angle ; and ( Eucl . II . 13 ) BC2 is less than AB + AC2 by 2AB.AD ; i . e . ( Eucl . III . 36 ) by 2AP2 . = B D 68. Let CFH , CGE be the circles touching 104 ...
Page 105
... tangents DE , DF . Then DE - DC . DG , and DF - DC . DH ; also the triangles DGA , DCB being similar , we have BC : DC - AG : DG , F or BC DC = AC : DG . And for the same reason we have AC : DC BH : DH , = or AC DC = BC : DH ; B H ...
... tangents DE , DF . Then DE - DC . DG , and DF - DC . DH ; also the triangles DGA , DCB being similar , we have BC : DC - AG : DG , F or BC DC = AC : DG . And for the same reason we have AC : DC BH : DH , = or AC DC = BC : DH ; B H ...
Page 108
... BC2 , also BE BD - DE BD - DC2 = ( BD + DC ) ( BD - DC ) = whence it follows that = = BC ( BD - DC ) ;. AC2 : AD2 = BC2 : BC ( BD – DC + BC ) = BC : 2BD . 91. Let the tangent SPT meet the radii CA , 108 MISCELLANEOUS THEOREMS AND PROBLEMS .
... BC2 , also BE BD - DE BD - DC2 = ( BD + DC ) ( BD - DC ) = whence it follows that = = BC ( BD - DC ) ;. AC2 : AD2 = BC2 : BC ( BD – DC + BC ) = BC : 2BD . 91. Let the tangent SPT meet the radii CA , 108 MISCELLANEOUS THEOREMS AND PROBLEMS .
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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