A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 52
... double of one side double of the adjacent side . . the circumscribing parm . is equilateral . = 13. Take fig . of Ex . 11. Then , by III . 17. Cor . and 1. 8 , LAOE = LAOH ; L BOE = L BOF ; △ DOG = DOH ; COG = L COF . . ' . △ a AOE ...
... double of one side double of the adjacent side . . the circumscribing parm . is equilateral . = 13. Take fig . of Ex . 11. Then , by III . 17. Cor . and 1. 8 , LAOE = LAOH ; L BOE = L BOF ; △ DOG = DOH ; COG = L COF . . ' . △ a AOE ...
Page 56
... double of the vertical , the pentagon is equilateral . Page 199 . 1. See fig . p . 199. Let tangent at D be parl . to AB . Then , if DC be perp . to tangent , the centre is in DC [ III . 19 ] . But DC .. DC bisects AB [ III . 3. ] Hence ...
... double of the vertical , the pentagon is equilateral . Page 199 . 1. See fig . p . 199. Let tangent at D be parl . to AB . Then , if DC be perp . to tangent , the centre is in DC [ III . 19 ] . But DC .. DC bisects AB [ III . 3. ] Hence ...
Page 63
... double of EF [ III . 3 ] . From E , F draw EG , FH perp . to XY ; and from E draw ĒK perp . to FH . Then XY is double of GH , that is , double of EK . But in the rt . - angled △ EKF , EF is greater than EK . .. PQ is greater than XY ...
... double of EF [ III . 3 ] . From E , F draw EG , FH perp . to XY ; and from E draw ĒK perp . to FH . Then XY is double of GH , that is , double of EK . But in the rt . - angled △ EKF , EF is greater than EK . .. PQ is greater than XY ...
Page 65
... double of QPR . Join AO , cutting PQ at B. Then AO bisects the PAQ [ III . 17 , Cor . ] , and also bisects PQ at rt . angles [ Ex . 2 , p . 182 ] : also PR is perp . to AP [ III . 18 ] . Hence from the rt . angled △ PAO , BPO , the PAO ...
... double of QPR . Join AO , cutting PQ at B. Then AO bisects the PAQ [ III . 17 , Cor . ] , and also bisects PQ at rt . angles [ Ex . 2 , p . 182 ] : also PR is perp . to AP [ III . 18 ] . Hence from the rt . angled △ PAO , BPO , the PAO ...
Page 78
... double of DAB [ III . 20 ] . .. DEB is also double of CEB , .. DEC = △ BEC . S Hence DCE , BCE are identically equal [ 1. 4 ] . 12. Join BQ . But Then APB = PQB [ III . 32 ] . < PQB = BPQ [ 111. 27 ] , .. LAPB = 4 BPQ . 13. For < BAD ...
... double of DAB [ III . 20 ] . .. DEB is also double of CEB , .. DEC = △ BEC . S Hence DCE , BCE are identically equal [ 1. 4 ] . 12. Join BQ . But Then APB = PQB [ III . 32 ] . < PQB = BPQ [ 111. 27 ] , .. LAPB = 4 BPQ . 13. For < BAD ...
Other editions - View all
A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H S 1848-1934 Hall No preview available - 2018 |
A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H. S. Hall No preview available - 2017 |
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A. W. VERRALL AABC AB˛ ABCD AC˛ angles Assistant Master AX˛ BC˛ bisector bisects Cambridge centre chord circle circum College concyclic constant describe diam diameter diff draw ELEMENTARY equiangular equilat FASNACHT Fcap fixed point G. E. FASNACHT given base given point given ratio given st GREEK Hence identically equal inscribed intersect Introduction and Notes ISAAC TODHUNTER isosceles Join Let ABC LL.D locus M.A. BOOK meet middle point middle pt orthocentre Owens College parš parm pedal triangle perp plane produced Prof Professor Radical Axis radius equal rect respectively segment shewn sides Similarly sum of sqq tangent touch Translated triangle Trinity College vert vols
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