A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 25
... proved by considering ABCX , DCX on a common base CX and of equal altitudes [ Ex . 13 , p . 64 ] . Or if the diagonals meet in O , the △ OBX , ODX are equal , and AODC , OBC are equal [ 1. 38 ] . 12 . ARBC QBC [ Ex . 2 , p . 96 and 1 ...
... proved by considering ABCX , DCX on a common base CX and of equal altitudes [ Ex . 13 , p . 64 ] . Or if the diagonals meet in O , the △ OBX , ODX are equal , and AODC , OBC are equal [ 1. 38 ] . 12 . ARBC QBC [ Ex . 2 , p . 96 and 1 ...
Page 26
... proved by a similar method . 17. If o lies between the parallel sides AB , CD , the perp . EOF to these sides is equal to the perp . from A to CD . Thus the △ OAB , OCD , ADC have equal bases , and the altitude of ADC is equal to the ...
... proved by a similar method . 17. If o lies between the parallel sides AB , CD , the perp . EOF to these sides is equal to the perp . from A to CD . Thus the △ OAB , OCD , ADC have equal bases , and the altitude of ADC is equal to the ...
Page 34
... proved that AOC is a rt . angle after the method of III . 31 . - ( iii ) Produce FG , DB to meet at M. Then since ... prove of two rt . angles . From A draw AX perp . to BC . AB = 2. BX : this may be done by joining X to the middle point ...
... proved that AOC is a rt . angle after the method of III . 31 . - ( iii ) Produce FG , DB to meet at M. Then since ... prove of two rt . angles . From A draw AX perp . to BC . AB = 2. BX : this may be done by joining X to the middle point ...
Page 35
... prove as in II . 4 that ( i ) the figs . LP , FM , YG are respectively the sqq . on AX , XY , YB . ( ii ) the fig . AF the fig . MC = the rect . AX , YB . ( iii ) the fig . EH = the fig . HQ : = - ( iv ) the fig . XK = the fig . KN ...
... prove as in II . 4 that ( i ) the figs . LP , FM , YG are respectively the sqq . on AX , XY , YB . ( ii ) the fig . AF the fig . MC = the rect . AX , YB . ( iii ) the fig . EH = the fig . HQ : = - ( iv ) the fig . XK = the fig . KN ...
Page 61
... proved in the course of 1. 47 , p . 82. ] Or : The on BC as diameter passes through D [ 11. 31 ] . And AC being perp . to the diameter is tangent at C ... sq . on tangent AC = rect . of segments of secant , AB , AD [ 111. 36 ] . 1 ...
... proved in the course of 1. 47 , p . 82. ] Or : The on BC as diameter passes through D [ 11. 31 ] . And AC being perp . to the diameter is tangent at C ... sq . on tangent AC = rect . of segments of secant , AB , AD [ 111. 36 ] . 1 ...
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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 |
Common terms and phrases
A. W. VERRALL AABC AB² ABCD AC² angles Assistant Master AX² BC² 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 par¹ 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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