A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements: Books I.- VI. and XI.Macmillan, 1905 - 229 pages |
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Page 5
... Let ABCD be a rhombus . Then in the △ ADB , CDB , AD = CD , being sides of a rhombus ; Because and BA BC , for the ... ABC . = Join AC . Then in the △ ABC , CDA , ABCD , by hypothesis , Because and BC = DA , " " [ 1. 8. ] and AC is ...
... Let ABCD be a rhombus . Then in the △ ADB , CDB , AD = CD , being sides of a rhombus ; Because and BA BC , for the ... ABC . = Join AC . Then in the △ ABC , CDA , ABCD , by hypothesis , Because and BC = DA , " " [ 1. 8. ] and AC is ...
Page 7
... Let ABC be the isosceles A , in which AB = AC ; and let AX bisect the vert . BAC , cutting BC at X. Because Then in the △ BAX , CAX , BACA , by hypothesis ; and AX is common ; and the BAX the CAX , by hypothesis ; -- ... BX CX ...
... Let ABC be the isosceles A , in which AB = AC ; and let AX bisect the vert . BAC , cutting BC at X. Because Then in the △ BAX , CAX , BACA , by hypothesis ; and AX is common ; and the BAX the CAX , by hypothesis ; -- ... BX CX ...
Page 8
... Let A be the vertex , and BC the base , of an isosceles A ABC ; 2nd let BC be bisected at D. Join AD . Then in the △ BDA , CDA , BD = CD , Because and DA is common to both ; | and AB = AC ; ... the ADB = the ADC ; .. these equal angles ...
... Let A be the vertex , and BC the base , of an isosceles A ABC ; 2nd let BC be bisected at D. Join AD . Then in the △ BDA , CDA , BD = CD , Because and DA is common to both ; | and AB = AC ; ... the ADB = the ADC ; .. these equal angles ...
Page 9
... ABC , let D and E be two points such that BD = CE . Join AD , AE . Then in the △ ABD , ACE , AB = AC , Because BD = CE , and the ABD = the ACE , ... AD AE . [ Hyp . ] [ Hyp . [ 1. 5. ] [ 1. 4. ] 4. Let ABCD be a quad ' , in which AB ...
... ABC , let D and E be two points such that BD = CE . Join AD , AE . Then in the △ ABD , ACE , AB = AC , Because BD = CE , and the ABD = the ACE , ... AD AE . [ Hyp . ] [ Hyp . [ 1. 5. ] [ 1. 4. ] 4. Let ABCD be a quad ' , in which AB ...
Page 11
... Let AB be the base , and P the length of the perp . Bisect AB at C ; and at C draw CX at rt . angles to AB [ 1. 11 ] ... ABC let BC be produced both ways to X and Y , and let the exterior 2 ABX , ACY be equal . Then since the ABC , ACB are ...
... Let AB be the base , and P the length of the perp . Bisect AB at C ; and at C draw CX at rt . angles to AB [ 1. 11 ] ... ABC let BC be produced both ways to X and Y , and let the exterior 2 ABX , ACY be equal . Then since the ABC , ACB are ...
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 |
Common terms and phrases
AB² ABCD AC² angles AP² arc AC AX² base BC BC² bisector bisects centre chord circum collinear common tangent concyclic constant cutting the given diagonals diam diameter diff draw drawn equiangular equilat fixed point given base given point given ratio given st greater half Hence identically equal inscribed intersect isosceles Join Let AB Let ABC Let AX locus middle point middle pt orthocentre par¹ parm pass pedal triangle perp plane polar produced Radical Axis radius equal rect respectively rhombus segment shewn sides Similarly solutions subtended sum of sqq tangent touch triangle vert vertex