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 7
... 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 . = [ Def . 24. ] [ 1. 8. ] [ I. 4. ] 2. Bisect the given straight line [ I ...
... 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 . = [ Def . 24. ] [ 1. 8. ] [ I. 4. ] 2. Bisect the given straight line [ I ...
Page 16
... vert . opp . 2 , AXO the BYO , being rt . angles , [ 1. 15. ] BO ; and AO ... AXBY . 5. In the △ ABC , let AX , the bisector of the BAC , be perp . [ Hyp . ] [ 1. 26. ] to the base BC . Then in the △ AXB , AXC , the BAX = the CAX ...
... vert . opp . 2 , AXO the BYO , being rt . angles , [ 1. 15. ] BO ; and AO ... AXBY . 5. In the △ ABC , let AX , the bisector of the BAC , be perp . [ Hyp . ] [ 1. 26. ] to the base BC . Then in the △ AXB , AXC , the BAX = the CAX ...
Page 17
... vert . opp . — AKQ . [ I. 15. ] 8. Let AB be the first given st . line , and OC , OD the given intersecting lines . Bisect the COD by a line which meets AB in X. From X draw XP , XQ perp . , respectively to OC , OD . Then the OXP , OXQ ...
... vert . opp . — AKQ . [ I. 15. ] 8. Let AB be the first given st . line , and OC , OD the given intersecting lines . Bisect the COD by a line which meets AB in X. From X draw XP , XQ perp . , respectively to OC , OD . Then the OXP , OXQ ...
Page 18
... vert . opp . ; [ I. 15. ] OAC = the OBD ; [ I. 4. ] and these are alternate angles ; ... AC and BD are parallel . [ 1. 27. ] 2. Let each of the st . lines AB , CD be perp . to a st . line which meets them at P and Q. Then the APQ , PQD ...
... vert . opp . ; [ I. 15. ] OAC = the OBD ; [ I. 4. ] and these are alternate angles ; ... AC and BD are parallel . [ 1. 27. ] 2. Let each of the st . lines AB , CD be perp . to a st . line which meets them at P and Q. Then the APQ , PQD ...
Page 23
... vert . opp . △ COD , - and AB = CD , .. △ AÒB , COD are identically equal , . ' . AO = OD , and CO = OB . 6. △ AOB , COD are equal in all respects [ I. 15 Hence AB , CD are equal and may be shewn parallel . fig . ABCD is a par TM . 7 ...
... vert . opp . △ COD , - and AB = CD , .. △ AÒB , COD are identically equal , . ' . AO = OD , and CO = OB . 6. △ AOB , COD are equal in all respects [ I. 15 Hence AB , CD are equal and may be shewn parallel . fig . ABCD is a par TM . 7 ...
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