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 12
... follows that DO , OB are in one st . line . Page 39 . [ I. 14. ] 1. If any two lines BA , CA meet at a point A , and are cut by a third st . line BC , then the two interior 2 ABC , ACB , on one side of BC are together less that two rt ...
... follows that DO , OB are in one st . line . Page 39 . [ I. 14. ] 1. If any two lines BA , CA meet at a point A , and are cut by a third st . line BC , then the two interior 2 ABC , ACB , on one side of BC are together less that two rt ...
Page 13
... follows that every triangle must have at least two acute angles ; .. the rt . angle is greatest angle ; .. the hypotenuse , which is opposite to the rt . angle , is the greatest side . 2. In the ABC , let the ABC = the ACB . Then AB ...
... follows that every triangle must have at least two acute angles ; .. the rt . angle is greatest angle ; .. the hypotenuse , which is opposite to the rt . angle , is the greatest side . 2. In the ABC , let the ABC = the ACB . Then AB ...
Page 22
... follows that ABCD is a par TM . 3. In the quadril . ABCD , let DAB = BCD , and ABC = L ADC ; then the sum of two adjacent < = 4 . sum of the 2 of fig . ABCD = 2 rt . $ ; .. the opposite sides are parallel . By Ex . 2 the fig is a par TM ...
... follows that ABCD is a par TM . 3. In the quadril . ABCD , let DAB = BCD , and ABC = L ADC ; then the sum of two adjacent < = 4 . sum of the 2 of fig . ABCD = 2 rt . $ ; .. the opposite sides are parallel . By Ex . 2 the fig is a par TM ...
Page 23
... follows at once by I. 4 . [ 1. 7. ] 13. Let AP , CQ be perp . to diag . BD . Then ADP = alt . △ QBC , △ APD = < CQB , being rt . 2o , and AD = BC ; .. A APD , BQC are identically equal , ... AP = CQ . [ 1. 26. ] 14. Since AX is equal ...
... follows at once by I. 4 . [ 1. 7. ] 13. Let AP , CQ be perp . to diag . BD . Then ADP = alt . △ QBC , △ APD = < CQB , being rt . 2o , and AD = BC ; .. A APD , BQC are identically equal , ... AP = CQ . [ 1. 26. ] 14. Since AX is equal ...
Page 27
... follows by Ex . 7 . 9. Since the equal sides contain supplementary angles the two △ can be placed having one side in common and the other two equal sides in same st . line . Thus we have two △ of same altitude on equal bases . 10. Let ...
... follows by Ex . 7 . 9. Since the equal sides contain supplementary angles the two △ can be placed having one side in common and the other two equal sides in same st . line . Thus we have two △ of same altitude on equal bases . 10. Let ...
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