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 3
... Join AC , BC . Then in the triangle ABC , AC = AN , and BC = BM . [ Def . 15. ] Page 17 . 1. In the A3 DAB , CBA , DA = CB , being sides of a square ; [ Def . 30. ] Because and AB is common ; and the DAB = the CBA , being right angles ...
... Join AC , BC . Then in the triangle ABC , AC = AN , and BC = BM . [ Def . 15. ] Page 17 . 1. In the A3 DAB , CBA , DA = CB , being sides of a square ; [ Def . 30. ] Because and AB is common ; and the DAB = the CBA , being right angles ...
Page 5
... Join BD . 1. Let ABCD be a rhombus . Then in the △ ADB , CDB , AD = CD , being sides of a rhombus ; Because and BA ... Join AC . Then in the △ ABC , CDA , ABCD , by hypothesis , Because and BC = DA , " " [ 1. 8. ] and AC is common to ...
... Join BD . 1. Let ABCD be a rhombus . Then in the △ ADB , CDB , AD = CD , being sides of a rhombus ; Because and BA ... Join AC . Then in the △ ABC , CDA , ABCD , by hypothesis , Because and BC = DA , " " [ 1. 8. ] and AC is common to ...
Page 6
... Join BD , FH ; and apply the fig . ABCD to the fig . EFGH , so that A falls on E , and AB falls along EF ; then B must fall on F , for AB EF . And since the BAD = the FEH [ Hyp . ] , ... AD must fall along EH , and consequently D must ...
... Join BD , FH ; and apply the fig . ABCD to the fig . EFGH , so that A falls on E , and AB falls along EF ; then B must fall on F , for AB EF . And since the BAD = the FEH [ Hyp . ] , ... AD must fall along EH , and consequently D must ...
Page 8
... Join AB . Then since OA OB [ Def . = and the equal sides OA , .. 15 ] , the AOAB is isosceles ; OB are produced to D and E : ... the BAD = the ABE . [ 1. 5 , Part 2. ] Page 33 . 1. Let A be the vertex , and BC the base , of an isosceles ...
... Join AB . Then since OA OB [ Def . = and the equal sides OA , .. 15 ] , the AOAB is isosceles ; OB are produced to D and E : ... the BAD = the ABE . [ 1. 5 , Part 2. ] Page 33 . 1. Let A be the vertex , and BC the base , of an isosceles ...
Page 9
... Join BD . Because ... the Then in the △ DAB , BCD , DA = BC , by hypothesis , AB = CD , and BD is common to both ; DAB = the BCD . [ 1. 8. ] Similarly , by joining AC , the ADC may be shewn equal to the ABC . 5. Join XY . Because Then ...
... Join BD . Because ... the Then in the △ DAB , BCD , DA = BC , by hypothesis , AB = CD , and BD is common to both ; DAB = the BCD . [ 1. 8. ] Similarly , by joining AC , the ADC may be shewn equal to the ABC . 5. Join XY . Because Then ...
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