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
... construction fails ; ( iii ) above the point A , in which case FA must be produced in order to bisect the given angle . 2. In the △ DFA , EFA , DF = EF , Because and FA is common to both ; also DA EA , by construction ; = ... the DFA ...
... construction fails ; ( iii ) above the point A , in which case FA must be produced in order to bisect the given angle . 2. In the △ DFA , EFA , DF = EF , Because and FA is common to both ; also DA EA , by construction ; = ... the DFA ...
Page 8
... construction as in the last example . The problem is impossible unless PQ is greater than half AB ; for otherwise the two circles will not intersect . .10 . ( i ) and ( iii ) In the A " ODB , OEA , Because OD = OE , being radii of the ...
... construction as in the last example . The problem is impossible unless PQ is greater than half AB ; for otherwise the two circles will not intersect . .10 . ( i ) and ( iii ) In the A " ODB , OEA , Because OD = OE , being radii of the ...
Page 11
... construction fails when AB is perp . to XY ; for then CP will not meet XY . Page 35 . 1. In the 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 respectively ...
... construction fails when AB is perp . to XY ; for then CP will not meet XY . Page 35 . 1. In the 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 respectively ...
Page 17
... , and 26 ] . line . [ I. 12. ] ACP , BCQ may be shewn equal in all respects .. AP = BQ . The construction is impossible if O , A , B , are in the same st . H.K.E. B Page 60 . 1. In the A $ AOC , EXERCISES ON BOOK I. 17 PAGE 55 .
... , and 26 ] . line . [ I. 12. ] ACP , BCQ may be shewn equal in all respects .. AP = BQ . The construction is impossible if O , A , B , are in the same st . H.K.E. B Page 60 . 1. In the A $ AOC , EXERCISES ON BOOK I. 17 PAGE 55 .
Page 23
... identically equal , ... AP = CQ . [ 1. 26. ] 14. Since AX is equal and par ' . to YC , it follows that AYCX is a parm . [ I. 33. ] Page 71 . 1. The construction consists of three steps EXERCISES ON BOOK I. 23 PAGE 70 .
... identically equal , ... AP = CQ . [ 1. 26. ] 14. Since AX is equal and par ' . to YC , it follows that AYCX is a parm . [ I. 33. ] Page 71 . 1. The construction consists of three steps EXERCISES ON BOOK I. 23 PAGE 70 .
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