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 99
... diam ' . drawn from A. .. APQ is a rt . angle [ III . 31 ] ; and since AP is also perp . to BC , .. PQ is par1 . to BC [ 1. 28 ] . 31 . Let SX be the perp . drawn from S the centre of the circum- on BC . Then by [ Ex . 29 , p . 245 ] AS ...
... diam ' . drawn from A. .. APQ is a rt . angle [ III . 31 ] ; and since AP is also perp . to BC , .. PQ is par1 . to BC [ 1. 28 ] . 31 . Let SX be the perp . drawn from S the centre of the circum- on BC . Then by [ Ex . 29 , p . 245 ] AS ...
Page 101
... diam . ( i ) If A is external , the locus is that part of the on AC which is intercepted within the given O. ( ii ) If A is on the Oce , the locus is a complete described on the radius AC as diam . , and having internal contact with the ...
... diam . ( i ) If A is external , the locus is that part of the on AC which is intercepted within the given O. ( ii ) If A is on the Oce , the locus is a complete described on the radius AC as diam . , and having internal contact with the ...
Page 124
... ( diam . ) 2 [ 11. 31 , and 1. 47 ] = 4 ( radius ) . ( ii ) AB2 + CD2 + 40P2 = PA2 + PB2 + 2PA . PB + PC2 + PD2 + 2PC . PD + 40P2 [ 11. 4 ] - = 4 ( radius ) 2 + 40P2 + 2PA . PB + 2PC . PD [ Ex . 3 ] = 4 ( radius ) 2 + 2 ( OP2 + PA . PB ) ...
... ( diam . ) 2 [ 11. 31 , and 1. 47 ] = 4 ( radius ) . ( ii ) AB2 + CD2 + 40P2 = PA2 + PB2 + 2PA . PB + PC2 + PD2 + 2PC . PD + 40P2 [ 11. 4 ] - = 4 ( radius ) 2 + 40P2 + 2PA . PB + 2PC . PD [ Ex . 3 ] = 4 ( radius ) 2 + 2 ( OP2 + PA . PB ) ...
Page 128
... diam . is PA . Hence S , is the centre about the AEPF . Similarly for S , and S .. Again [ Ex . 2 and 3 , p . 104 ] , S , S1⁄2 , S1⁄2SÅ , SÅS , are par1 . to AB , BC , CA , and equal to half of these lines , .. the SSS , is equiangular ...
... diam . is PA . Hence S , is the centre about the AEPF . Similarly for S , and S .. Again [ Ex . 2 and 3 , p . 104 ] , S , S1⁄2 , S1⁄2SÅ , SÅS , are par1 . to AB , BC , CA , and equal to half of these lines , .. the SSS , is equiangular ...
Page 130
... diam . describe a . ce At any point T on the ce draw a tangent TP , making TP equal to K. Take the centre O , and draw PQOR cutting the at P , Q. Then shall PQ , PR be the required lines . For rect . PR , PQ = the sq . on PT [ III . 36 ] ...
... diam . describe a . ce At any point T on the ce draw a tangent TP , making TP equal to K. Take the centre O , and draw PQOR cutting the at P , Q. Then shall PQ , PR be the required lines . For rect . PR , PQ = the sq . on PT [ III . 36 ] ...
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