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 21
... four angles of the quadril . = 4 rt . " ; .. twice DOC = Page 67 . CBA , BAD . 1. ( i ) The six 4 , with 4 rt . 2o , are together equal to 12 rt . 2o , [ 1. 32 , Cor . 1. ] that is , the six together 8 rt . 2 ; .. each rt . 2 . = ( ii ) ...
... four angles of the quadril . = 4 rt . " ; .. twice DOC = Page 67 . CBA , BAD . 1. ( i ) The six 4 , with 4 rt . 2o , are together equal to 12 rt . 2o , [ 1. 32 , Cor . 1. ] that is , the six together 8 rt . 2 ; .. each rt . 2 . = ( ii ) ...
Page 26
... four BED = the suppt . of △ DAB . rt . 4 , the other pair of opp . < are supplementary . of the fig . are together equal to four Join AC , BD . Then in A DEB , ABC , DEB = suppt . of BCD = ¿ ABC ; [ 1. 29. ] and DE , EB = AB , BC ...
... four BED = the suppt . of △ DAB . rt . 4 , the other pair of opp . < are supplementary . of the fig . are together equal to four Join AC , BD . Then in A DEB , ABC , DEB = suppt . of BCD = ¿ ABC ; [ 1. 29. ] and DE , EB = AB , BC ...
Page 46
... . of ACB = △ ECK , and △ BCM , ECK are identically equal [ 1. 4 ] . Therefore sq . on EK = sq . on BM = sum of sqq . on BA , AM [ 1. 47 ] sq . on BA with four times sq . on AC . ( iii ) Sq , on EK = sq . 46 KEY TO EUCLID .
... . of ACB = △ ECK , and △ BCM , ECK are identically equal [ 1. 4 ] . Therefore sq . on EK = sq . on BM = sum of sqq . on BA , AM [ 1. 47 ] sq . on BA with four times sq . on AC . ( iii ) Sq , on EK = sq . 46 KEY TO EUCLID .
Page 47
... four times the sum of the sqq . on BQ , CP = four times the sum of the sqq . on PQ , BC . But four times the sq . on PQ = sq . on BC [ Ex . 3 , p . 105 ] . .. four times the sum of the sqq . on BQ , CP = five times the sq . on BC . 46 ...
... four times the sum of the sqq . on BQ , CP = four times the sum of the sqq . on PQ , BC . But four times the sq . on PQ = sq . on BC [ Ex . 3 , p . 105 ] . .. four times the sum of the sqq . on BQ , CP = five times the sq . on BC . 46 ...
Page 49
... four equal As having their vertices at the inters " . of the diagonals . Thus the problem is the same as in Ex . 10 , and the required locus is a st . line through the inters " , of the diagonals par1 . to the given base . 2PD 12. Let ...
... four equal As having their vertices at the inters " . of the diagonals . Thus the problem is the same as in Ex . 10 , and the required locus is a st . line through the inters " , of the diagonals par1 . to the given base . 2PD 12. 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