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 5
... proved . 4. In the two △ BAD , CAD , BA CA , by hypothesis ; = Because and AD is common to both ; also BD = CD ; .. the BAD = the CAD , [ 1. 8. ] [ 1. 8. ] and the BDA = the CDA . 5. In Ex . 4 it has been shewn that the BAD = the ...
... proved . 4. In the two △ BAD , CAD , BA CA , by hypothesis ; = Because and AD is common to both ; also BD = CD ; .. the BAD = the CAD , [ 1. 8. ] [ 1. 8. ] and the BDA = the CDA . 5. In Ex . 4 it has been shewn that the BAD = the ...
Page 6
... . 4. ] ( iii ) Because Join AM . Then in the " ALM , ANM , ALAN , being halves of equal sides ; LM NM , proved in ( i ) ; = and AM is common to both ; .. the ALM = the ANM . [ 1. 8. ] Page 28 . 1. The point F might fall in 6 KEY TO EUCLID .
... . 4. ] ( iii ) Because Join AM . Then in the " ALM , ANM , ALAN , being halves of equal sides ; LM NM , proved in ( i ) ; = and AM is common to both ; .. the ALM = the ANM . [ 1. 8. ] Page 28 . 1. The point F might fall in 6 KEY TO EUCLID .
Page 11
... proved equal to the CAZ . L ... BZ = CZ ; also the AZB = the AZC ; and these , being adjacent , are rt . angles . 13. Let AB be the base , and P the length of the perp . Bisect AB at C ; and at C draw CX at rt . angles to AB [ 1. 11 ] ...
... proved equal to the CAZ . L ... BZ = CZ ; also the AZB = the AZC ; and these , being adjacent , are rt . angles . 13. Let AB be the base , and P the length of the perp . Bisect AB at C ; and at C draw CX at rt . angles to AB [ 1. 11 ] ...
Page 12
... proved . Page 36 . 1. In the CDA , because DA = DC , .. the DAC = the Then in the △ DAO , DCO , DA = DC , Because and AO = CO , and the DAO = the DCO ; DOC ; [ I. 13. ] [ 1. 13. ] [ Hyp . ] [ Hyp . ] DCA . [ 1. 5. ] [ Hyp . ] Hyp ...
... proved . Page 36 . 1. In the CDA , because DA = DC , .. the DAC = the Then in the △ DAO , DCO , DA = DC , Because and AO = CO , and the DAO = the DCO ; DOC ; [ I. 13. ] [ 1. 13. ] [ Hyp . ] [ Hyp . ] DCA . [ 1. 5. ] [ Hyp . ] Hyp ...
Page 16
... [ Proved . ] [ 1. 26. ] XBC , being half of equal ̃25 ; and BC is common to both ; ... the YBC the XCB in all respects . = 2. In the isosceles △ ABC , let BX , CY be drawn perp . re- spectively to the equal sides AC , AB . Then in the ...
... [ Proved . ] [ 1. 26. ] XBC , being half of equal ̃25 ; and BC is common to both ; ... the YBC the XCB in all respects . = 2. In the isosceles △ ABC , let BX , CY be drawn perp . re- spectively to the equal sides AC , AB . Then in the ...
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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