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 37
... parl . to AC to meet ED produced in H. Then GH is a par TM . and EH . Also △ BFD , BHD are identically equal [ 1. 26 ] , so that That is , BG sum of DE and DF . BG DH = DF . 23 . S Take D in CB produced , then with the same lettering ...
... parl . to AC to meet ED produced in H. Then GH is a par TM . and EH . Also △ BFD , BHD are identically equal [ 1. 26 ] , so that That is , BG sum of DE and DF . BG DH = DF . 23 . S Take D in CB produced , then with the same lettering ...
Page 67
... parl . to the given direction , will be the chord re- quired . 5. Let O be the centre : and AX , BY , OZ the perp3 . on PQ . Then OZ = the sum or difference of AX and BY , according as A and B are on the same or opposite sides of PQ ...
... parl . to the given direction , will be the chord re- quired . 5. Let O be the centre : and AX , BY , OZ the perp3 . on PQ . Then OZ = the sum or difference of AX and BY , according as A and B are on the same or opposite sides of PQ ...
Page 110
... parl . middle point of PL , .. X is the middle point of OP But K is the IV . [ Ex . 1 , p . 104 ] . ON THE CIRCLE IN CONNECTION WITH RECTANGLES . Page 251 . 2 . S Since the AEB , ADB are rt . angles , .. the four points A , E , D , B ...
... parl . middle point of PL , .. X is the middle point of OP But K is the IV . [ Ex . 1 , p . 104 ] . ON THE CIRCLE IN CONNECTION WITH RECTANGLES . Page 251 . 2 . S Since the AEB , ADB are rt . angles , .. the four points A , E , D , B ...
Page 166
... parl . to DEF cutting BE and CF in G and H. Then AG = DE , and GH = EF . - and Also AB BC = AG GH [ VI . 2 ] ; .. AB BC = DE : EF . 3. Because EF , EG are par1 . to bases AC , AD ; .. AE : EB = CF : FB [ VI . 2 ] , AE : EB = DG : GB ...
... parl . to DEF cutting BE and CF in G and H. Then AG = DE , and GH = EF . - and Also AB BC = AG GH [ VI . 2 ] ; .. AB BC = DE : EF . 3. Because EF , EG are par1 . to bases AC , AD ; .. AE : EB = CF : FB [ VI . 2 ] , AE : EB = DG : GB ...
Page 173
... parl . to EB . CF shall be two - sevenths of AB . Page 346 . Let AB be the given line , and ACD any other line , divided at C so that AC : CD = the given ratio . Join DB and draw CH par1 . to DB . This must cut AB in some pt . H , so ...
... parl . to EB . CF shall be two - sevenths of AB . Page 346 . Let AB be the given line , and ACD any other line , divided at C so that AC : CD = the given ratio . Join DB and draw CH par1 . to DB . This must cut AB in some pt . H , so ...
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