A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page vi
... and with a radius equal to half the sum of the other two sides , it will touch the circles described on these sides as diameters . " Page 235 , Ex . 18. Add , " and F , B , C , G are concyclic . " Page 247 , Ex . 7. Read , " P vi PREFACE .
... and with a radius equal to half the sum of the other two sides , it will touch the circles described on these sides as diameters . " Page 235 , Ex . 18. Add , " and F , B , C , G are concyclic . " Page 247 , Ex . 7. Read , " P vi PREFACE .
Page 48
... diameters DAE , FBG . Then , because AD = AC , .. LADC = 2 ACD , .. ext . EAC = twice ACD . Similarly , CBF = twice ... diameter , AD any other chord . Then CBCD ; .. AB = AC + CD > AD . And if AF is nearer to AB than AD , the two sides ...
... diameters DAE , FBG . Then , because AD = AC , .. LADC = 2 ACD , .. ext . EAC = twice ACD . Similarly , CBF = twice ... diameter , AD any other chord . Then CBCD ; .. AB = AC + CD > AD . And if AF is nearer to AB than AD , the two sides ...
Page 50
... diameter draw a line perp . to the diameter . These will be the tangents , ( i ) and ( ii ) , required . 2. The tangents are perp . to the same diameter , and there- fore parallel [ 1. 28 ] . 3. The pt . of contact is in the line of ...
... diameter draw a line perp . to the diameter . These will be the tangents , ( i ) and ( ii ) , required . 2. The tangents are perp . to the same diameter , and there- fore parallel [ 1. 28 ] . 3. The pt . of contact is in the line of ...
Page 51
... diameter is perp . to the diameter . .. the chords par . to it are bisected by the diameter [ III . 3 ] . 5. The required locus is the perp . to the given st . line through the given pt . [ II . 19 ] . 6. The required locus is the st ...
... diameter is perp . to the diameter . .. the chords par . to it are bisected by the diameter [ III . 3 ] . 5. The required locus is the perp . to the given st . line through the given pt . [ II . 19 ] . 6. The required locus is the st ...
Page 52
... diameter produced . Draw BA perp . to EB and equal to the required length . Join AE cutting the in D. Draw DF perp . to ED meeting EBF in F. Then the tangent DF = AB , the given length . Hence F is the required pt . 17. See fig . p ...
... diameter produced . Draw BA perp . to EB and equal to the required length . Join AE cutting the in D. Draw DF perp . to ED meeting EBF in F. Then the tangent DF = AB , the given length . Hence F is the required pt . 17. See fig . p ...
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
A. W. VERRALL AABC AB² ABCD AC² angles Assistant Master AX² BC² bisector bisects Cambridge centre chord circle circum College concyclic constant describe diam diameter diff draw ELEMENTARY equiangular equilat FASNACHT Fcap fixed point G. E. FASNACHT given base given point given ratio given st GREEK Hence identically equal inscribed intersect Introduction and Notes ISAAC TODHUNTER isosceles Join Let ABC LL.D locus M.A. BOOK meet middle point middle pt orthocentre Owens College par¹ parm pedal triangle perp plane produced Prof Professor Radical Axis radius equal rect respectively segment shewn sides Similarly sum of sqq tangent touch Translated triangle Trinity College vert vols
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