A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 12
... contain supplementary angles the two As can be placed having one side in common and the other two equal sides in same st . line . Thus we have two As of same altitude on equal bases . 10. Let AB , BC be bisected in X , Y respectively ...
... contain supplementary angles the two As can be placed having one side in common and the other two equal sides in same st . line . Thus we have two As of same altitude on equal bases . 10. Let AB , BC be bisected in X , Y respectively ...
Page 52
... Draw DF perp . to ED meeting EB in F. Then DFE = BAE = complement of BEA = half the given angle . Hence the tangents from F contain the angle required [ III . 17. Cor . ] . B the Draw 18. Let A be the pt . 52 KEY TO EUCLID .
... Draw DF perp . to ED meeting EB in F. Then DFE = BAE = complement of BEA = half the given angle . Hence the tangents from F contain the angle required [ III . 17. Cor . ] . B the Draw 18. Let A be the pt . 52 KEY TO EUCLID .
Page 58
... given base describe a segment containing an to the given 2. The pt . or pts . in which the arc of the segment cuts the given st . line give the required vertex . 2. The required vertex is the intersection of the arc 58 KEY TO EUCLID .
... given base describe a segment containing an to the given 2. The pt . or pts . in which the arc of the segment cuts the given st . line give the required vertex . 2. The required vertex is the intersection of the arc 58 KEY TO EUCLID .
Page 59
... containing an equal to the given △ , and ( i ) The circle , whose centre is an extremity of the base and radius is ... containing an equal to the given K ; also another segment containing an angle greater by a right than K. From centre ...
... containing an equal to the given △ , and ( i ) The circle , whose centre is an extremity of the base and radius is ... containing an equal to the given K ; also another segment containing an angle greater by a right than K. From centre ...
Page 67
... containing the given angle . Take C the centre of the O , and join CA , CP . bisects the APB [ III . 17 , Cor . ] . 8 Hence in the ACAP , the - CAP , CPA , and the side CA are constant ; .. CP is constant [ 1. 26 ] . .. the locus of P ...
... containing the given angle . Take C the centre of the O , and join CA , CP . bisects the APB [ III . 17 , Cor . ] . 8 Hence in the ACAP , the - CAP , CPA , and the side CA are constant ; .. CP is constant [ 1. 26 ] . .. the locus of 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 AB˛ ABCD AC˛ angles Assistant Master AX˛ BC˛ 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 parš 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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