A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 44
... chords are not par1 . , bisect each at rt . s . If they are par1 . , join their extremities : and bisect each of these new chords at rt . s . The pt . of intersection of the bisectors is the required centre . B , C be the three given ...
... chords are not par1 . , bisect each at rt . s . If they are par1 . , join their extremities : and bisect each of these new chords at rt . s . The pt . of intersection of the bisectors is the required centre . B , C be the three given ...
Page 45
... chord will be bisected at the given pt . 9. Let O be the common centre , ABCD the st . line cutting the inner in B ... chords , is perp . to the other [ 1. 29 ] . And this st . line bisects both chords . Hence , the st . line joining the ...
... chord will be bisected at the given pt . 9. Let O be the common centre , ABCD the st . line cutting the inner in B ... chords , is perp . to the other [ 1. 29 ] . And this st . line bisects both chords . Hence , the st . line joining the ...
Page 48
... chord : A the centre , and ADE the radius bisecting BC at rt . s in D. Let G be any pt . in BD , and GF perp . to BD , cutting the arc BEC in F. Draw AH perp . to FG . Then AE AF > HF . And AD = HG ; .. the whole or remainder DE > whole ...
... chord : A the centre , and ADE the radius bisecting BC at rt . s in D. Let G be any pt . in BD , and GF perp . to BD , cutting the arc BEC in F. Draw AH perp . to FG . Then AE AF > HF . And AD = HG ; .. the whole or remainder DE > whole ...
Page 49
... chord CAD perp . to AB , and any other chord EAF through A. BG perp . to EF . Then the hypotenuse BA > BG . .. chord CD chord EF ; that is , CD is the least chord through A. H. K. E. 4 2. Let XZY , X'Z'Y ' be two chords bisected ...
... chord CAD perp . to AB , and any other chord EAF through A. BG perp . to EF . Then the hypotenuse BA > BG . .. chord CD chord EF ; that is , CD is the least chord through A. H. K. E. 4 2. Let XZY , X'Z'Y ' be two chords bisected ...
Page 50
... chord PQ of required length in the O. [ See solution of Ex . 4 , p . 173 or iv . 1. ] Let O be centre of given 0 , and AB the given chord upon which the middle pt . of the required chord is to lie . Draw ON perp . to PQ . With centre O ...
... chord PQ of required length in the O. [ See solution of Ex . 4 , p . 173 or iv . 1. ] Let O be centre of given 0 , and AB the given chord upon which the middle pt . of the required chord is to lie . Draw ON perp . to PQ . With centre O ...
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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