A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page vii
... passes through the three escribed centres . " Page 284. In place of Ex . 13 read , " Given the orthocentre , the centre of the nine - points - circle , and the middle point of the base , construct the triangle . " October , 1892 . H. S. ...
... passes through the three escribed centres . " Page 284. In place of Ex . 13 read , " Given the orthocentre , the centre of the nine - points - circle , and the middle point of the base , construct the triangle . " October , 1892 . H. S. ...
Page 23
... pass , XY the st . line in which the base is to be . At X draw XZ equal to the given altitude . Through Z draw ZKL par1 . to XY . Then by Ex . 7 , page 49 , draw through PQ two lines PK , QK making equal angles with ZKL . Produce KP ...
... pass , XY the st . line in which the base is to be . At X draw XZ equal to the given altitude . Through Z draw ZKL par1 . to XY . Then by Ex . 7 , page 49 , draw through PQ two lines PK , QK making equal angles with ZKL . Produce KP ...
Page 32
... passes through A. In this case any pt . in DE may be taken as the vertex of the required A , and the number of solutions is unlimited . 5. Let ABC be the given △ on base BC . Draw AD par1 . to Bisect BC at E and draw ED perp . to BC ...
... passes through A. In this case any pt . in DE may be taken as the vertex of the required A , and the number of solutions is unlimited . 5. Let ABC be the given △ on base BC . Draw AD par1 . to Bisect BC at E and draw ED perp . to BC ...
Page 43
... pass through H. Hence BE . EF = EH2 = K2 . [ Proof as in II . 14. ] 40. Let AB and X be the two given st . lines . Analysis . Let AB be bisected at P and produced to Q. AQ . QB - PQ2 - PB2 . [ 11. 6. ] AQ . QB = X2 . Then Required Hence ...
... pass through H. Hence BE . EF = EH2 = K2 . [ Proof as in II . 14. ] 40. Let AB and X be the two given st . lines . Analysis . Let AB be bisected at P and produced to Q. AQ . QB - PQ2 - PB2 . [ 11. 6. ] AQ . QB = X2 . Then Required Hence ...
Page 44
... passing through both centres . 2. Let the bisector of BAC cut BC in D. ADB , ADC , it follows that DB = DC and ADB = .. AD passes through the centre . Then in As ADC [ 1. 4 ] . 3. If the chords are not par1 . , bisect each at rt . s ...
... passing through both centres . 2. Let the bisector of BAC cut BC in D. ADB , ADC , it follows that DB = DC and ADB = .. AD passes through the centre . Then in As ADC [ 1. 4 ] . 3. If the chords are not par1 . , bisect each at rt . s ...
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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