A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 45
... passes through the centre . 11. The st . line , through the centre , perp . to one of the par1 . chords , is perp . to all of them [ 1. 29 ] . And this st . line bisects all the chords . Hence it is the required locus . 12. Let the two ...
... passes through the centre . 11. The st . line , through the centre , perp . to one of the par1 . chords , is perp . to all of them [ 1. 29 ] . And this st . line bisects all the chords . Hence it is the required locus . 12. Let the two ...
Page 47
... pass through B. But if CX is par1 . to the given st . line no circle can be described as required . Finally , if CX cuts the given st . line in X , the circle described with centre X and radius CA or CB is the circle required . = Draw ...
... pass through B. But if CX is par1 . to the given st . line no circle can be described as required . Finally , if CX cuts the given st . line in X , the circle described with centre X and radius CA or CB is the circle required . = Draw ...
Page 48
... passes through C. Then 9. Let A , B be the centres of the two Os ; and D , E the pts . where AB cuts the circles . Let PQ be any other st . line cutting the circles in P and Q. Let QA cut the ' A ' circle in R. QP > QR ( III . 8 ) ...
... passes through C. Then 9. Let A , B be the centres of the two Os ; and D , E the pts . where AB cuts the circles . Let PQ be any other st . line cutting the circles in P and Q. Let QA cut the ' A ' circle in R. QP > QR ( III . 8 ) ...
Page 53
... pass . pt . on the given st . line which the O is to touch . Join AB . BC perp . to the given line , and make BAC = ABC . CA = CB . .. C is the centre of the required . [ See solution of Ex . 28 , p . 220. ] Then 19. Let the line drawn ...
... pass . pt . on the given st . line which the O is to touch . Join AB . BC perp . to the given line , and make BAC = ABC . CA = CB . .. C is the centre of the required . [ See solution of Ex . 28 , p . 220. ] Then 19. Let the line drawn ...
Page 54
... and C on CA and AB , P , Q , R , Y and P , Q , R , Z are concyclic . But only one circle can pass through P , Q , R [ III . 10 ] . Hence the six pts . P , Q , R , X , Y , Z are concyclic . Page 196 . DAB on arc BD = L ADC 54 KEY TO EUCLID .
... and C on CA and AB , P , Q , R , Y and P , Q , R , Z are concyclic . But only one circle can pass through P , Q , R [ III . 10 ] . Hence the six pts . P , Q , R , X , Y , Z are concyclic . Page 196 . DAB on arc BD = L ADC 54 KEY TO EUCLID .
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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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