A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page vi
... 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 .
... 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 46
... touch the given O. Then the with centre C and radius CP will touch the given at P. And OC = the sum or the differ- ence of OP and CP . Hence the required locus is a circle with centre O and radius equal to the sum or the difference of ...
... touch the given O. Then the with centre C and radius CP will touch the given at P. And OC = the sum or the differ- ence of OP and CP . Hence the required locus is a circle with centre O and radius equal to the sum or the difference of ...
Page 47
... touch the given circle at P : but , if the given radius is equal to the radius of the given circle , one of the two circles so described will coincide with the given circle . 4. Let A be the centre of the given O , B the given pt . Let ...
... touch the given circle at P : but , if the given radius is equal to the radius of the given circle , one of the two circles so described will coincide with the given circle . 4. Let A be the centre of the given O , B the given pt . Let ...
Page 48
... touching ex- ternally at C. Then ACB is a st . line [ 111. 12 ] . Draw the parallel diameters DAE , FBG . Then , because AD = AC , .. LADC = 2 ACD , .. ext . EAC = twice ACD . Similarly , CBF = twice BCG . But EAC = CBF , because AE ...
... touching ex- ternally at C. Then ACB is a st . line [ 111. 12 ] . Draw the parallel diameters DAE , FBG . Then , because AD = AC , .. LADC = 2 ACD , .. ext . EAC = twice ACD . Similarly , CBF = twice BCG . But EAC = CBF , because AE ...
Page 50
... touching AB and AC in B and C. Then OB = OC , OA is common , and $ ABO , ACO are rt . 43 [ III . 18 ] , .. in the rt . - angled △ AOB , AOC , OAB = △ OAC [ Ex . 12 , p . 91 ] . 8 2. Let AO cut BC in D. .. in △ 50 KEY TO EUCLID .
... touching AB and AC in B and C. Then OB = OC , OA is common , and $ ABO , ACO are rt . 43 [ III . 18 ] , .. in the rt . - angled △ AOB , AOC , OAB = △ OAC [ Ex . 12 , p . 91 ] . 8 2. Let AO cut BC in D. .. in △ 50 KEY TO EUCLID .
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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