A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 23
... Note to Ex . 1. ] 3. See fig . on p . 89. Let AB be the given sum , then using the construction and proof given on p . 90 , it is shewn that AX = XC , and BX = BC . Thus CBX is the required triangle . 5. This is clearly a particular ...
... Note to Ex . 1. ] 3. See fig . on p . 89. Let AB be the given sum , then using the construction and proof given on p . 90 , it is shewn that AX = XC , and BX = BC . Thus CBX is the required triangle . 5. This is clearly a particular ...
Page 43
... , Q is determined . 41. This is the same as dividing a line externally in medial section . [ See Ex . 21 , p . 146 , and p . 139 , note . ] 42. Draw the rect . ABDH , contained by AB THEOREMS AND EXAMPLES ON BOOK II . PAGE 148. 43.
... , Q is determined . 41. This is the same as dividing a line externally in medial section . [ See Ex . 21 , p . 146 , and p . 139 , note . ] 42. Draw the rect . ABDH , contained by AB THEOREMS AND EXAMPLES ON BOOK II . PAGE 148. 43.
Page 66
... NOTE . The Ex . 36 , p . 228. ] BOC , POQ = one rt . angle + half the at A. [ See 7. Let ABCD be the quad ' . , and P , Q , R , S the points of contact of the sides AB , BC , CD , DA . Then ASAP [ III . 17 , Cor . ] and DS = DR ; .. by ...
... NOTE . The Ex . 36 , p . 228. ] BOC , POQ = one rt . angle + half the at A. [ See 7. Let ABCD be the quad ' . , and P , Q , R , S the points of contact of the sides AB , BC , CD , DA . Then ASAP [ III . 17 , Cor . ] and DS = DR ; .. by ...
Page 67
... NOTE . This problem is a special case of the following : If any two circles are touched one internally and one externally by a third circle , the sum or difference of the distances of this third circle from the centres of the given ...
... NOTE . This problem is a special case of the following : If any two circles are touched one internally and one externally by a third circle , the sum or difference of the distances of this third circle from the centres of the given ...
Page 82
... NOTE . The locus of in Ex . 36 and the locus of 1 are conjugate arcs of the same O. 39. Let the bisectors meet at X. Then △ PAB , QBA together two rt . angles [ 1. 29 ] . = = .. △ XAB , XBA together one rt . angle [ Hyp ...
... NOTE . The locus of in Ex . 36 and the locus of 1 are conjugate arcs of the same O. 39. Let the bisectors meet at X. Then △ PAB , QBA together two rt . angles [ 1. 29 ] . = = .. △ XAB , XBA together one rt . angle [ Hyp ...
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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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