A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements |
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Page 40
... middle point of AC and BD [ p . 64 , Ex . 5 ] . Then by the last Ex . , from △ ABC , AB2 + BC2 = 2A02 + 20B2 . Also ... middle points of the sides AB , BC , CD , DA . Then PQRS is a parm . [ Ex . 9 , p . 97 ] and AC = 2PQ , also BD ...
... middle point of AC and BD [ p . 64 , Ex . 5 ] . Then by the last Ex . , from △ ABC , AB2 + BC2 = 2A02 + 20B2 . Also ... middle points of the sides AB , BC , CD , DA . Then PQRS is a parm . [ Ex . 9 , p . 97 ] and AC = 2PQ , also BD ...
Page 57
... centre of the given ☺ . If the pt . is without the ce , the locus is confined within the two tangents to the O. If the pt . is on the Oce , the locus is the on the radius through the point as diameter . [ See solution of Ex . 40 , p ...
... centre of the given ☺ . If the pt . is without the ce , the locus is confined within the two tangents to the O. If the pt . is on the Oce , the locus is the on the radius through the point as diameter . [ See solution of Ex . 40 , p ...
Page 59
... centre is the middle pt . of the base and radius equal to the given median ; ( iv ) The perp . to the base drawn through the given point . 3. Because arc AP : = arc BP ; .. LACP = BCP . 4. Because .. ACB = K , and AXB = 1K , XBC = K [ 1 ...
... centre is the middle pt . of the base and radius equal to the given median ; ( iv ) The perp . to the base drawn through the given point . 3. Because arc AP : = arc BP ; .. LACP = BCP . 4. Because .. ACB = K , and AXB = 1K , XBC = K [ 1 ...
Page 64
... point , B the centre of the O , Q any point on the Oce , and P the middle point of AQ . quired to find the locus of P. Bisect AB at O , and join OP . Then because O , P are the middle points of AB and AQ , .. OP is half of QB [ Ex . 3 ...
... point , B the centre of the O , Q any point on the Oce , and P the middle point of AQ . quired to find the locus of P. Bisect AB at O , and join OP . Then because O , P are the middle points of AB and AQ , .. OP is half of QB [ Ex . 3 ...
Page 65
... middle point , and O the centre of the . Join OP . Then OP is perp . to AB [ 11. 3 ] , and is of fixed length for all positions of AB [ III . 14 ] ; .. the locus of P is a concentric O , which is touched by AB at P , since AB is perp ...
... middle point , and O the centre of the . Join OP . Then OP is perp . to AB [ 11. 3 ] , and is of fixed length for all positions of AB [ III . 14 ] ; .. the locus of P is a concentric O , which is touched by AB at P , since AB is perp ...
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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