A Key to the Exercises and Examples Contained in a Text-book of Euclid's Elements: Books I.- VI. and XI.Macmillan, 1905 - 229 pages |
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Results 1-5 of 40
Page 59
... fixed point ; .. the locus of A is a circle , whose centre is at X. 31 . Since CB is a median of the But ACD , .. DC2 + CA2 = 2AB2 + 2BC2 [ Ex . 24 , CA2 AB2 [ Hyp . ] = .. DC2 = AB2 + 2BC2 . p . 161 ] . 32. Let ABC be a Art . angled at ...
... fixed point ; .. the locus of A is a circle , whose centre is at X. 31 . Since CB is a median of the But ACD , .. DC2 + CA2 = 2AB2 + 2BC2 [ Ex . 24 , CA2 AB2 [ Hyp . ] = .. DC2 = AB2 + 2BC2 . p . 161 ] . 32. Let ABC be a Art . angled at ...
Page 61
... point X in BF , or BF produced , draw XY perp . to BF , making XY equal to K. Through Y draw YHH ' par ' . to BF ... fixed point , Q is determined . 41 . This is the same as dividing a line externally in medial section . [ See Ex . 21 ...
... point X in BF , or BF produced , draw XY perp . to BF , making XY equal to K. Through Y draw YHH ' par ' . to BF ... fixed point , Q is determined . 41 . This is the same as dividing a line externally in medial section . [ See Ex . 21 ...
Page 79
... fixed , and B approaches A. Then the perp . EF ultimately coincides with the perp . from A to the tangent at A ; and ... point of contact . 3. If the pts . of intersection of two come to coincide , the proof that they cannot have the same ...
... fixed , and B approaches A. Then the perp . EF ultimately coincides with the perp . from A to the tangent at A ; and ... point of contact . 3. If the pts . of intersection of two come to coincide , the proof that they cannot have the same ...
Page 82
... fixed point ; .. the locus of P is a whose radius is equal to half the radius of the given . 15. Complete the Os of which the equal segments are parts . Let C and D be their centres , C and Q being on opp . sides of AB , also P and D ...
... fixed point ; .. the locus of P is a whose radius is equal to half the radius of the given . 15. Complete the Os of which the equal segments are parts . Let C and D be their centres , C and Q being on opp . sides of AB , also P and D ...
Page 83
... fixed length , P its middle point , and O the centre of the . Join OP . Then OP is perp . to AB [ III . 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 ...
... fixed length , P its middle point , and O the centre of the . Join OP . Then OP is perp . to AB [ III . 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 ...
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
AB² ABCD AC² angles AP² arc AC AX² base BC BC² bisector bisects centre chord circum collinear common tangent concyclic constant cutting the given diagonals diam diameter diff draw drawn equiangular equilat fixed point given base given point given ratio given st greater half Hence identically equal inscribed intersect isosceles Join Let AB Let ABC Let AX locus middle point middle pt orthocentre par¹ parm pass pedal triangle perp plane polar produced Radical Axis radius equal rect respectively rhombus segment shewn sides Similarly solutions subtended sum of sqq tangent touch triangle vert vertex