Page:Carroll - Euclid and His Modern Rivals.djvu/25

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ARGUMENT OF DRAMA.
xxi

PAGE

Extension of limit of 'angle' to sum of four right angles
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99
'Straight' angles
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101
Meaning of 'direction'
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103
'Opposite' directions
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105
'Same' and 'different' directions
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106
Axiom 'different Lines may have the same direction,' discussed
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108
Property 'same direction,' when asserted of different Lines, can neither be defined, nor constructed, nor tested
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109
'Separational directions' not identical with 'identical directions'
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110
Virtual assumption of 'separational Lines are real' (which Euclid proves in I. 27), as Axiom
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113
Axiom 'different Lines may have different directions' discussed
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114
Axiom 'different Lines may have the same direction,' rejected, and Axiom 'different Lines may have different directions' granted with limitations
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115
Axiom 'different Lines which meet one another have different directions' granted
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115
Axiom 'Lines with different directions would meet' discussed
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115
and rejected
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116
Diagram of 'same' and 'different' directions condemned
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117
'Different but with same direction' accepted as (ideal) definition of Pair of Lines
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118
'Parallel,' as used by Wilson, to be replaced by term 'sepcodal'
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118
Definition discussed
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119
Theorem 'sepcodal Lines do not meet' accepted
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121