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