Page:Carroll - Euclid and His Modern Rivals.djvu/26

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xxii
ARGUMENT OF DRAMA.

PAGE

Theorem 'Lines, sepcodal to a thirds are so to each other,' discussed, and condemned as a 'Petitio Principii'
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121
Axiom 'Angle may be transferred, preserving directions of sides' discussed
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122
If angle be variable, it involves fallacy 'A dicto secundum Quid ad dictum Simpliciter'
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123
If it be constant, the resulting Theorem (virtually identical with the Axiom) involves fallacy 'Petitio Principii'
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125
If angle be constant, the Axiom involves two assumptions : viz. that
 
(1)
there can be a Pair of different Lines that make equal angles with any transversal
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127
(2)
Lines, which make equal angles with a certain transversal, do so with any transversal
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128
Axiom rejected
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129
Ideas of 'direction' discussed
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130
Theory of 'direction' unsuited for teaching
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131
Test for meeting of finite Lines discussed:—
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132
 
it virtually involves Euclid's Axiom
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133
 
or if not, it causes hiatus in proofs
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133
List of Euclid's Propositions which are omitted
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134
General survey of book:—
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135
 
A false Corollary
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135
 
A plethora of negatives
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136
 
A superfluous datum
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137
 
Cumbrous proof of Euc. I. 24
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137
 
An unintelligible Corollary
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138
 
A unique 'Theorem of equality'
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139
 
A bold assumption
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139
 
Two cases of 'Petitio Principii'
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139
 
A Problem 3½ pages long
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139