Page:Carroll - Euclid and His Modern Rivals.djvu/26
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xxii
ARGUMENT OF DRAMA.
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Theorem 'Lines, sepcodal to a thirds are so to each other,' discussed, and condemned as a 'Petitio Principii'
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121 |
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Axiom 'Angle may be transferred, preserving directions of sides' discussed
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122 |
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If angle be variable, it involves fallacy 'A dicto secundum Quid ad dictum Simpliciter'
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123 |
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If it be constant, the resulting Theorem (virtually identical with the Axiom) involves fallacy 'Petitio Principii'
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125 |
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If angle be constant, the Axiom involves two assumptions : viz. that
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| (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 |
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Axiom rejected
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129 |
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Ideas of 'direction' discussed
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130 |
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Theory of 'direction' unsuited for teaching
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131 |
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Test for meeting of finite Lines discussed:—
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132 |
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it virtually involves Euclid's Axiom
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133 |
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or if not, it causes hiatus in proofs
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133„ |
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List of Euclid's Propositions which are omitted
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134 |
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General survey of book:—
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135 |
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A false Corollary
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135„ |
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A plethora of negatives
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136 |
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A superfluous datum
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137 |
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Cumbrous proof of Euc. I. 24
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137„ |
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An unintelligible Corollary
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138 |
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A unique 'Theorem of equality'
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139 |
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A bold assumption
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139„ |
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Two cases of 'Petitio Principii'
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139„ |
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A Problem 3½ pages long
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139„ |