Page:Carroll - Euclid and His Modern Rivals.djvu/27

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ARGUMENT OF DRAMA.
xxiii

PAGE

 
A fifth case of 'Petitio Principii'
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140
 
A sixth
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141
Summing-up, and rejection of Manual
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141

§ 2. Pierce.

Treatment of Line
....................................................................................................................................................................................................................................................
144
Introduction of Infinitesimals
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145
Treatment of Parallels
....................................................................................................................................................................................................................................................
145
Angle viewed as 'difierence of direction'
....................................................................................................................................................................................................................................................
146
Assumption of Axiom 'different Lines may have the same direction'
....................................................................................................................................................................................................................................................
147
List of Euclid's Theorems which are omitted
....................................................................................................................................................................................................................................................
148
Manual not adapted for beginners
....................................................................................................................................................................................................................................................
148

§ 3. Willock.

Treatment of Parallels
....................................................................................................................................................................................................................................................
150
Virtual assumption of Axiom 'different Lines may have the same direction'
....................................................................................................................................................................................................................................................
150
Assumption of Axiom 'separational Lines have the same direction'
....................................................................................................................................................................................................................................................
152
General survey of book:—
....................................................................................................................................................................................................................................................
153
 
Difficulties introduced too soon
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153
 
Omission of 'coincidental' Lines
....................................................................................................................................................................................................................................................
155
 
'Principle of double conversion' discussed, and condemned as illogical
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155
 
Mysterious passage about 'incommensurables'
....................................................................................................................................................................................................................................................
157
Manual rejected
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157