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