The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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Page 17
... obtained by sub- stituting a for b by virtue of their equality as ex- pressed in the first equation ab , the second equation b c being that in which substitution is C effected . One equation is active and the other is THE TRUE PRINCIPLE ...
... obtained by sub- stituting a for b by virtue of their equality as ex- pressed in the first equation ab , the second equation b c being that in which substitution is C effected . One equation is active and the other is THE TRUE PRINCIPLE ...
Page 18
... obtained by a similar act of reasoning in which b c is the active equation , as shown below : - = b = c hence ။ a a . My warrant for this view of the matter is to be found in the fact that the negative form of the axiom is now easily ...
... obtained by a similar act of reasoning in which b c is the active equation , as shown below : - = b = c hence ။ a a . My warrant for this view of the matter is to be found in the fact that the negative form of the axiom is now easily ...
Page 22
... obtain the equation a = c + p + q , which , owing to the like signs of p and q , is a representation in a more exact and clear manner of the conclusion a > c . On the other hand , the formula a > b < e would evidently lead to the ...
... obtain the equation a = c + p + q , which , owing to the like signs of p and q , is a representation in a more exact and clear manner of the conclusion a > c . On the other hand , the formula a > b < e would evidently lead to the ...
Page 23
... obtained without the use of an equation , a disguised sub- stitution is really performed by the mind , exactly such as represented in the equations . But I can only assert my belief of this from the examina- tion of the process in my ...
... obtained without the use of an equation , a disguised sub- stitution is really performed by the mind , exactly such as represented in the equations . But I can only assert my belief of this from the examina- tion of the process in my ...
Page 26
... obtaining the equation , = Whatever has exchangeable value whatever is useful , transferable , and limited in supply . Where we have one affirmative proposition or equation , and one negative proposition , we still find the former ...
... obtaining the equation , = Whatever has exchangeable value whatever is useful , transferable , and limited in supply . Where we have one affirmative proposition or equation , and one negative proposition , we still find the former ...
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Common terms and phrases
A B C D abacus ABCDE affirmative proposition Algebra analogy applied Aristotle ARISTOTLE'S DICTUM ARITHMETIC assert axiom BEGINNERS Bentham Boole Boole's BROOKE FOSS WESTCOTT CALCULUS Cambridge canon Christ's College Church Clifton College cloth combinations conclusion CONIC SECTIONS consists copula Crown 8vo denote EDUCATIONAL BOOKS Edward Thring ELEMENTARY TREATISE English equal Euclid Examination Papers Examples expression Extra fcap fallacy Fellow of St follows forms of reasoning formula GEOMETRY George Bentham Grammar Head Master hence HISTORY identity illustrated indirect inequalities inference Iron J. S. Mill John's College late Fellow Latin law of duality Laws of Thought ledge logicians ment metals are elements method MIXED MATHEMATICS ordinary oxygen predicate premises problem quantification quantity reader represented Schools Second Edition self-evident SHILLING BOOK slips student substitution of similars syllogism symbols System of Logic thing Third Edition tion triangle true undecomposable substance
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