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" Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Side 262
av Euclides - 1834
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The Metaphysics of the School: Book4. Principles of being; Book 5. Causes of ...

Thomas Harper - 1881
...Principle in order of reduction. PROLEGOMENON I. The Law of equality is usually expressed in this wise: Things which are equal to the same are equal to one another. Here, at length, a Principle is set before us, which seems to carry on its front a capacity for becoming...
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Christian evidence lectures

Christian evidence society - 1879
...things, this maxim we apply to the actual material of this world. Did we apply, eg, the axiom that things which are equal to the same are equal to one another to actual things, we should first have to ascertain the fact that the two things were exactly equal,...
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Works, Volum 3

Herbert Spencer - 1881
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — "Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...
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Pamphlets, Religious: Miscellaneous, Volum 14

1881
...premises, the science of mathematics is " fundamentally wrong," and that it is an error to believe that things which are equal to the same, are equal to one another, or that the whole is greater than its parts. Accordingly, were it true that Freethinkers differed from...
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Macmillan's Magazine, Volum 43

1881
...always begin with an invocation to the Pleiades, thus fixing the original November date of the feast. " Things which are equal to the same are equal to one another." I have already adduced evidence to show that the Serbian Christmas feast is substantially a more primitive...
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The Principles of Psychology, Volum 2

Herbert Spencer - 1882
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — " Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...
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The World's Cyclopedia of Biography, Volum 3

1883
...straight and crooked would have no more meaning to him than red and blue to the Wind. The axiom, that things which are equal to the same are equal to one another, is only a particular case of the predication of similarity ; if there were no impressions, it is obvious...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volum 1

Euclides - 1884
...angles CBE, EBA, ABD. But the angles CBE, EBD have been proved equal to the same three angles ; and things which are equal to the same are equal to one another ; therefore the angles CBA, ABD are equal to the angles CBE, EBD. ' (Ax. 1) But CBE, EBD are two right...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...but it has been proved that CA is equal to AB ; therefore CA, CB, are each of them equal to AB ; but things which are equal to the same are equal to one another ; therefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another ; and the triangle ABC...
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The Fundamental Science

Henry James Clarke - 1885 - 265 sider
...the unreasonableness of such a desire. What then am I to do ? I need not ask how I am to prove that things which are equal to the same are equal to one another : this truth is one of which I have a clear perception ; I feel sure that I know it by immediate intuition,...
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