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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 ... - Page 306
by Euclid - 1835 - 513 pages
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The Principles of Psychology, Volume 2

Herbert Spencer - Psychology - 1882 - 722 pages
...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, Volume 3

Biography - 1883 - 836 pages
...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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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 pages
...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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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...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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The Fundamental Science

Henry James Clarke - Philosophical theology - 1885 - 332 pages
...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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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885 - 340 pages
...AB . BE is equal to the figure AE. Hence the rectangle AB . CB is equal to the figure AE. And since things which are equal to the same are equal to one another, the rectangle AC . CB, together with the square, on CB, is equal to the rectangle AB . CB. , Or thus...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...is the centre of the circle ACE, BC is equal to BA. Hence we have proved. AC = AB, and BC = AB. But things which are equal to the same are equal to one another (Axiom i.) ; therefore AC is equal to BC ; therefore the three lines AB, BC, CA are equal to one another....
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Christian Thought, Volume 1

Apologetics - 1886 - 436 pages
...same time be and not be ; (2) that if equals be added to equals the wholes are equal ; and (3) that things which are equal to the same are equal to one another. It so happens that each of these propositions which he has assumed to be true is, if true, much more...
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Picture Logic

Alfred James Swinburne - Logic - 1887 - 224 pages
...middle terms is called the minor premiss. The former always comes first. Unless the principle that " things which are equal to the same are equal to one another " were true, it would not follow that " Socrates " and " mortal," which are equal to the same (" man...
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Alluring Absurdities: Fallacies of Henry George

Michael William Meagher - Economics - 1889 - 226 pages
...says the trunk lines of railroads unite to raise rates, just as robbers unite to plunder in concert. Things which are equal to the same are equal to one another. If, then, railroad companies unite to raise rates, and workingmen unite to raise rates of wages, and...
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