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" AB; but things which are equal to the same are equal to one another... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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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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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...triangle. Because A is the centre of BCD, AC is equal to AB ; and because B is the centre of ACE, BC'is equal to BA, but it has been proved that CA is equal to AR ; therefore CA, CB, are each of them equal to AB , but things which are equal to the same are equal...
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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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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885
...because B 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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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 sider
...because B 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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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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Christian Thought, Volum 1

1886
...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 - 1887 - 188 sider
...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 - 1889 - 193 sider
...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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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...ie Elementary Problems whose construction it is to be taken for granted we can effect. AXIOMS.1 1. Things which are equal to the Same are Equal to One Another. 2. If equals te Added to equals, the Wholes are equal. 3. If equals be Taken from equals, the Remainders...
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