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" THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders are equal. "
The philosophical and mathematical commentaries of Proclus ... on the first ... - Page 11
by Proclus (Diadochus.) - 1789
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...are the Postulates, to geometrical magnitudes. AXIOMS. I. Things which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders are equal. IV. If equals and unequals be added together, the wholes...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 pages
...be described from any centre, at any distance from that centre. AXIOMS. I. Things equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the rwnainderi are equal. IV. If equals be added to unequals, the wholes are...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...centre, at any distance from that centre. AXIOMS. I. Magnitudes which are equal to the same magnitude, are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are...
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The Largest Number Smaller Than Five

Chris Hobbs, Richard Perryman - 2007 - 130 pages
...proved. The first few of these are: (i) Things which are equal to the same thing are equal to each other. (ii) If equals be added to equals, the wholes are equal. (iii) If equals be taken from equals, the remainders are equal. In these axioms, Euclid of Alexandria is talking about...
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