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" If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. "
The philosophical and mathematical commentaries of Proclus ... on the first ... - Page 12
by Proclus (Diadochus.) - 1789
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 588 pages
...wholes arĀ« equal. III. If equals be taken from equals, the remainder* are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainder are unequal. VI. Doubles of the same are equal to one another. VII. Halves of the same are...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...the wholes are equal. m. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal, V. If equals...be taken from unequals, the remainders are unequal. VL Things which are double of the same, are equal to one another. VIL Things which are halves of the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - Euclid's Elements - 1881 - 236 pages
...wholes are equal. m. If equals be taken from equals, the remainders are equal. IV. If equals be addod to unequals, the wholes are unequal. V. If equals...be taken from unequals, the remainders are unequal. yfc Things which are double of the same, are equal to oae another VH Things which ate halves of the...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...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 unequal. V. If equals...taken from unequals, the remainders are unequal. VI. . . Magnitudes which are double of the same magnitude, are equal to one another. VII. Magnitudes which...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 pages
...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 unequal. V. If equals...taken from unequals, the remainders are unequal. VI. Doubles of the same are equal to one another. VII. Halves or the same are equal to one another. VIII....
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Hawkins' Mechanical Dictionary: A Cyclopedia of Words, Terms, Phrases and ...

Nehemiah Hawkins - Industrial arts - 1909 - 714 pages
...remainders are equal. IV. When equals are added to nnequals the wholes are unequal. V. When equals are taken from unequals the remainders are unequal. VI. Things which are double of the same thine, or equal things are equal to each other. VII. Things which are halves of the same thing,...
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