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" If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same are equal to one another. "
A Course of Mathematics: For the Use of Academies as Well as Private Tuition ... - Page 281
by Charles Hutton - 1831
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877 - 58 pages
...the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...equals the remainders are equal. 4. When equals are added to unequals the sums are unequal. 5. Wben equals are taken from unequals the remainders are unequal. 6. Things which are double the same thing, or equal things, are equal to each other. 7. Things which are halves of the same thing,...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 pages
...the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8....
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...the remainders are equal. 4. If equals be added to uncquala the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8....
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...equals are taken from equals the remainders are equal. 4. When equals are added to unequals the sums are unequal. 5. When equals are taken from unequals...remainders are unequal. 6. Things which are double the same thing, or equal things, are equal to each other. 7. Things which are halves of the same thing,...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...3. When equals are taken from equals the remainders are equal. 4. When equals are added to uijequals the wholes are unequal. 5. When equals are taken from...remainders are unequal. 6. Things which are double the same thing, or equal things, are equal to each other. 7. Things which are halves of the same thing,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...the remainders are equal. 4. If equals bo added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same tiling are equal to one another. 8....
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to cue another. Although...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same thing are equal to one another. 7. Things which are halves of the same thing are equal to one another. 8....
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which are doubles of equal things are equal. 1. Things which are halves of equal things are equal. 8. The whole...
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