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" If equals be added to equals, the wholes are equal. 3. 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... "
A Course of Mathematics for the Use of Academies: As Well as Private Tuition - Side 281
av Charles Hutton - 1825
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 sider
...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 one another. 8. Magnitudes...
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Pure mathematics, Volum 1

Edward Atkins - 1874 - 426 sider
...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 one another. 8. Magnitudes...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 436 sider
...unequal. 5. When 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, or of equal things, are equal to each other. * 8. The whole is greater than any of its parts. 9. The...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877 - 58 sider
...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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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 sider
...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 - 1880 - 426 sider
...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 - 1881 - 266 sider
...unequal. 5. When 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, or of equal things, are equal to each other. 8. The whole is greater than any of its parts. 9. The...
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Intellectual and Practical Lightning Calculator: The Unity and Decimal System

John Alexander Henderson - 1882 - 232 sider
...5. If equals be taken from unequals, the remainders will be unequal. 6. Things which are doubles of equal things, are equal to each other. 7. Things which are halves of equal things, are equal to each other. 8. The whole is greater than any of its parts. 9. The whole...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 sider
...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 ..., Volum 1

Euclides - 1884 - 182 sider
...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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