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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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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 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 one another. 8. Magnitudes...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 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 or of equals, are equal to one another. 7. Things, which are halves of the same or of equals, are equal...
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Mechanics' Magazine, and Journal of the Mechanics' Institute, Volume 4

Industrial arts - 1835 - 398 pages
...equate are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders are equal. 4. When equals are added to unequals, the wholes are unequal. 6. When equals are taken from unequals, the remainders are unequal. 6. Thinge which are double of the...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 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 one another. 8. Magnitudes...
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Chambers's Information for the People, Volume 2

William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals he 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 came, are equal to one another. 8. Magnitudes...
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842 - 744 pages
...equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from uneqnals, 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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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...equal. 4. If to unequals, equals be added, the wholes are unequal. 5. If from unequals, equals be taken, the remainders are unequal. 6. Things which are double of the same, or of equals, are equal to one another. 7. Things which are halves of the same, or of equals, are equal...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders are equal. 4. When equals are added to 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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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 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 one another. 8. Magnitudes...
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An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables ...

Janet Taylor - Nautical astronomy - 1851 - 674 pages
...equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders are equal 4. When equals are added to unequals, the...unequals, the remainders are unequal. 6. Things which are like multiples of the same, or of equal things, are equal to each other. 7. Things which are like parts...
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