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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 and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...equals, the remainders are equal. 4. If equals are added to unequals, the wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which are doubles of the same thing are equal to each other. 7. Things which are halves of the same thing are...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be takea from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to one another. 7. Things which are another. halves of the same, are equal to one II. The...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...equals, the remainders are equal. 4. If equals are added to unequals, the wholes are unequal. 5. If equals are taken from unequals, the remainders are unequal. 6. Things which are doubles of the same thing are equal to each other. 7. Things which are halves of the same thing are...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 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. . -,3 7. Things which are halves of the same, are equal. -. , 8. Magnitudes which coincide...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - Mathematics - 1860 - 1014 pages
...are taken from equals, the remainders are equ.iL 4. When equals ara added to unequals, the n liólos are unequal. 5. When equals are taken from unequals, the remainders are 6. Things which are double of the same thing, or equal things, are <»rH ш each other. 7. Things which...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 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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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 pages
...remainders are equal. 4. If equals be added to unequals, the wholes are unequal. •I. 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. II. The...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 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, triple, etc., of the same thing, or of equal things, are equal to one another. 7. Things which are...
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An English primer; compiled under the superintendence of E.C. Lowe

Edward Clarke Lowe - 1866 - 172 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 Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 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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