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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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Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 256 sider
...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 equal to each other. 8. Magnitudes which coincide with each other, that is, which exactly fill the same space,...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 sider
...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 Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 470 sider
...are equal. 4. When equals are added to unequals the wholes are unequal. 5. When equals are taken from unequals the remainders are unequal. 6. Things which...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. Every...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - 1860 - 1020 sider
...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 are halves of the same thing, are equal. 8. Every whole is equal...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 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. . -,3 7. Things which are halves of the same, are equal. -. , 8. Magnitudes which coincide...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 532 sider
...from unequals, the remainders will be unequal. 6. Things which are double of the same thing, or of 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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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 518 sider
...from unequals, the remainders will be unequal. 6. Things which are double of the same thing, or of 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's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 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 Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 504 sider
...from unequals, the remainders will be unequal. 6. Things which are double of the same thing, or of 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's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 sider
...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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