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" If equal quantities be divided by the same quantity, or by equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed. "
An Elementary Treatise on Algebra: For the Use of Students in High Schools ... - Page 3
by Thomas Sherwin - 1841 - 300 pages
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...supposition made either in the enunciation of a proposition, or in the course of a demonstration. Axioms. 22. Two quantities, each of which is equal to a third, are equal to one another. 23. The whole is greater than its part. 24. The whole is equal to the sum of all its parts....
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...made either in the enunciation of a proposition, or in the course of a demonstration. / 9 Axioms. 22. Two quantities, each of which, is equal to a third, are equal to one another. 23. The whole is greater than its part. 24. The whole is equal to the sum of all its parts....
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...supposition made either in the enunciation of a proposition, or in the course of a demonstration. Axioms. 22. Two quantities, each of which is equal to a third, are equal to one another. 23. The whole is greater than its part. 24. The whole is equal to the sum of all its parts....
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...other two ratios make a proportion. For ratios are nothing more than fractions, and two fractions, each of which is equal to a third, are equal to each other. Therefore these two make a proportion. Thus if we have 6 : 9 : • 10 : 15 and 6 : 9 : : 16 : 24, then...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...means the square-root of the product of A and B, or the mean proportional between them. Axioms. 22. Two quantities, each of which is equal to a third, are equal to each other. 23. The whole is greater than any of its parts. 24. The whole is equal to the sum of all its parts....
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1831 - 166 pages
...a proportion. For ratios are / nothing more than fractions, and two fractions, each • / t \'fl .k of which is equal to a third, are equal to each other. Therefore these two make a proportion. Thus if we have 6 : 9 : : 10 : 15 and 6 : 9 : : 16 : 24, then...
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Introductory Discourse, and the Lectures Delivered Before the ..., Volume 5

American Institute of Instruction - Education - 1835 - 318 pages
...proportion, he seldom sees any reason why this is the case ; but after having recognised the axiom, that two quantities, each of which is equal to a third, are equal to each other, he readily perceives, that, if one member of one equation is equal to one member of another, the two...
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Remains of Rev. Joshua Wells Downing: With a Brief Memoir

Joshua Wells Downing - Methodism - 1841 - 346 pages
...disbelieve them without doing violence to our nature. Thus we believe in certain first truths; as, " Two quantities, each of which is equal to a third, are equal to another." " The whole is greater than its part." " The whole is equal to the sum of all its parts,"...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...supposition made either in the enunciation of a proposition, or in the course of a demonstration. Axioms, 22. Two quantities, each of which is equal to a third, are equal to one another. 23. The whole is greater than its part. 24. The whole is equal to the sum of all its parts....
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Remains of Rev. Joshua Wells Downing ...

Joshua Wells Downing - Methodist Church - 1842 - 346 pages
...disbelieve them without doing violence to our nature. Thus we believe in certain first truths; as, " Two quantities, each of which is equal to a third, are equal to another." " The whole is greater than its part." " The whole is equal to the sum of all its parts,"...
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