If the same operations are performed upon equal quantities, the results will be equal. Hence, — Both members of an equation may be increased, diminished, multiplied, or divided by the same quantity, without destroying the equality. New Elementary Algebra - Page 105by Benjamin Greenleaf - 1879Full view - About this book
| Benjamin Peirce - Algebra - 1837 - 300 pages
...83. The reduction and solution of all equations depends upon the self-evident proposition, that Both members of an equation may be increased, diminished^...the same quantity, without destroying the equality. 84. Corollary. If all the terms of an equation have a common factor, this factor may be suppressed.... | |
| Benjamin Peirce - Algebra - 1837 - 302 pages
...83. The reduction and solution of all equations depends upon the self-evident proposition, that Both members of an equation may be increased, diminished,...the same quantity, without destroying the equality. 84. Corollary. If all the terms of an equation have a common factor, this factor may be suppressed.... | |
| Benjamin Peirce - Algebra - 1855 - 308 pages
...109. The reduction and solution of all equations depends upon the self.evident proposition, that Both members of an equation may be increased, diminished,...the same quantity, without destroying the equality. 110. Corollary. If all the terms of an equation have a common factor, this factor may be suppressed.... | |
| Samuel Alsop - Algebra - 1856 - 152 pages
...first of the above principles it follows that by changing the sign of any quantity it may be transposed from one member of an equation to the other, without destroying the equality. Thus, in the equation 4 x — 20 = 3 x + 56, the addition of 20 to both members gives 4 x = Зa: +... | |
| Education - 1863 - 744 pages
...by Davies, thus : — In Robinson's New Elementary. "Transposition is the process of changing a term from one member of an equation to the other, without destroying the equality." (See Art. 135, p. 109.) In Dames' New Elementary. " Transposition is the operation of changing a term... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...OASE I. 1«5O. To transpose the terms of an equation. Transposition is the process of changing a term from one member of an equation to the other, without destroying the equality. To exhibit the law of transposition, let us consider the three following examples : 1. — Let 05-fa... | |
| Benjamin Greenleaf - Algebra - 1864 - 420 pages
...If the same operations are performed upon equal quantities, the results will be equal; hence, Both members of an equation may be increased, diminished,...or divided by the same quantity, without destroying t/ie equality. CASE I. 151 • To transpose terms of an equation. TRANSPOSITION is the process of changing... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...CASE I. ISO. To transpose the terms of an equation. Transposition is the process of changing a term from one member of an equation to the other, without destroying the equality. To exhibit the law of transposition, let us consider the three following examples : 1. — Lot x-\-a... | |
| Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...CASE I. 135. To transpose any term of an equation. Transposition is the process of changing a term from one member of an equation to the other, without destroying the equality. 1. In x + a = b, transpose a to the second member. OPERATION. ANALYSIS. Since the equality . _ , of the... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...must be involved or evolved to the same degree. TRANSPOSITION. lOOi TRANSPOSITION is the changing of terms from one member of an equation to the other, without destroying the equality. The object of transposition is to bring all the unknown terms into one member and all the known into... | |
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