 | George Boole - Logic, Symbolic and mathematical - 1854 - 442 pages
...equation x - z = y, (8) which must therefore be a deduction from (7). Thus a term z has been removed from one side of an equation to the other by changing its sign. This is in accordance with the algebraic rule of transposition. But instead of dwelling upon particular... | |
 | Barnard Smith - 1857 - 740 pages
...one unknown quantity, may be reduced to the four following : RULE 1. Any quantity may be transferred from one side of an equation to the other, by changing its sign. This rule is founded on Ax. 1. Let x + a = b, Subtract a from each side of the equation. Then & + a... | |
 | Archibald Montgomerie - Algebra - 1857 - 116 pages
...equals, the quotients are equal. General Principles. — 1. Any quantity may be transposed from the one side of an equation to the other by changing its sign. 2. A coefficient or multiplier may be removed by dividing both sides of the equation by it. 3. An equation... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...Fractions — How by means of Least Common Multiple — Advantage of this Method, (115) . — How any term may be Transposed from one Side of an Equation to the other, (116). — Change of the Signs in an Equation, (117). RULE XVII. For the Solution of a Simple Equation... | |
 | Philip Kelland - Algebra - 1860 - 308 pages
...of equals are equal (A), From the first and second axiom, we conclude that a quantity may be taken from one side of an equation to the other, by changing its sign : For, 1st, let P - a = Q represent the equation, then, by adding a to each side, P — a + a = Q +... | |
 | Isaac Todhunter - 1860 - 620 pages
...multiply by 12, which is the L. c. M. of 2, 3 and 4. Thus we obtain at once 6x + ±x + 3x = 156. 156. Any quantity may be transposed from one side of an equation to ttie other side by changing its sign. Thus suppose, x — a = b — y. Add a to each side, (Art. 98);... | |
 | Art - 1865 - 480 pages
...Logical System under consideration is, that, in the latter as well as in the former, a literal symbol may be transposed from one side of an equation to the other by changing the sign of operation, + or — . But there is an important relation which subsists in the science... | |
 | Thomas Kimber - Mathematics - 1865 - 302 pages
...deduced a rule for facilitating the reduction of equations, that : — Any quantity may be removed from one side of an equation to the other by changing its sign. It is also manifest, that any quantity which is found on both sides of an equation may be expunged.... | |
 | James A. Christie - 1865 - 454 pages
...shares = £42- x 2- = £84- = A's portion. TRANSPOSITION IN EQUATIONS. Any Quantity preceded by + or — may be Transposed from one side of an Equation to the other, if its sign be reversed. That is to say, in Transposing, + must be exchanged for — — must be exchanged... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...Subtracting 6 from both sides, Ax. 2, X-\- b — b=c — 5; Or, x=c — 6. Rule of Transposition. — Any quantity may be transposed from one side of an equation to the other, if, at the tame time, its sign lie changed. 151. To Clear an Equation of Fractions. — 1. Let it be... | |
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Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed. 
