 | Webster Wells - Algebra - 1885 - 370 pages
...quantities be multiplied by equal quantities, the products will be equal. 4. If equal quantities be divided by equal quantities, the quotients will be equal....from another, the value of the latter will not be changed. 6. If a quantity be both multiplied and divided by another, the value of the former will not... | |
 | Webster Wells - Algebra - 1885 - 372 pages
...quantities be multiplied by equal quantities, the products will be equal. 4. If equal quantities be divided by equal quantities, the quotients will be equal....from another, the value of the latter will not be changed. 6. If a quantity be both multiplied and divided by another, the value of the former will not... | |
 | Webster Wells - Algebra - 1885 - 382 pages
...Art. 12.) Thus, — 3 a& is equivalent to — ab — ab — a6. 26. In Arithmetic, if the same number be both added to and subtracted from another, the value of the latter will not be changed. Thus, Similarly, in Algebra, if any quantity b be both added to and subtracted from another... | |
 | George Albert Wentworth - Algebra - 1886 - 284 pages
...5. If equal numbers be divided by equal numbers, the quotients will be equal. 6. If the same number be both added to and subtracted from another, the value of the latter will not be altered. Ex. 1. If a -.---• 1, b = 2, с = 3, d = 4, с = 5, /= 0, find the numerical values of the following... | |
 | Webster Wells - Algebra - 1889 - 584 pages
...quantities be multiplied by equal quantities, the products will be equal. а. If equal quantities be divided by equal quantities, the quotients will be equal....from another, the value of the latter will not be changed. 6. If a quantity be both multiplied and divided by another, the value of the former will not... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...results are equal. (iv.) Like roots or powers of equal quantities are equal. (v.) If the same quantity be added to and subtracted from another, the value of the latter will not be changed. (vi.) If a quantity be both multiplied and divided by another, its value will not be changed.... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...terms with their respective signs. 47. By (1), Art. 42, a - 6 + b = a. That is, if the same number is both added to and subtracted from another, the value of the latter will not be changed. In other words, terms of equal absolute value, but opposite sign, in an expression, neutralize... | |
 | George W. Lilley - Algebra - 1892 - 420 pages
...trinomial consisting of two trinomial factors depends upon the following axiom : 5. If the same number be both added to and subtracted from another, the value of the latter will not be changed. EXAMPLE 1. Factor ж4 + я2 z2 + «4. Solution. Adding and subtracting as*s, we have x* +... | |
 | St. George Jackson Mivart - Science - 1894 - 412 pages
...be divided by the same, or equal quantities, the quotients will be equal. 5. If the same quantity be added to and subtracted from another, the value of the latter will not be altered. 6. If the same quantity be used both to multiply and divide any quantity, the value of the latter will not... | |
 | George P. Lilley - Algebra - 1894 - 522 pages
...trinomial consisting of two trinomial factors depends upon the following axiom : 5. If the same number be both added to and subtracted from another, the value of the latter will not be changed. EXAMPLE 1. Factor x* + a2z2 + a4. Solution. Adding and subtracting asr2, we have x* + 2 а?х*+а'... | |
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If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 
