 | George Albert Wentworth - Algebra - 1886 - 284 pages
...products will be equal. 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... | |
 | Webster Wells - Algebra - 1889 - 584 pages
...equal quantities be divided 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. 6. If a quantity be both multiplied and divided by another, the value of the former will not be changed.... | |
 | 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. 24. Algebra... | |
 | 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 each... | |
 | George W. Lilley - Algebra - 1892 - 420 pages
...for factoring a trinomial consisting of two trinomial factors depends upon the following axiom : 5. If the same number be both added to and subtracted...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* + 2a2i2 + a4... | |
 | George P. Lilley - Algebra - 1894 - 522 pages
...fur factoring a trinomial consisting of two trinomial factors depends upon the following axiom : 5. If the same number be both added to and subtracted...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'... | |
 | 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... | |
 | George Washington Hull - Algebra - 1895 - 358 pages
...will be equal. 4. If equals be divided by equals, 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. 6. If a quantity be both multiplied and divided by the same quantity, the former will not be changed.... | |
 | Webster Wells - Algebra - 1897 - 434 pages
...the above result may also be expressed с + a — e — d — b, — d — b + c — e + a, etc. 29. If the same number be both added to, and subtracted...another, the value of the latter will not be changed (§ 9). That is, a + b — b = a. Hence, terms of equal absolute value, but opposite sign, in an expression,... | |
 | Webster Wells - Algebra - 1897 - 422 pages
...: 1. If the same operation be performed upon equal numbers, the resulting numbers will be equal. 2. If the same number be both added to, and subtracted...another, the value of the latter will not be changed. 3. If a number be both multiplied and divided by another, the value of the former will not be changed.... | |
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If equal quantities be divided by the same quantity, or 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. 
