| Benjamin Greenleaf - 1864 - 420 σελίδες
...or any quantity which, multiplied by the divisor a3, will equal the dividend a5, must be aa, or a2. Hence, The EXPONENT of a letter in the quotient is...dividend, diminished by its exponent in the divisor. 2. Let it be required to divide a" by a". Then, ~n = a"-" = a°; but ~n = 1. Therefore (Ax. 7), a°... | |
| Daniel Barnard Hagar - 1873 - 278 σελίδες
...xy, is the same as axy •*- a, which is equal to xy ; for xy xa = axy. 3. The exponent of a factor in the quotient is equal to its exponent in the dividend diminished by its exponent in the divisor. Thus, a5 -*- a2, or a5 with the factor a2 omitted, is equal to a3, for a* xa* = a5. 4. The quotient... | |
| Benjamin Greenleaf - 1879 - 322 σελίδες
...and a3 = aaa, it is evident that the quotient, or the — a2 quantity which, multiplied by the diet2 visor a2, will equal the dividend a5, must be aa,...is the exponent of a letter in the quotient equal ? 70. When the exponents of the same letter in the dividend and divisor are equal, the letter may be... | |
| Benjamin Greenleaf - 1879 - 376 σελίδες
...aaa, it is evident that the quotient, or the . __ fl2 quantity which, multiplied by the di(f visor a3, will equal the dividend a5, must be aa, or a2. The...division what do like signs produce ? Unlike signs ? How manv cases in division of algebraic quantities ? Explain the first operation un, dcr Case I. The second.... | |
| Webster Wells - 1879 - 468 σελίδες
...required must be such a quantity as when multiplied by a3 will produce a3. That quantity is evidently a2. Hence, The exponent of a letter in the quotient is...dividend diminished by its exponent in the divisor. Or, in general, am -=- a" = am~n. 94. If we apply the rule of Art. 93 to finding the quotient of am... | |
| Webster Wells - 1880 - 498 σελίδες
...a quantity as when multiplied by «3 \vill produce a6. That quantity is evidently a'2. Hence, T/ie exponent of a letter in the quotient is equal to its...dividend diminished by its exponent in. the divisor. Or, in general, am -;- a" = am~n. 94. If we apply the rule of Art. 93 to finding the quotient of a"'... | |
| William James Milne - 1881 - 360 σελίδες
...to t1ie coefficient of ike dividend divided by t1iat of the divisor. 3. The exponent of any quantity in the quotient is equal to its exponent in the dividend diminished by its exponent in t1ie divisor. 89. The principle relating to the signs in division may be illustrated as follows: +... | |
| Webster Wells - 1885 - 368 σελίδες
...quantity which, when multiplied by «3, will produce cf. That quantity is evidently a? ; hence That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. For example, — = ara~". a" DIVISION OF MONOMIALS. 90. We derive... | |
| Webster Wells - 1885 - 324 σελίδες
...multiplied by a3, will produce cf. That quantity is evidently a2 ; hence a5 « — = a2. a3 That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. am For example, — = a"-*, a" DIVISION OF MONOMIALS. 90. We derive... | |
| Webster Wells - 1885 - 370 σελίδες
...quantity which, when multiplied by will produce as. That quantity is evidently a2 ; hence That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. For example, — = a*~". DIVISION OF MONOMIALS. 90. We derive from... | |
| |