Algebra for the Use of Colleges and Schools: With Numerous Examples |
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a+b+c a₁ algebraical arithmetical arithmetical mean ax˛ b₁ Binomial Theorem black balls coefficient common measure contains continued fraction cube root digits divergent divided divisible divisor equal event example expansion expression Extract the square factors find the number find the value Geometrical Progression given equations greater than unity Hence infinite continued fraction least common multiple less than unity letters logarithm miles multiply negative quantity nth term number of combinations number of terms obtain P₁ positive integers positive quantity preceding Article prime number probability proper fraction quadratic equation quotient radix ratio remainder result scale series is convergent shew shillings Similarly solution Solve square root subtraction suppose surd unknown quantities white balls whole number zero
Popular passages
Page 16 - bd. 48. From considering the above cases we arrive at the following rule for multiplying two binomial expressions : Multiply each term of the multiplicand by each term of the multiplier ; if the terms have the same sign, prefix the sign + to their product, if they have different signs prefix the sign -; then collect
Page 59 - be fraction be divided by the same number the value of the fraction is not altered. 136. Hence, an algebraical fraction may be reduced to another of equal value by dividing both numerator and denominator by any common measure ; when both numerator and denominator are divided by their G.
Page 331 - XXXVIII. LOGARITHMS. 531. Suppose a* =n, then x is called the logarithm of n to the base a ; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The logarithm of
Page 142 - part of the root already found. Moreover, we must add such a quantity to the second column as to obtain there three times the square of the part of the root already found. This is conveniently effected thus: we have
Page 331 - logarithm of the base itself is unity, For a" = a when x = 1. 535. The logarithm of a product is equal to the sum of the logarithms of its factors. For let x = log
Page 253 - -Z>; 446. It appears from Art. 444 that a number is divisible by 9 when the sum of its digits is divisible by 9 ; and that when any number is divided by 9, the remainder is the same as if the sum of the digits of that number were divided by 9.
Page 343 - in which the successive terms are formed by some regular law, and the number of the terms is unlimited, is called an infinite series. 554. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be.
Page 240 - 418. One quantity is said to vary directly as a second and inversely as a third, when it varies jointly as the second and the reciprocal of the third. Or if A = — ^ , where m is constant, A is said to vary directly
Page 231 - c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. If a : b :: с : d, then a + b
Page 144 - 3 , •which is three times the square of the part of the root already found. Now divide the remainder in the third column by the expression just obtained, and we arrive at c*