## An Elementary Treatise on Algebra: To which are Added Exponential Ewquations and Logarithms |

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added approximate values arithmetical becomes body called coefficient consequently contained continued fraction continued product Corollary corresponding decimal denominator denote derivative difference Divide dividend division Elimination equal roots EXAMPLES exponent expression Extract factor figure Find Find the greatest Find the square Find the sum fourth fraction Free function given equation gives greater greatest common divisor Hence imaginary increased integral known last term less letter limit logarithm means method monomials multiplied negative number of real number of terms obtained polynomial positive preceding Problem progression proportion quotient ratio real roots reduced remainder result reverse row of signs Solution Solve the equation square root substitution subtracted successive Theorem third true unity unknown quantity variable whence zero

### Popular passages

Page 44 - Likewise, the sum of the first two terms is to their difference, as the sum of the last two is to their difference.

Page 51 - If this number be divided by the sum of its digits, the quotient is 48; but if 198 be subtracted from it, then we obtain for the remainder a number consisting of the same digits, but in an inverted order.

Page 123 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 188 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.

Page 264 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 264 - We have, by arts. 13 and 9, log. — = log. 1 — log. n = — log. n ; that is, the logarithm of the reciprocal of a number is the negative of the logarithm of the number.

Page 59 - A term may be transposed from one member of an equation to the other by changing its sign.

Page 41 - C; that is, the mean proportional between two quantities is the square root of their product.

Page 276 - Problem. To find the quotient of one number divided by another by means of logarithms. Solution. Subtract the logarithm of the divisor from that of the dividend, and the number, of which the remainder is the logarithm, is, by art.

Page 183 - ... which the first term is /, and the common difference — r. Hence the mth term of this series, that is, the mth term counting from the last of the given series, is /_(,„_ 1 ) r . 248.