An Elementary Treatise on Algebra: To which are Added Exponential Ewquations and Logarithms
1855 - Algebra - 288 pages
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according added approximate values body called coefficient consequently contain continued product Corollary corresponding denominator denotes derivative difference Divide dividend division dollars Elimination enunciation equal equal roots EXAMPLES exponent expression factor Find Find the greatest Find the sum follows fourth fraction Free function gallons given equation gives greater greatest common divisor Hence increased known last term least less letter limit logarithm means method monomials Multiply negative obtained polynomial positive preceding Problem progression proportion putting quotient radical ratio real roots receive reduced regarded remainder represented result reverse row of signs shillings Solution Solve the equation square root substituted subtracted successive suppressed taken Theorem third tions true unity unknown quantity whence wine
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.