An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms
J. Munroe, 1843 - Algebra - 284 pages
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Common terms and phrases
approximate values arithmetical becomes body called coefficient consequently contained continued product Corollary corresponding decimal denominator denote derivative difference Divide dividend division Elimination equal roots EXAMPLES exponent Extract factor figure Find Find the greatest Find the square Find the sum follows 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 places polynomial positive preceding Problem progression proportion putting 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
Page 48 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 192 - 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 268 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.
Page 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 186 - I = the last term, r = the common difference, n = the number of terms, S = the sum of all 'the terms.
Page 55 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Page 32 - The 2d line of col. 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new divisor ; the remainder of the division is the 4th line of col.
Page 127 - Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend. III. Double the root already found and place it on the left for a divisor.
Page 232 - Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.
Page 47 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference. Ratio of Sum of two first Terms to that of two last. Moreover, in finding...