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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 extracted factor figure Find Find the square Find the sum fourth fraction Free function given equation gives greater greatest common divisor Hence imaginary increased integral known last term least less letter limit logarithm means method monomials multiplied negative number of real obtained places 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 tion 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 190 - 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 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 97 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes f; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
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 125 - 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 69 - Ans. — r — . mjH 13. Divide the number 46 into two parts, so that when the one is divided by 7, and the other by 3, the sum of the quotients = 10. Ans. 28 and 18. 14. All my journeyings taken together, says a...
Page 230 - Theorem. A complete equation cannot have a greater number of positive roots than there are variations in the row of signs of its terms, nor a greater number of positive roots than there are permanences in this row of signs. Proof. If the equation is that of art. 295, the values of «, U, U', &c.
Page 94 - B next divided with A and C, and after this, C with A and B. If, then, by these means, the intended equal division is effected, how much booty did each soldier make 1 Ans.
Page 235 - Vimit of the positive roots, we have that is, a superior limit of the positive roots is unity, increased by that root of the greatest negative coefficient, whose index is equal to the excess of the degree of the equation above the exponent of the first negative term. 306. Problem. To find an inferior limit of the positive roots. Solution. Substitute in the given equation for...