The Elements of Algebra: Designed for the Use of Students in the University

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John William Parker ; sold by Deightons, 1837 - 539 sider

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Side 349 - From half the sum of the three sides, subtract each side separately. Multiply the half sum and the three remainders together, and the square root of the product is the area.
Side 107 - A and B can do a piece of work in m days, B and C in n days, and C and A in p days. In what time can each alone jjerform the work ? 39.
Side 373 - The coefficient of the second term of an equation, with its proper sign, is the sum of the roots, with their signs changed ; the coefficient of the third term is the sum of the products of...
Side 138 - A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms.
Side 146 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Side 145 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Side 115 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Side 35 - If the proposed quantity consists of more terms, it is evident that we have only to consider a-\-b in the place of a, and then by the same process another term of the root will be obtained, and so on ; and hence we have the following GENERAL RULE. 'Arrange the terms in the order of the magnitudes of the indices of some one quantity. Find the square root of the first term, and subtract its square from the proposed quantity. Bring down the next two terms, and find the next term of the root by dividing...
Side 137 - Ratio is the relation which one quantity bears to another of the same kind, the comparison being made by considering what multiple, part, or parts, one quantity is of the other.
Side 132 - Find two numbers whose product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.

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