Elements of Algebra

A. S. Barnes, 1842 - 358 σελίδες

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Σελίδα 181 - C' then A is said to have the same ratio to B that C has to D ; or, the ratio of A to B is equal to the ratio of C to D.
Σελίδα 183 - D, we have — =— , (Art. 169) ; nj\ and by clearing the equation of fractions, we have BC=AD; that is, of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Σελίδα 122 - These expressions may sometimes be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square roots of these factors; or, in algebraic language, V'abed . . . = i/a.
Σελίδα 181 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Σελίδα 114 - ... the entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root, and a remainder of 40, which shows that 665 is not a perfect square. But is the square of 25 the greatest perfect square contained in 665 ? that is, is 25 the entire part of the root ? To prove this, we will first show that, the difference between the squares of two consecutive numbers, is equal to twice the less number augmented by unity.
Σελίδα 28 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Σελίδα 33 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Σελίδα 267 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 146 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Σελίδα 90 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.

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