The Scholar's Algebra: An Introductory Work on Algebra

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Clarendon Press, 1875 - Algebra - 258 pages
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Page 71 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 64 - 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.
Page 36 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 70 - A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms.
Page 195 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Page 110 - Substitution consists in finding the value of one of the unknown quantities in...
Page 211 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 81 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 101 - У j (2) a + b ax + by = a* + 6*J 10. A traveller sets out from A for B, and walks 3 miles per hour. Fifteen minutes afterwards, another traveller sets out from В for A, and walks 3| miles per hour ; and he goes 2 miles beyond the middle point between В and A before he meets the first traveller. Find the distance between A and B.
Page 104 - A person walked to the top of a mountain at the rate of 2 - miles an hour, and down the same way at the rate of 3- miles an hour, and was out 5 hours. How far did he walk 2G altogether ? 5Q.

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