A University Algebra

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Sheldon & Company, 1878
 

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Page 125 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 6 - A Positive Integral Exponent signifies that the number affected by it is to be taken as a factor as many times as there are units in the exponent. It is a kind of symbol of multiplication.
Page 123 - One variable number is said to vary directly as a second and inversely as a third, when it varies jointly as the second and the reciprocal of the third. Thus...
Page 28 - The Greatest Common Divisor of two or more numbers is the greatest number that will exactly divide each of them. Thu4, 18 is the greatest, common divisor of 36 and 54, since it is the greatest number that will divide each of them without a remainder.
Page 131 - But, if we add the square of half the co-efficient of the second term to the first member to make it a complete square, we must add it to the second member to preserve the equality of the members.
Page 19 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.
Page 59 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Page 35 - A common divisor of two numbers is a divisor of their sum and also of their difference.
Page 19 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second.

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