New Elementary Algebra: Designed for Common and High Schools and Academies

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J.B. Lippincott & Company, 1879 - 332 σελίδες
 

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Σελίδα 59 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Σελίδα 293 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the • proportion a : b = с : d, a and d are the extremes, and b and с the means.
Σελίδα 61 - The number by which we divide is called the divisor. The number which shows how many times the divisor is contained in the dividend is called the quotient. 56. The sign of division is -=-. It is read divided by.
Σελίδα 68 - 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.
Σελίδα 224 - 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.
Σελίδα 121 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 30 - If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Σελίδα 30 - The following axioms underlie the principles of all algebraic operations : 1. If the same quantity or equal quantities be added to equal quantities, the sums will be equal. 2. If the same quantity or equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same, or equal quantities, the products will be equal.
Σελίδα 192 - RULE. Find an expression for the value of one of the unknown quantities in one of the equations, and substitute this value for the same unknown quantity in the other equation.

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