# An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

Hezekiah Howe, 1831 - 332 σελίδες

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Σελίδα 59 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 217 - In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 300 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 31 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 156 - The equality of the two sides is not affected by this alteration, because we only change one quantity x for another •which is equal to it. By this means we obtain an equation which contains only one unknown quantity.
Σελίδα 72 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Σελίδα 233 - 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.
Σελίδα 165 - Divide the number 90 into 4 such parts, that the first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall all be equal.
Σελίδα 124 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 188 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.