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

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Durrie & Peck, 1839 - 332 pages
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Page 59 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 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.
Page 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.
Page 292 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 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.
Page 20 - If the same quantity or equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied into the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered. 6. If a quantity be both multiplied and divided by another, the value of the former...
Page 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.
Page 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.
Page 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.
Page 53 - Multiply each numerator into all the denominators except its own for a new numerator ; and all the denominators together, for a common denominator.

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