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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Peck, White & Peck, 1859 - 404 σελίδες
 

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Σελίδα 47 - 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 381 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Σελίδα 36 - This, according to the definition (Art. 90.) is taking the multiplicand as many times, as there are units in the multiplier.
Σελίδα 215 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c. are all equal ; the quantities are said to be in continued proportion. The consequent of each preceding ratio is, then, the antecedent of the following one.
Σελίδα 220 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Σελίδα 378 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Σελίδα 35 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Σελίδα 146 - Art. 257, may be applied to every case in evolution. But when the quantity whose root is to be found, is composed of several factors, there will frequently be an advantage in taking the root of each of the factors separately. This is done upon the principle that the root of the product of several factors, is equal to the product of their roots.
Σελίδα 289 - After arranging the terms according to the powers of one of the letters, take the root of the first term, for the first term of the required root, and subtract the power from the given quantity.
Σελίδα 130 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.

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