An Easy Algebra for Beginners: Being a Simple, Plain Presentation of the Essentials of Elementary Algebra, and Also Adapted to the Use of Those who Can Take Only a Brief Course in this Study

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University Publishing Company, 1880 - 157 σελίδες

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Σελίδα 21 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (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 first by the second, plus the square of the second.
Σελίδα 26 - 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 101 - In a proportion the antecedents and consequents of the two ratios are respectively the antecedents and consequents of the proportion. The first and fourth terms are called the extremes, and the second and third the means.
Σελίδα 136 - To what is the square of the difference of two quantities equal ? 82. To what is the product of the sum and difference of two quantities equal ? 83. How may the reciprocal of any quantity be expressed ? How may any factor be transferred from one term of a fraction to the other? In what other form may a"1 be written ? a—'
Σελίδα 74 - Raise the absolute value of the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Σελίδα 64 - Three methods of elimination are usually given. such numbers as will make the coefficients of one of the unknowns the same in both.
Σελίδα 103 - Hence if any three terms of a proportion are given, the fourth may be found. Thus...
Σελίδα 108 - Multiply one half the sum of the first and last terms by the number of terms. Thus, the sum of eight terms of the series whose first term is 3 and last term 38 is 8 x * (3 + 38) = 164.
Σελίδα 82 - ... the divisor. Multiply the divisor thus increased, by the second term of the root, and subtract the product from the remainder.
Σελίδα 35 - ... thing, viz. 12 : so, likewise, 3 multiplied by 4 multiplied by 5 is 60, and will be 60 in whatever order we take them — -3 by 4 by 5, or 4 by 3 by 5, or 5 by 3 by 4 ; when, therefore, we have obtained one denominator, it is sufficient. Hence the usual rule to reduce fractions to a common denominator : Multiply each numerator by all the denominators except its own for new numerators, and all the denominators together for the common denominator. 6. We are now prepared to add two or more fractions...

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