## An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry |

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An Introduction to Algebra: With Notes and Observations; Designed for the ... John Bonnycastle Uten tilgangsbegrensning - 1834 |

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Algebra answer arise arithmetical arithmetical mean arithmetical series binomial coefficients consequently cube root cubic equation decimal denominator denoted determined divisor equal EXAMPLES FOR PRACTICE expression factors find the root find the square find the sum find the value find two numbers former formula four roots fraction geometrical geometrical mean give given equation given number greatest common measure Hence improper fraction infinite series integral last term latter logarithms means method multiplied negative nth root number of terms observed orders of differences perpendicular PROBLEM proportion quadratic equation quadratic surd question quotient rational remain Required the sum required to divide required to find resolved result rule second term side square number square root substituted subtracted taken third transposition unknown quantity Whence whole numbers

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Side 45 - ... be the power required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer.

Side 43 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.

Side 27 - 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.

Side 87 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.

Side 126 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.

Side 112 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Side 126 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.

Side 29 - If there is a remainder after the last division, write it over the divisor in the form of a fraction, and annex it with its proper sign to the part of the quotient previously obtained.

Side 224 - N .•. def. (2), x— x1 is the logarithm of that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power of n. N" =a

Side 126 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.