## The Complete Algebra: Designed for Use in Schools, Academies, and Colleges |

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algebraic arithmetical arithmetical mean ax² binomial factors Binomial Formula CHAPTER coefficient common divisor cube root dividend divisible equal equation whose roots equivalent EXAMPLES exponent expression Find the L. C. M. find the numbers Find the square Find the sum Find the value geometrical mean given equation given fraction given quantities greater greatest common divisor hence inequality integer less letters logarithm miles minuend monomial nth power nth root number of terms polynomial positive roots prime factors problem quadratic quan radical sign ratio real root Reduce remainder RULE second degree second member second term simple radical quantity simultaneous equations Solve the equations square root Sturm's Theorem Substituting Subtracting Suppose surd SYNOPSIS FOR REVIEW theorem third term tion unknown quantities whence

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Page 30 - 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.

Page 160 - RULE. 1. Separate the given number into periods of three figures each, beginning at the units place.

Page 156 - Divide this dividend, omitting the figure on the right, by double the part of the root already found, and annex the quotient to that part, and also to the divisor ; then multiply the divisor thus completed by the figure of the root last obtained, and subtract the product from the dividend.

Page 304 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.

Page 286 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 97 - A vessel can be emptied by three taps ; by the first alone it could be emptied in 80 minutes, by the second alone in 200 minutes, and by the third alone in 5 hours. In what time will the vessel be emptied if all the taps are opened ? 29.

Page 303 - The combinations of things are the different collections that can be formed out of them, without regarding the order in which the things are placed. Thus the combinations of the letters a, b, c, taken two at a time are ab, ас, Ъс; ab and ba though different permutations forming the same combination.

Page 80 - The First Member of an equation is the quantity on the left of the sign of equality ; and The Second Member is the quantity on the right of the sign...

Page 417 - ROBINSON'S PROGRESSIVE COURSE OF MATHEMATICS, being the most complete and scientific course of Mathematical Text-books published, is more extensively used in the Schools and Educational Institutions of the United States than any competing series. In its preparation two objects...

Page 396 - Hence the number of real positive roots of the equation f (x) = 0 cannot exceed the number of variations in the signs of its terms.