## Advanced AlgebraThis text is arranged to follow a first year course, and meets the requirements in algebra for both college of liberal arts, technical schools, and high schools with advanced courses. The text begins with a review of the first year course, which aims to unify arithmetic, algebra, and plane geometry as effectively as possible. The second part of the text advances to treat the remaining topics belonging to elementary algebra, and finishes with the topics belonging to advanced algebra. The aim of the entire volume is to address all topics with simplicity, clearness, and conciseness without sacrificing rigor. |

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### Common terms and phrases

a₁ algebra angle arithmetic ax² b₁ binomial binomial coefficients c₁ Calculate chance changed coefficients COLLINS'S ADV cologarithm column completing the square complex numbers Construct the graphs continued fraction convergent coördinates corresponding cube root d₁ decimal places degree denominator denote determinant diagram divided divisor equa equal equations containing EXAMPLE Extract factors Find formula fractional exponent given equation gives Hence imaginary integral left member letter logarithm mantissa mathematical induction method monomial Mult multiplied negative roots notation order of differences polynomial positive preceding problem proportion quadratic equation quantity quotient radical radicand ratio remainder result right member rule side Simultaneous Equations SOLUTION Solve square root student substituting subtract SUGGESTION synthetic division theorem tion triangle unknown verify

### Popular passages

Page 16 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.

Page 72 - Multiply both numerator and denominator of the fraction by such a quantity as will make the denominator a perfect power of the same degree as the radical; Proceed as in Art.

Page 67 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be -the power required.

Page 188 - My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.

Page 151 - The first term of a ratio is called the antecedent, and the second term the consequent. Thus, in the ratio a : b, a is the antecedent, and b is the consequent. The first and fourth terms of a proportion are called the extremes, and the second and third terms the means.

Page 53 - ... is found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place.

Page 160 - ... is equal to the ratio of the corresponding sides of the other triangle.

Page 113 - The angles opposite the equal sides of an isosceles triangle are equal.

Page 151 - In any proportion, the product of the extremes equals the product of the means.

Page 171 - Exponents. lu 32 = 9, we can say 2 is the logarithm of 9 to base 3. Similarly, since 34 = 81, 4 is the logarithm of 81 to base 3. In logarithms three different numbers are always involved: (1) A number. (2) Its logarithm. (3) The base used. The logarithm of a given number is the exponent of the power to which a base must be raised to produce this number. A system of logarithms is a set of numbers with their logarithms all taken to the same base. Notice that the logarithm of 1 in any system is 0,...