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 ab² algebra angle answer arithmetic ax² Axiom b₁ binomial Calculate changing the sign coefficient COLLINS'S ADV complex numbers Construct the graphs continued fraction coördinates corresponding cube root decimal places denominator denoted diagram divided dividend division divisor equa equal equation containing EXAMPLES Exercise Extract factors formula fractional exponent given equation gives Hence hyperbola imaginary integral irrational left member letter logarithm mantissa mathematical induction method minuend monomial Mult multiply notation points polynomial positive preceding problem proportional quadratic equation quotient radical radicand radius ratio remainder result right member rule side Simultaneous Equations SOLUTION Solve square root student substituting subtracted SUGGESTION synthetic division theorem tion unknown verify whole number
Popular passages
Page 113 - Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.
Page 14 - 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 112 - An angle formed by two chords intersecting within a circle is measured by one-half the sum of the intercepted arcs.
Page 186 - 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 149 - 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 70 - 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 158 - ... is equal to the ratio of the corresponding sides of the other triangle.
Page 149 - In any proportion, the product of the extremes equals the product of the means.
Page 111 - The angles opposite the equal sides of an isosceles triangle are equal.
Page 112 - The angle bisector of a triangle divides the opposite side into segments which are proportional to the other two sides. Given in A ABC, BD bisecting Z ABC.