## Elements of Algebra: Including Sturms' Theorem |

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### Common terms and phrases

affected algebraic quantities arithmetical arithmetical means arithmetical progression binomial binomial theorem called co-efficient common difference consequently contain contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nº root number of terms obtain operation ounces perfect power perfect square permutations polynomial positive roots problem progression proportion proposed equation quan quotient radical sign Reduce remainder result rule second degree second member second term simplest form square root substituted subtract suppose take the equation third tion total number transposing units unity unknown quantity whence whole number

### Popular passages

Page 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.

Page 348 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 294. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to the number of permanences.

Page 277 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.

Page 29 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.

Page 181 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.

Page 172 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 41 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...

Page 51 - To reduce fractions having different denominators to equivalent fractions having a common denominator. RULE. Multiply each numerator into all the denominators except its own, for the new numerators, and all the denominators together for a common denominator. EXAMPLES. 1. Reduce ^, £, and |, to a common denominator.

Page 92 - 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.

Page 36 - I. Divide the coefficient of the dividend by the coefficient of the divisor.