Elements of Algebra: Including Sturms' Theorem |
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Page 17
... consequently , 86 43 the greater , 2 - 30 19 43 - 19 24 the less General Solution of this Problem . The sum of two numbers is a , and their difference is b . What are the two numbers ? Let then will , XC the less number ; x + b the ...
... consequently , 86 43 the greater , 2 - 30 19 43 - 19 24 the less General Solution of this Problem . The sum of two numbers is a , and their difference is b . What are the two numbers ? Let then will , XC the less number ; x + b the ...
Page 19
... consequently , 86 x = 43 the greater , 2 - ac · 1943 - 19 24 the less General Solution of this Problem . The sum of two numbers is a , and their difference is b . What are the two numbers ? Let then will , the less number x + b = the ...
... consequently , 86 x = 43 the greater , 2 - ac · 1943 - 19 24 the less General Solution of this Problem . The sum of two numbers is a , and their difference is b . What are the two numbers ? Let then will , the less number x + b = the ...
Page 26
... Consequently , this result is numerically less than a . To distinguish this sum from an arithmetical sum , it is called the algebraic sum . Thus , the polynomial , 2a3-3a2b3b2c . is an algebraic sum , so long as it is considered as the ...
... Consequently , this result is numerically less than a . To distinguish this sum from an arithmetical sum , it is called the algebraic sum . Thus , the polynomial , 2a3-3a2b3b2c . is an algebraic sum , so long as it is considered as the ...
Page 32
... consequently , they cannot be similar to any of them . This remark , the truth of which is deduced from exponents , will be very useful in division . the law of the Multiply by 5a4b2 + 3a2b · ab4 - 2ab3 a2b ― ab2 5a6b3 + 3a4b2 - 5a5b4 ...
... consequently , they cannot be similar to any of them . This remark , the truth of which is deduced from exponents , will be very useful in division . the law of the Multiply by 5a4b2 + 3a2b · ab4 - 2ab3 a2b ― ab2 5a6b3 + 3a4b2 - 5a5b4 ...
Page 38
... consequently , the signs of the terms in the quotient must be such as to give proper signs to the partial products . Since , in multiplication , the product of two terms having the same sign is affected with the sign + , and the product ...
... consequently , the signs of the terms in the quotient must be such as to give proper signs to the partial products . Since , in multiplication , the product of two terms having the same sign is affected with the sign + , and the product ...
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Common terms and phrases
affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example exponent factors figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm method monomial multiply nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient real roots Reduce remainder resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing unity unknown quantity whence whole number
Popular passages
Page 30 - 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 275 - 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 27 - 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 179 - 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 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 90 - 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 346 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. 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 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 202 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.