Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA. S. Barnes & Burr, 1860 - 400 páginas |
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Página 40
... quotient must have such a sign that when multiplied by the divisor the product will have the sign of the dividend ... quotient is + ; the quotient is divisor the quotient is if the dividend is - and the ― and the divisor - - ; ; the ...
... quotient must have such a sign that when multiplied by the divisor the product will have the sign of the dividend ... quotient is + ; the quotient is divisor the quotient is if the dividend is - and the ― and the divisor - - ; ; the ...
Página 41
... quotient , 5a3bc . Now , since the quotient must be such a quantity as multiplied by the divisor will produce the dividend , the co - efficient of the quotient multiplied by 7 must give 35 ; hence , it is 5 . Again , the exponent of ...
... quotient , 5a3bc . Now , since the quotient must be such a quantity as multiplied by the divisor will produce the dividend , the co - efficient of the quotient multiplied by 7 must give 35 ; hence , it is 5 . Again , the exponent of ...
Página 42
... quotient remains un- der the form of a monomial fraction ; that is , a monomial expression , necessarily containing the algebraic sign of division . Such expressions may frequently be reduced . Take , for example , 12a4b2cd 3a2bd ...
... quotient remains un- der the form of a monomial fraction ; that is , a monomial expression , necessarily containing the algebraic sign of division . Such expressions may frequently be reduced . Take , for example , 12a4b2cd 3a2bd ...
Página 43
... quotient . But if it is desirable to preserve the trace of this letter in the quotient , we may apply to it the rule for exponents ( Art . 51 ) , which gives b2 b2 b2-2 * com 6o . The symbol 6o , indicates that the letter b enters 0 ...
... quotient . But if it is desirable to preserve the trace of this letter in the quotient , we may apply to it the rule for exponents ( Art . 51 ) , which gives b2 b2 b2-2 * com 6o . The symbol 6o , indicates that the letter b enters 0 ...
Página 44
... quotient , then , by dividing this term oʻ the dividend by that term of the divisor , we should obtain one term of the required quotient . Now , from the third remark of Art . 46 , the term 10a4 , con taining the highest power of the ...
... quotient , then , by dividing this term oʻ the dividend by that term of the divisor , we should obtain one term of the required quotient . Now , from the third remark of Art . 46 , the term 10a4 , con taining the highest power of the ...
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Términos y frases comunes
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient contrary signs cube root decimal places deduce denote the number derived polynomial Divide dividend entire number example exponent extract the square figures Find the factors Find the square find the values following RULE formula fourth fractional unit given equation given number gives greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier negative roots nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots remainder required root required to find result second degree second member second term simplest form square root substituted subtract suppose supposition take the equation taken third unknown quantity whence whole number write
Pasajes populares
Página 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Página 290 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 117 - The first ten numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Roots.
Página 136 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.
Página 200 - RULE I. Separate the given number into periods. of three figures each, beginning at the right hand ; the left hand period will often con tain less than three places of figures.
Página 100 - 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 will it take each person to perform the same work alone.
Página 62 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator. EXAMPLES FOR PRACTICE.
Página 154 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Página 222 - Consequently, teueя the index of the radical is divisible by the exponent of the power to which it is to be raised, perform the division, leaving the quantity under the radical sign unchanged.