The Elements of Algebra |
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Page 2
... coefficient , thus a is the coefficient of ax , 3b of 3bx . We must also observe that when unity is the coefficient , it is never expressed in writing , thus we put a and not la ; but where we have to add or to subtract a 2 INTRODUCTION .
... coefficient , thus a is the coefficient of ax , 3b of 3bx . We must also observe that when unity is the coefficient , it is never expressed in writing , thus we put a and not la ; but where we have to add or to subtract a 2 INTRODUCTION .
Page 3
... coefficient is unity . 3. Again , if a number as a be multiplied by itself , instead of writing a xa , or aa , we put a2 ; the 2 which is written above a and a little to the right hand , is called the index or exponent of a , and is ...
... coefficient is unity . 3. Again , if a number as a be multiplied by itself , instead of writing a xa , or aa , we put a2 ; the 2 which is written above a and a little to the right hand , is called the index or exponent of a , and is ...
Page 8
... coefficients when the coefficients have the same sign , and the difference of the coefficients with its proper sign , when they have different signs , and writing the sum or difference before the letter . Thus , 7a + 12a = 19a , and 4a2 ...
... coefficients when the coefficients have the same sign , and the difference of the coefficients with its proper sign , when they have different signs , and writing the sum or difference before the letter . Thus , 7a + 12a = 19a , and 4a2 ...
Page 9
... coefficient is c + a - 1 , whence we obtain the result given above . SUBTRACTION . 11. In subtraction when the quantities are like we take the difference between the coefficients , and write after this difference , the literal quantity ...
... coefficient is c + a - 1 , whence we obtain the result given above . SUBTRACTION . 11. In subtraction when the quantities are like we take the difference between the coefficients , and write after this difference , the literal quantity ...
Page 11
... coefficient of a2 in the upper 1 line is and in the lower it is 1 Also — and – 1 2 13 and 1 1 5 + 1 = 2 3 and 6 - 2 are the coefficients of a2 , and 2 1 3 - 1 6 ++ ( - ) - 1-1-1-1-- and - ( - 1 ) = 1 + 1 = 2 = 14 4 2 4 4 = 4 4 • These ...
... coefficient of a2 in the upper 1 line is and in the lower it is 1 Also — and – 1 2 13 and 1 1 5 + 1 = 2 3 and 6 - 2 are the coefficients of a2 , and 2 1 3 - 1 6 ++ ( - ) - 1-1-1-1-- and - ( - 1 ) = 1 + 1 = 2 = 14 4 2 4 4 = 4 4 • These ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.