An Introduction to Algebra, and to the Solution of Numerical Equations1851 - 12 páginas |
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Página 69
... suggested by the form which the square of a compound quantity takes . The square of the binomial a + b , we know to be a2 + 2ab + b2 ; and from this square , we can return to the root thus : The square root of the lead- ing term is a ...
... suggested by the form which the square of a compound quantity takes . The square of the binomial a + b , we know to be a2 + 2ab + b2 ; and from this square , we can return to the root thus : The square root of the lead- ing term is a ...
Página 70
... + c + d + . . . . . . . . . . l ) 2 = a2 + ( 2a + b ) b + { 2 ( a + b ) + c } c + { 2 ( a + b + c ) + a } .. + 12 : a form which suggests the rule in all cases . d + ...... ( 2 ) 9x - 12x + 10x * -28x3 70 INTRODUCTION TO ALGEBRA .
... + c + d + . . . . . . . . . . l ) 2 = a2 + ( 2a + b ) b + { 2 ( a + b ) + c } c + { 2 ( a + b + c ) + a } .. + 12 : a form which suggests the rule in all cases . d + ...... ( 2 ) 9x - 12x + 10x * -28x3 70 INTRODUCTION TO ALGEBRA .
Página 71
... suggests : the corrected factors are- ( 2x3 - x - 1 + √ - 3 ) ( 2x2 - x - 1 - √ — 3 ) ; for by the theorem at page 44 , so often referred to , the product of these is ( 2 x3 — x — 1 ) 3 — ( - 3 ) = ( 2x2 - x - 1 ) + 3 = 4x - 4x3 - 3x2 ...
... suggests : the corrected factors are- ( 2x3 - x - 1 + √ - 3 ) ( 2x2 - x - 1 - √ — 3 ) ; for by the theorem at page 44 , so often referred to , the product of these is ( 2 x3 — x — 1 ) 3 — ( - 3 ) = ( 2x2 - x - 1 ) + 3 = 4x - 4x3 - 3x2 ...
Página 74
... suggests the first term of the true or com- plete divisor , which first term is called the trial divisor : that the trial divisor suggests the second term of the root , which second term , when found , enables us to complete the divisor ...
... suggests the first term of the true or com- plete divisor , which first term is called the trial divisor : that the trial divisor suggests the second term of the root , which second term , when found , enables us to complete the divisor ...
Página 76
... suggested which is very conveniently suitable to algebra , though not to arithmetic : we shall here explain it . As headings for the two columns of which the work will consist , write the word Root on the left , and Remainder on the ...
... suggested which is very conveniently suitable to algebra , though not to arithmetic : we shall here explain it . As headings for the two columns of which the work will consist , write the word Root on the left , and Remainder on the ...
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An Introduction to Algebra, and to the Solution of Numerical Equations John Radford Young Sin vista previa disponible - 2015 |
Términos y frases comunes
actually algebraists arithmetic brackets called changed coefficients common denominator complete square Completing the square compound quantity consequently cube root difference divi Divide dividend equa equal EXAMPLES FOR EXERCISE exponents extract the square Extracting the root factors figure formula given greatest common measure hence imaginary improper fraction indicated known leading term learner least common multiple letters logarithms multiplication and division multiplied namely notation nth root operation pair polynomial positive preceding principle proper signs proposed equation quadratic equation quadratic surd question quotient radical sign ratic rational reduced remainder represent result rule rule of signs second term side simple equation simple quantity simultaneous equations solution solved square root step substitution symbols thing third tion transformed equation Transposing transposition trial divisor unknown quantity unknown terms write zero
Pasajes populares
Página 69 - ... subtract the product from the dividend, and to the remainder annex the next period for the next dividend.
Página 144 - If the number be divided by the sum of the digits, the quotient will be 26; but, if 198 be added to it, the digits will be inverted.
Página 144 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, the sum, difference, product, and quotient so obtained, will be all equal to each other.
Página 182 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Página 141 - If A and в together can perform a piece of work in 8 days, A and с together in 9 days, and в and с in 10 days, how many days will it take each person to perform the same work alone.
Página 142 - What fraction is that, to the numerator of which, if 4 be added, the value is 1, but if 7 be added to its denominator, its value will be | ? Ans.
Página 130 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Página 180 - A farmer bought some sheep for £72, and found that if he had received 6 more for the same money, he would have paid £1 less for each. How many sheep did he buy ?
Página 142 - ... 6. There is a number consisting of two digits, which is equal to four times the sum of those digits; and if 18 be added to it, the digits will be inverted. What is the number?
Página 126 - Two workmen A and B were engaged to work for a certain number of days at different rates. At the end of the time, A who had played 4 of those days had 75 shillings to receive ; but B who had played 7 of those days received only 48 shillings.