An Introduction to Algebra, and to the Solution of Numerical Equations1851 - 12 páginas |
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Página 39
... determined in the order here stated . The subject naturally divides itself into three cases : — CASE I. — When the factors are both simple quantities : RULE - First : Observe whether the signs of the factors are like or unlike . If they ...
... determined in the order here stated . The subject naturally divides itself into three cases : — CASE I. — When the factors are both simple quantities : RULE - First : Observe whether the signs of the factors are like or unlike . If they ...
Página 46
... determine the sign of the quotient from the principle that , in both multiplication and division , like signs give plus , and unlike signs minus . Then , to the quotient of the coefficients , annex the quotient of the letters , and the ...
... determine the sign of the quotient from the principle that , in both multiplication and division , like signs give plus , and unlike signs minus . Then , to the quotient of the coefficients , annex the quotient of the letters , and the ...
Página 58
... determine its second , third , fourth , & c . root , the operation necessary , except in the simplest case , that of the second or square root , 58 INTRODUCTION TO ALGEBRA . CHAPTER II INVOLUTION AND EVOLUTION 89 Preliminary remarks and ...
... determine its second , third , fourth , & c . root , the operation necessary , except in the simplest case , that of the second or square root , 58 INTRODUCTION TO ALGEBRA . CHAPTER II INVOLUTION AND EVOLUTION 89 Preliminary remarks and ...
Página 59
... determining powers : in the latter , they are nothing but multiplications throughout ; but , in the former , the operation for the cube root differs considerably from that for the square root ; and in the case of odd roots especially ...
... determining powers : in the latter , they are nothing but multiplications throughout ; but , in the former , the operation for the cube root differs considerably from that for the square root ; and in the case of odd roots especially ...
Página 64
... determined , may always be approximated to as nearly as we please ; which language seems to imply the existence of ... determine the exact root of the quan- tity under the radical ( because such exact root does not exist ) , yet we can ...
... determined , may always be approximated to as nearly as we please ; which language seems to imply the existence of ... determine the exact root of the quan- tity under the radical ( because such exact root does not exist ) , yet we can ...
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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.