An Introduction to Algebra, and to the Solution of Numerical Equations1851 - 12 sider |
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Side 17
... equal to 8 : and 4b + 6b = 106 , means that 4 times b plus 6 times b are equal to 10 times b . 8. The figure which is thus prefixed to a letter , or to any algebraic expression , as a multiplier , is called the coefficient of that ...
... equal to 8 : and 4b + 6b = 106 , means that 4 times b plus 6 times b are equal to 10 times b . 8. The figure which is thus prefixed to a letter , or to any algebraic expression , as a multiplier , is called the coefficient of that ...
Side 26
... equal , the product is then called a power . There is a very convenient notation for powers : instead of writing the factors one after the other , as we do in the multiplication of unequal factors , merely one of the equal factors is ...
... equal , the product is then called a power . There is a very convenient notation for powers : instead of writing the factors one after the other , as we do in the multiplication of unequal factors , merely one of the equal factors is ...
Side 44
... equal to the sum of the squares of the individual quantities PLUS twice their product . And from Ex . 3 , that the square of a quantity of two terms , separated by is equal to the sum of the squares of the individual quan tities MINUS ...
... equal to the sum of the squares of the individual quantities PLUS twice their product . And from Ex . 3 , that the square of a quantity of two terms , separated by is equal to the sum of the squares of the individual quan tities MINUS ...
Side 56
... equal to it . In this demonstration , we have connected the remainder with the product of quotient and divisor , by the plus sign : this is allowable , though the remainder itself be negative ; for any negative quantity , though ...
... equal to it . In this demonstration , we have connected the remainder with the product of quotient and divisor , by the plus sign : this is allowable , though the remainder itself be negative ; for any negative quantity , though ...
Side 58
... equal factors : it is the name given to the process by which powers of any quantity are obtained . The relation between power and root has already been defined : the latter generates the former by involution . Any quantity being ...
... equal factors : it is the name given to the process by which powers of any quantity are obtained . The relation between power and root has already been defined : the latter generates the former by involution . Any quantity being ...
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An Introduction to Algebra, and to the Solution of Numerical Equations John Radford Young Ingen forhåndsvisning - 2015 |
Almindelige termer og sætninger
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
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Side 69 - ... subtract the product from the dividend, and to the remainder annex the next period for the next dividend.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 130 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Side 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 ?
Side 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?
Side 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.