An Introduction to Algebra, and to the Solution of Numerical Equations1851 - 12 sider |
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Side ix
... Compound Quantities Division of Simple Quantities .... Remarks on the peculiar character of Algebraic Division Cases in which the operation is interminable ..... Proof of the property that if any Polynomial in x , when divided by xa ...
... Compound Quantities Division of Simple Quantities .... Remarks on the peculiar character of Algebraic Division Cases in which the operation is interminable ..... Proof of the property that if any Polynomial in x , when divided by xa ...
Side x
... Quantities ..... Case II . Compound Quantities 71 On the decomposition of a Polynomial into a pair of unequal factors Different forms for the incomplete Square Root of an expression ... 72 On the Extraction of the Cube Root of a Compound ...
... Quantities ..... Case II . Compound Quantities 71 On the decomposition of a Polynomial into a pair of unequal factors Different forms for the incomplete Square Root of an expression ... 72 On the Extraction of the Cube Root of a Compound ...
Side 17
... quantity 4b ; and 10 is the coefficient of b in 10b . In like manner 7 is the coefficient of xyz in the quantity ... compound quantity : the follow- ing are compound quantities : a + b , 3z - 2y , 5x + 3y - 2 ab , 4 abx - 3c + 2d , & c ...
... quantity 4b ; and 10 is the coefficient of b in 10b . In like manner 7 is the coefficient of xyz in the quantity ... compound quantity : the follow- ing are compound quantities : a + b , 3z - 2y , 5x + 3y - 2 ab , 4 abx - 3c + 2d , & c ...
Side 20
... Quantities or terms are said to be like quantities , or like terms , when they consist of the same letters ; or , to ... compound to a simple quantity , by the actual performance of the additive and subtractive operations indicated in it ...
... Quantities or terms are said to be like quantities , or like terms , when they consist of the same letters ; or , to ... compound to a simple quantity , by the actual performance of the additive and subtractive operations indicated in it ...
Side 21
... quantities ; so that the sum of the second vertical row of quantities is plus 8 by , and the positive sign is in- serted to complete the compound result 10 ax + 8 by . ( 4 ) . Here the sum of the positive coefficients in the first ...
... quantities ; so that the sum of the second vertical row of quantities is plus 8 by , and the positive sign is in- serted to complete the compound result 10 ax + 8 by . ( 4 ) . Here the sum of the positive coefficients in the first ...
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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.