An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to GeometryEvert Duyckinck, Daniel D. Smith and George Long, 1818 - 260 sider |
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Side 61
... rational parts , and the quotient of the surds , and the two joined together , with their common radical sign between them , will give the whole quotient required . But if the surds are of different kinds , they must be reduced to a ...
... rational parts , and the quotient of the surds , and the two joined together , with their common radical sign between them , will give the whole quotient required . But if the surds are of different kinds , they must be reduced to a ...
Side 64
... rational part , will give the whole power required . And if it be a compound quantity , mul- tiply it by itself the proper number of times , according to the usual rule . ( u ) EXAMPLES . 1. It is required to find the square of 2./3/ 3 ...
... rational part , will give the whole power required . And if it be a compound quantity , mul- tiply it by itself the proper number of times , according to the usual rule . ( u ) EXAMPLES . 1. It is required to find the square of 2./3/ 3 ...
Side 65
... rational part , will give the whole root required . And if it be a compound quantity , find its root by the usual rule . ( x ) EXAMPLES . 1. It is required to find the square root of 93/3 . Here ( 92/3 ) * = 9a × 3a × ± = 9a × 3 * = 34 ...
... rational part , will give the whole root required . And if it be a compound quantity , find its root by the usual rule . ( x ) EXAMPLES . 1. It is required to find the square root of 93/3 . Here ( 92/3 ) * = 9a × 3a × ± = 9a × 3 * = 34 ...
Side 67
... rational quantities , the root will con- sist either of two surds , or of a rational part and a surd , which are the only cases of the rule that are useful . EXAMPLES . 1. It is required to find the square root of 11 + √72 , or √11 + ...
... rational quantities , the root will con- sist either of two surds , or of a rational part and a surd , which are the only cases of the rule that are useful . EXAMPLES . 1. It is required to find the square root of 11 + √72 , or √11 + ...
Side 68
... rational . RULE . 1. When one or both of the terms are any even roots , multiply the given binomial , or residual , by the same ex- pression , with the sign of one of its terms changed ; and repeat the operation in the same way , as ...
... rational . RULE . 1. When one or both of the terms are any even roots , multiply the given binomial , or residual , by the same ex- pression , with the sign of one of its terms changed ; and repeat the operation in the same way , as ...
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Vanlige uttrykk og setninger
Algebra arithmetical arithmetical mean arithmetical series bers coefficient common denominator compound quantity consequently cube root cubic equation decimal denoted Diophantus dividend divisor equal EXAMPLES FOR PRACTICE find the difference find the least find the product find the square find the sum find the value find two numbers fraction required geometrical geometrical progression geometrical series give given number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied negative nth root number of terms number required PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder Required the difference Required the sum required to convert required to divide required to find required to reduce result rithm rule second term side simple form square number square root square sought substituted subtracted sum required surd tion triangle unknown quantity Whence α α
Populære avsnitt
Side 10 - 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.
Side 20 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Side 27 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Side 173 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...
Side 77 - 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...
Side 93 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Side 93 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
Side 94 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
Side 30 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.