A Treatise on Algebra, in Practice and Theory: With Notes and Illustrations; Containing a Variety of Particulars Relating to the Discoveries and Improvements that Have Been Made in this Branch of Analysis, Volum 1J. Johnson, 1813 - 428 sider |
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Side 14
... taking of one quantity from another ; or the method of finding the dif- ference between any two quantities of the same kind ; which is performed as follows : ( e ) ( e ) The term subtraction , used for this rule , is liable to the same ...
... taking of one quantity from another ; or the method of finding the dif- ference between any two quantities of the same kind ; which is performed as follows : ( e ) ( e ) The term subtraction , used for this rule , is liable to the same ...
Side 47
... taking the root both of its numerator and denominator . Note . The square root , the fourth root , or any other even root , of an affirmative quantity , may be either + or Thus , √ a2 = + a ora , and b + b or -b , & c . But the cube ...
... taking the root both of its numerator and denominator . Note . The square root , the fourth root , or any other even root , of an affirmative quantity , may be either + or Thus , √ a2 = + a ora , and b + b or -b , & c . But the cube ...
Side 78
... taking them as real quantities . Thus , ( + √ −α ) × ( + √ − b ) , or ( −√ - a ) x ( −√ — b ) = −√ab ; and , consequently , ( + √ −α ) × ( + √− a ) , or - ( −√ − a ) × ( −√ — a ) = — a . And if one of the imaginary ...
... taking them as real quantities . Thus , ( + √ −α ) × ( + √ − b ) , or ( −√ - a ) x ( −√ — b ) = −√ab ; and , consequently , ( + √ −α ) × ( + √− a ) , or - ( −√ − a ) × ( −√ — a ) = — a . And if one of the imaginary ...
Side 96
... taking any quantity from one side of an equation , and placing it on the other , with a contrary sign . 2. If all the terms of any two equal quantities , be multiplied , or divided , by the same quantity , the products , or quotients ...
... taking any quantity from one side of an equation , and placing it on the other , with a contrary sign . 2. If all the terms of any two equal quantities , be multiplied , or divided , by the same quantity , the products , or quotients ...
Side 126
... taking such a root , or power of the result , as is denoted by the reduced index of the unknown quantity . Thus , if there be taken any general equation of this kind , as x2m + ax TM = b , we shall have , by taking the square root of x2 ...
... taking such a root , or power of the result , as is denoted by the reduced index of the unknown quantity . Thus , if there be taken any general equation of this kind , as x2m + ax TM = b , we shall have , by taking the square root of x2 ...
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A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volum 1 John Bonnycastle Uten tilgangsbegrensning - 1820 |
Vanlige uttrykk og setninger
4th power algebra arise arithmetical arithmetical mean arithmetical series ax² binomial coefficients consequently continued fraction cube root cubic equation cx² decimal denoted determined Diophantus divisor dx³ equa equal roots equation x² expression factors find the four find the least find the square find the sum find the value find two numbers former formula four roots frac geometrical given equation given number Hence infinite series integral kind last term latter least values logarithms method multiplied negative number of terms observed proportion proposed equation quadratic equation question quotient rational readily Required the sum required to divide required to find required to reduce resolved result rule scale of relation simple fractions square number square root substituting subtracted surd three roots tion unknown quantity value of x Whence whole numbers
Populære avsnitt
Side 39 - 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 23 - 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 123 - 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 137 - 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 3 - Q/~\—C = equal to, the sign of equality; signifying that the quantities between which it is placed are equal to each other. Thus...
Side 119 - A person bought a chaise, horse, and harness for 60?.; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each ? Ans. 13/.
Side 33 - 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 360 - N .•. def. (2), x— x1 is the logarithm of that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power of n. N" =a
Side 123 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Side 49 - ... 2. Subtract the square of the root, thus found from the first term, and bring down the two next terms to the remainder for a dividend.