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, Τόμος 1J. Johnson, 1813 - 428 σελίδες |
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Σελίδα xii
... answer . " g Y But this , as well as several other branches of ma- thematical knowledge , was more particularly culti- ( e ) The most remarkable circumstance in the algebra of this author is , that in the denoting of powers , he ...
... answer . " g Y But this , as well as several other branches of ma- thematical knowledge , was more particularly culti- ( e ) The most remarkable circumstance in the algebra of this author is , that in the denoting of powers , he ...
Σελίδα 58
... answer in decimals , will be readily per- ceived from considering the 1st question above given , where it is found that 414 ; in which case it is only necessary to ex- tract the square root of the whole number 14 , ( or to find it in ...
... answer in decimals , will be readily per- ceived from considering the 1st question above given , where it is found that 414 ; in which case it is only necessary to ex- tract the square root of the whole number 14 , ( or to find it in ...
Σελίδα 77
... answer . This being premised , it is only necessary farther to observe , that the method of adding and subtract- ing imaginary radicals , is the same as for real quan- tities ; there being no other difference in the com- mon operations ...
... answer . This being premised , it is only necessary farther to observe , that the method of adding and subtract- ing imaginary radicals , is the same as for real quan- tities ; there being no other difference in the com- mon operations ...
Σελίδα 109
... answer . And , in effect , if the three equations be properly examined , it will be found , that the third is merely the difference of the first and second , and consequently involves no condition but what is contained in the other two ...
... answer . And , in effect , if the three equations be properly examined , it will be found , that the third is merely the difference of the first and second , and consequently involves no condition but what is contained in the other two ...
Σελίδα 147
... answer . = 2. Given x - 6x = 12 , to find the value of x . Here a being equal to 6 , and b equal to 12 , we shall have , by the second formula , 2 x = √6 + √ ( 36 −8 ) + 3⁄4 { 6 + √ ( 36 −8 ) } 2 √ ( 6+ √28 ) = √ ( 6 +5.2915 ) + ...
... answer . = 2. Given x - 6x = 12 , to find the value of x . Here a being equal to 6 , and b equal to 12 , we shall have , by the second formula , 2 x = √6 + √ ( 36 −8 ) + 3⁄4 { 6 + √ ( 36 −8 ) } 2 √ ( 6+ √28 ) = √ ( 6 +5.2915 ) + ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 3 - Q/~\—C = equal to, the sign of equality; signifying that the quantities between which it is placed are equal to each other. Thus...
Σελίδα 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/.
Σελίδα 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.
Σελίδα 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
Σελίδα 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.
Σελίδα 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.