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 xiv
... become imaginary in pairs ; as also that the even roots of positive quantities are either affirma- tive or negative ; that the odd roots of negative quantities are real and negative ; and that the even roots of them are imaginary . It ...
... become imaginary in pairs ; as also that the even roots of positive quantities are either affirma- tive or negative ; that the odd roots of negative quantities are real and negative ; and that the even roots of them are imaginary . It ...
Σελίδα 26
... which the pro- cess is regulated , is less than the first term of the divisor ; as the remaining part of the quotient , after this , would become frac tional . 3. The division of quantities may also be some- times 26 DIVISION .
... which the pro- cess is regulated , is less than the first term of the divisor ; as the remaining part of the quotient , after this , would become frac tional . 3. The division of quantities may also be some- times 26 DIVISION .
Σελίδα 29
... become negative , they may have their signs changed , or be taken affirmatively , without altering the truth of the result ; and if the first term of a divisor should not be exactly contained in the first term of the dividend , the ...
... become negative , they may have their signs changed , or be taken affirmatively , without altering the truth of the result ; and if the first term of a divisor should not be exactly contained in the first term of the dividend , the ...
Σελίδα 51
... become x x2 3x3 3.5x4 3.5.7x5 1+ -- + + 2 2.4 2.4.6 2.4.6.8 2.4 6.8.10 & c . where the law of the series is manifest ( w ) . EXAMPLES FOR PRACTICE . 2. Required the square root of a * + 4a3x + 6a2x2 + 4αx3 + x * . 3. Required the square ...
... become x x2 3x3 3.5x4 3.5.7x5 1+ -- + + 2 2.4 2.4.6 2.4.6.8 2.4 6.8.10 & c . where the law of the series is manifest ( w ) . EXAMPLES FOR PRACTICE . 2. Required the square root of a * + 4a3x + 6a2x2 + 4αx3 + x * . 3. Required the square ...
Σελίδα 72
... of the binomial surd are odd roots , the rule becomes more complicated ; but for the sum , or difference , of two cube roots , which is the most useful case , the multiplier will be a 72 IRRATIONAL QUANTITIES , OR SURDS .
... of the binomial surd are odd roots , the rule becomes more complicated ; but for the sum , or difference , of two cube roots , which is the most useful case , the multiplier will be a 72 IRRATIONAL QUANTITIES , OR SURDS .
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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.