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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Resultat 1-5 av 88
Side xviii
... result ; in support of which proof he lays down a rule for the extraction of the roots of certain bino- mial surds , and shows that the radical parts , in some particular , numeral examples of the kind above mentioned , will destroy ...
... result ; in support of which proof he lays down a rule for the extraction of the roots of certain bino- mial surds , and shows that the radical parts , in some particular , numeral examples of the kind above mentioned , will destroy ...
Side xxv
... resulting equation may be depressed one degree lower than the pro- posed equation ( m ) . Besides which he also annexed ( m ) It was also farther shown by Rolle , in his Algebra , printed in 1690 , that the roots of the equation , thus ...
... resulting equation may be depressed one degree lower than the pro- posed equation ( m ) . Besides which he also annexed ( m ) It was also farther shown by Rolle , in his Algebra , printed in 1690 , that the roots of the equation , thus ...
Side 1
... letters a , b , c , & c . it is obvious that the results , so obtained , will be general ; and that any par- ticular case , of a similar kind , may be readily derived from them R tween which it is placed is to be taken from.
... letters a , b , c , & c . it is obvious that the results , so obtained , will be general ; and that any par- ticular case , of a similar kind , may be readily derived from them R tween which it is placed is to be taken from.
Side 17
... result , with the proper sign prefixed , will be the product required ( f ) . EXAMPLES . + 5a -6.x - 12a 3b -2ȧ + 4b -9ae 5bx 36ab - 8ab - - 30ах + 45bxs 7ab -6a2x -2xy — 5ac + 5x -xy - 7axy + 6ay 3a2b 12a2x - 6xyz - a2xy 2ba -2xy + ay ...
... result , with the proper sign prefixed , will be the product required ( f ) . EXAMPLES . + 5a -6.x - 12a 3b -2ȧ + 4b -9ae 5bx 36ab - 8ab - - 30ах + 45bxs 7ab -6a2x -2xy — 5ac + 5x -xy - 7axy + 6ay 3a2b 12a2x - 6xyz - a2xy 2ba -2xy + ay ...
Side 20
... result by the third , and so on to the last factor , as below . x + a x + b x2 + ax 2 + bx + ab x2 + ( a + b ) x + ab x + c x3 + ( a + b ) x2 + abx + cx2 + c ( a + b ) x + abc ' x3 + ( a + b + c ) x2 + ( ab + ac + bc ) x + abc x - a x ...
... result by the third , and so on to the last factor , as below . x + a x + b x2 + ax 2 + bx + ab x2 + ( a + b ) x + ab x + c x3 + ( a + b ) x2 + abx + cx2 + c ( a + b ) x + abc ' x3 + ( a + b + c ) x2 + ( ab + ac + bc ) x + abc x - a x ...
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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.