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 xxii
... relations of the coefficients of the several terms ; from which , though not so strict a method of investigation as the subject requires , many of the most important properties of equations have since been derived . He also greatly ...
... relations of the coefficients of the several terms ; from which , though not so strict a method of investigation as the subject requires , many of the most important properties of equations have since been derived . He also greatly ...
Σελίδα 81
... relation which two quantities , of the same kind , have to each other with respect to their difference . Hence , agreeably to this definition , three quanti- ties are said to be in arithmetical proportion , when the difference of the ...
... relation which two quantities , of the same kind , have to each other with respect to their difference . Hence , agreeably to this definition , three quanti- ties are said to be in arithmetical proportion , when the difference of the ...
Σελίδα 86
... relation of two quantities of the same kind , which arises from considering what part , or parts , the one is of the other , or how often it is contained in it . When four quantities are compared together , the first and third are ...
... relation of two quantities of the same kind , which arises from considering what part , or parts , the one is of the other , or how often it is contained in it . When four quantities are compared together , the first and third are ...
Σελίδα 89
... relation of their terms ; but as these are , in general , of little use , besides being very burdensome to the memory , the tendency , of late , has been to discard them , and to substitute the corresponding equations in their stead ...
... relation of their terms ; but as these are , in general , of little use , besides being very burdensome to the memory , the tendency , of late , has been to discard them , and to substitute the corresponding equations in their stead ...
Σελίδα 94
... relations to others which are known . This is done by making certain algebraic . ex- pressions equal to each other ; which formula , in that case , is called an equation ; and then working by the rules of the art , till the quantity ...
... relations to others which are known . This is done by making certain algebraic . ex- pressions equal to each other ; which formula , in that case , is called an equation ; and then working by the rules of the art , till the quantity ...
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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.