Articoli correlati a Theory of conjugate functions, or algebraic couples
Sinossi
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1835 Excerpt: ...other and from the product, may be called (by analogy to arithmetic) the algebraic division of the given fractional product as a dividend, by the given fractional factor as a divisor; and the result, which may be called the quotient, may always be found by algebraically multiplying the proposed dividend by the reciprocal of the proposed divisor. This more general conception of quotient, agrees with the process of the 15th article, for the division of one whole number by another, when that process gives an accurate quotient in whole numbers; and when no such integral and accurate quotient can be found, we may still, by our present extended definitions, conceive the numerator of any fraction to be divided by the denominator, and the quotient of this division will be the fractional number itself. In this last case, the fractional number is not exactly equal to any whole number, but lies between two successive whole numbers, a next preceding and a next succeeding, in the general progression of numbers; and these may be discovered by the process of approximate division above mentioned, while each of the two remainders of that approximate division is the numerator of a new fraction, which retains the proposed denominator, and must be added algebraically as a correction to the corresponding approximate integer quotient, in order to express, by the help of it, the quotient of the accurate division. For example, 8302.082 03-=-+! =--+ 2, and--=-+92=---+61. 00 0 Ep » 0 In general, a fractional number may be called a mixed number, when it is thus expressed as the algebraic sum of a whole number and a proper fraction, this last name being given to a fractional number which lies between zero and positive or contrapositive one. We may remark that an ordinal relation ...
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