The Mathematician, Vol 1 Classic Reprint

Excerpt from The Mathematician, Vol. 1

The coefficients now under consideration, are always introduced into analysis, subjected to a series of specified conditions and, as they never appear unaccompanied by these conditions, the term here chosen appears to be a very appropriate one. It is, therefore, adopted in the present and some succeeding papers in this work. This term has also the advantage of distinct and expressive application to another class of functions, nearly allied in its philosophical principles to this - known by the name of inde terminate multipliers. Or arbitrary multipliers. These multipliers are only introduced conditionally; that is, the several products are subjected to predetermined combinations, or made to fulfil certain specified conditions. It is, therefore, proposed to call these conditional multipliers.

The ordinary method of establishing the fundamental proposition respecting conditional coefficients, has often been objected to; and with good reason too, whether the following views shall be found correct, or not. It is, in fact, one of the most striking instances of what Berkeley terms shifting the hypothesis; that is, making a new hypothesis for the purposes of reasoning, which is inconsistent with the existence of the original one, upon which the proposition is founded. The method of making a: alternately zero and arbitrary is, however, the only one used in almost every work, even the most modern, that has been written for academical purposes, either in England or France. About eight years ago, however.

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