Elements of analysis as applied to the mechanics of engineering and machinery . d y are termed variables^ orvariable magnitudes^ whilst those that are determined, or to be re-garded as determined, and, therefore, prescribe the algebraic processby which y proceeds from x^ are called constants^ or constant magni-tudes. That one of the variable magnitudes which is to be assumedarbitrarily, is termed the independent variable,, but that one which isdetermined as a function of the latter by a prescribed jjrocess, iscalled the dependent variable. In ?/ = a ^™, a and m are the con-stants, whilst X is
Elements of analysis as applied to the mechanics of engineering and machinery . d y are termed variables^ orvariable magnitudes^ whilst those that are determined, or to be re-garded as determined, and, therefore, prescribe the algebraic processby which y proceeds from x^ are called constants^ or constant magni-tudes. That one of the variable magnitudes which is to be assumedarbitrarily, is termed the independent variable,, but that one which isdetermined as a function of the latter by a prescribed jjrocess, iscalled the dependent variable. In ?/ = a ^™, a and m are the con-stants, whilst X is the independent, and y the dependent, variable. The dependence of one magnitude z upon two others x and y isexpressed by z =/(a7, y). In this case z is, at the same time, func-tion of X and ^, and here, therefore, we have to consider two inde-pendent variable magnitudes. Art. 2. Every dependence of one magnitude y upon another x^expressed by a function, or formula y =/(^), may be representedby a plane curve, or curved line AP Q^ Eigs. 1 and 2; the abscissas Fig. 1. Fig. A M N ^ ? T M N ^ A Jf, A N^ &c., of the curve, correspond to the difierent values ofthe independent variable x, and the ordinates MP^ N Q, &c., to the1 (1) ELEMENTS OF ANALYSIS. [Art.
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