Elements of analysis as applied to the mechanics of engineering and machinery . -^^uv^rr) COS. a^ (u^ — ^uv -f- v^) w^ -f- 2wu -f- -u^ u 2wu -\- v^ b 4:UV sm. a^ ELEMENTS OF ANALYSIS. 19 Art. 13.] from which there results the so-called equation of asymptotes ofthe hyperbola: u V e e -—, or -u = —. It is, therefore, easy to draw the hyperbola between the given asymp- totes. The co-ordinates for the vertex A are GE = EA =-^, whilst Fig. 22. -T ^. those for the point K are C B ^r= e and BK —; we have, further, -, i —, &C. for the abscissas 2e, 3e, 4e, &c, the ordinates J , ^ Art. 13. If, in th
Elements of analysis as applied to the mechanics of engineering and machinery . -^^uv^rr) COS. a^ (u^ — ^uv -f- v^) w^ -f- 2wu -f- -u^ u 2wu -\- v^ b 4:UV sm. a^ ELEMENTS OF ANALYSIS. 19 Art. 13.] from which there results the so-called equation of asymptotes ofthe hyperbola: u V e e -—, or -u = —. It is, therefore, easy to draw the hyperbola between the given asymp- totes. The co-ordinates for the vertex A are GE = EA =-^, whilst Fig. 22. -T ^. those for the point K are C B ^r= e and BK —; we have, further, -, i —, &C. for the abscissas 2e, 3e, 4e, &c, the ordinates J , ^ Art. 13. If, in the elementary ratio -^-, or in the formula for the tangent (tang. «, Art. 6,) of the tangential angle, we substitute suc-cessively different values for ^, there will result the different posi-tions of the line of contact of the appurtenant curve. If we takeX = 0^ we obtain the tangent of the tangential angle at the originof the co-ordinates; but if we take ^ = oo, we have the tangent foran infinitely distant point of the curve. The points where the tan-gent to a curve runs parallel with one of the axes of the co-ordinatesare the most important; because, here, as a rule, the one or the otherof the co-ordinates x and y has its maximum or viinimum value;or is, as we sa}^, a maximum or a minimum. For the parallelismwith the axis of abscissas, we have a = 0; therefore, also, tang. a:=:0;and for the parallelism with the axis of or
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