Methodus inveniendi lineas curvas

64 DE METHODO MAX. ET MIN. ber $y^{1-n}p/p+C = y^{1-n}p+y^{n-1}p/p$, sive $y^{n-1}p=C$; quæ est ea ipsa æquatio, quam ante pro eodem casu in solutione Exempli invenimus. Hanc ob rem ad Exempla huic Problemati propria progrediamur. EXEMPLUM II. Fig. 5. §. 51. Invenire curvam Am, quæ cum sua evoluta AR & radio osculi mR in quovis loco applicato, minimum spatium ARm includat. Positis abscissa $AM=x$, applicata $Mm=y$; erit radius osculi $mR = \frac{(1+pp)^{\frac{3}{2}}}{q}$; area autem $ARm$ est $\int mR. dx \sqrt{(1+pp)}$; ex qua minimum esse oportet hanc formulam $\int \frac{(1+pp)^2}{q} dx$. Erit itaque $Z = \frac{(1+pp)^2}{q}$, & $dZ = \frac{4(1+pp)pdp}{q} - \frac{(1+pp)^2 dq}{qq}$; unde fit $M=0$, $N=0$, $P = \frac{4(1+pp)p}{q}$, & $Q = -\frac [TRUNCATED]