Methodus inveniendi lineas curvas

80 DE METHODO MAX. ET MIN. $0 = Axq - Bq + C + Z - Rr + \frac{rdS}{dx} - \frac{rddT}{dx^2} - Ap - Ss + \frac{sdT}{dx} - Tt \quad \&c.$ feu $0 = A(xq-p) - Bq + C + Z - Rr + \frac{rdS-Sdr}{dx} - \frac{rddT-drdT+Tddr}{dx^2} + \&c.$ CASUS VII. 69. Si fuerit $M=0$, $N=0$, $P=0$, & $Q=0$, ita ut fit $dZ=Rdr+Sds+Tdt+\&c.$ Ob $N=0$, & $Q=0$, Casus tertius istam suppeditat aequationem pro curva jam ter integratam, $0 = Ax^2 - Bx + C - R + \frac{dS}{dx} - \frac{ddT}{dx^2} + \&c.$ ad quam per $dr=sdx$ multiplicatam addatur $0 = -dZ + Rdr + Sds + Tdt + \&c.$ quo facto prodibit ista aequatio, $0 = Ax^2dr - Bxdr + Cdr - dZ + sdS - \frac{sddT}{dx} + [TRUNCATED]