Methodus inveniendi lineas curvas

AD CURVAS INVENIENDAS ABSOLUTA. 73 Ad horum valorum incrementa, ex translatione puncti $n$ in $v$ oriunda, invenienda, singulos hos valores differentiari, locoque differentialium $dy, dp, dq, dr, ds, dt$ cum ipsorum derivativis valores supra assignatos & per $nv$ expressos substitui oportet; eritque ut sequitur: $d.Zdx = nv.dx(\frac{T}{dx^2})$ $d.Z'dx = nv.dx(\frac{S'}{dx^3} - \frac{5T'}{dx^4})$ $d.Z''dx = nv.dx(\frac{R''}{dx^3} - \frac{4S''}{dx^4} + \frac{10T''}{dx^5})$ $d.Z'''dx = nv.dx(\frac{Q'''}{dx^3} - \frac{3R'''}{dx^4} + \frac{6S''''}{dx^5} - \frac{10T'''''}{dx^6})$ $d.Z''''dx = nv.dx(\frac{P''''}{dx^3} - \frac{2Q'''''}{dx^4} + \frac{3R''''''}{dx^5} - \frac{4S'''''''}{dx^6} + \frac{5T''''''''}{dx^ [TRUNCATED]