Methodus inveniendi lineas curvas

MAX. ET MIN. RELATIVA. 181 $q = \frac{y''-p}{dx}$; erit valor differentialis ipfius $q' = \frac{nv}{dx}$; ipfius $q'' = \frac{o\omega}{dx^2} - \frac{2nv}{dx^2}$; ipfius $q''' = -\frac{2o\omega}{dx^3} + \frac{nv}{dx^3}$; ipfius $q'''' = \frac{o\omega}{dx^4}$. Hocque modo similiter progredi licet ad sequentes quantitates $r, s$, &c. cum suis derivativis; hincque nascetur sequens Tabella, qua singularum harum quantitatum valores differentiales exhibentur. $d. y''' = nv$ $d. y'''' = o\omega$ $d. p''' = \frac{nv}{dx}$ $d. p'''' = -\frac{nv}{dx} + \frac{o\omega}{dx}$ $d. p''''' = -\frac{o\omega}{dx}$ $d. q'' = \frac{nv}{dx}$ $d. q''' = -\frac{2nv}{dx^2} + \frac{o\omega}{dx^2}$ $d. q'''' = \frac{nv}{dx^3} - \frac{2o\omega}{dx^3}$ $d. q''''' = \frac{o\omega}{dx^4}$ $d. r' = +\frac{nv}{dx^2}$ $d. r'' = -\frac{3nv}{dx^3} + \frac{o\omega}{dx^3}$ $d. r''' = +\frac{3nv}{dx^4} - \frac{3o\omega}{dx^4}$ $d. r'''' = -\frac{nv}{dx^5} + \frac{3o\omega}{dx^5}$ $d. r''''' = -\frac{o\omega}{dx^5}$ $d. s = +\frac{nv}{dx^3}$ $d. s' = -\frac{4nv}{dx^4} + \frac{o\omega}{dx^4}$ $d. s'' = +\frac{6nv}{dx^5} - \frac{4o\omega}{dx^5}$ $d. s''' = -\frac{4nv}{dx^6} + \frac{6o\omega}{dx^6}$ $d. s'''' = +\frac{nv}{dx^7} - \frac{4o\omega}{dx^7}$ $d. s''''' = +\frac{o\omega}{dx^8}$ &c. Ex hac Tabella perspicitur, in valoribus differentialibus totidem terminos particula $o\omega$ affectos occurrere, ac particula $n$; atque in utrisque pares adesse coefficientes: discrimen vero in hoc consistere, ut cuilibet termino particula $o\omega$ affecto respondeat Z 3