Methodus inveniendi lineas curvas

AD CURVAS INVENIENDAS ABSOLUTA. 115 valores §.30 indicati substituatur. Quoniam autem insuper in haec differentialia ingrediuntur $d\pi$, $d\pi'$, $d\pi''$, &c. ponamus corum valores ex $n\nu$ oriundos tantisper, donec eos inveniamus, esse hos: $d\pi = n\nu . \alpha$ $d\pi''' = n\nu . \delta$ $d\pi'''''' = n\nu . \eta$ $d\pi' = n\nu . \beta$ $d\pi'''' = n\nu . \epsilon$ $d\pi''''''' = n\nu . \theta$ $d\pi'' = n\nu . \gamma$ $d\pi''''' = n\nu . \zeta$ &c. Hinc itaque erunt valores differentiales $d.Z\,dx = n\nu . dx (L\alpha + \frac{Q}{dx})$ $d.Z'dx = n\nu . dx (L'\beta + \frac{P'}{dx} - \frac{2Q'}{dx^2})$ $d.Z''dx = n\nu . dx (L''\gamma + N' - \frac{P''}{dx} + \frac{Q''}{dx^2})$ $d.Z'''dx = n\nu . dx L'''\delta$ $d.Z''''dx = n\nu . dx L''''\epsilon$ $d.Z'''''dx = n\nu . dx. L'''''\zeta$ &c. Ut nunc valores litterarum $\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$, &c. definiamus; notandum est esse $d\pi$, $d\pi'$, $d\pi''$, &c. valores differentiales quantitatum $\pi$, $\pi'$, $\pi''$, &c. Est vero $\pi = \int [Z]dx$ $\pi' = \int [Z]dx + \int [Z']dx$ $\pi'' = \int [Z]dx + \int [Z']dx + \int [Z'']dx$ $\pi''' = \int [Z]dx + \int [Z']dx + \int [Z'']dx + \int [Z''']dx$ &c. ubi $\int [Z]dx$, per hypothesin, a particula $n\nu$ non afficitur. Valores igitur differentiales formularum $[Z]dx$, $[Z']dx$, $[Z'']dx$ &c. sunt investigandi, qui erunt P 2 $d.[Z]dx$