Methodus inveniendi lineas curvas

288 DE CURVIS inventam resolvens; qui angulus cum sit recto major, ponatur $\frac{a}{c} = \frac{1}{2}\pi + \Phi$; existente $\Phi$ angulo recto minore. Hinc, ob $\sin \frac{a}{c} = \cos \Phi$, & $\cos \frac{a}{c} = -\sin \Phi$, obtinebitur duplex æquatio. $e^{\frac{a}{c}} = \frac{1 \mp \cos\Phi}{\sin\Phi}$. quæ præbet, vel $e^{\frac{a}{c}} = \tan \frac{1}{2}\Phi$, vel $e^{\frac{a}{c}} = \cot \frac{1}{2}\Phi$, quarum posterior minorem dabit valorem pro angulo $\Phi$; quæ ergo ad casum propositum erit accommodata. 72. Sequentes possibiles oscillationum modi reperientur, si pro $\frac{a}{c}$ ponantur anguli duobis rectis majores, tribus vero minores. Sic posito $\frac{a}{c} = \frac{3}{2}\pi - \Phi$, erit $\sin \frac{a}{c} = -\cos \Phi$, & $\cos \frac{a}{c}$ $= -\sin \Phi$; unde fit $e^{\frac{a}{c}} = \frac{1+\cos\Phi}{\sin\Phi}$, [TRUNCATED]