Methodus inveniendi lineas curvas

284 DE CURVIS curvae $BMa$, quam lamina inter ofcillandum induit, nosse. Sit igitur $AP=x$, $PM=y$, arcus $aM=s$, & radius ofculi in $M=R$; & intervallum minimum $Aa=b$; atque, ex conditione memorata, erit arcus $s$ proxime æqualis abfcissæ $x$, ac proinde pro $ds$ fumi poterit $dx$: præ $dx$ enim evanescet $dy$. Et cum, pofito $dx$ conftante, fit generatim radius ofculi $=\frac{ds^3}{dxddy}$, erit præsenti casu $R=\frac{dx^2}{ddy}$; nam curva $BMa$ convexitatem axi $BA$ obvertit, & quia lamina in $B$ muro firmiter est infixa, erit recta $AB$ tangens curvæ in puncto $B$. 66. His pofitis, tam ad naturam curvæ $BMa$ quam ad ipsum motum ofcillatorium determinandum, fit $f$ longitudo penduli simplicis isochroni: ofcillationes enim minimas esse isochronas, cum natura rei declarat, tum ipse calculus instituendus monstrabit. Acceleratio ergo, qua laminæ punctum $M$ versus $P$ urgetur, erit $=\frac{PM}{f}=\frac{y}{f}$. Qu [TRUNCATED]