Introductio in analysin infinitorum

EX CIRCULO ORTIS. 107 CAP. VIII. tang. $a$ + tang. $b$ & tang. $b = \frac{1-\text{tang. }a}{1+\text{tang. }a}$. Sit nunc tang. $a = \frac{1}{2}$, erit tang. $b = \frac{1}{3}$, hinc uterque Arcus $a$ & $b$ per Seriem rationalem multo magis, quam superior, convergentem exprimetur, eorumque summa dabit valorem Arcus $\frac{\pi}{4}$; hinc itaque erit $\pi = 4. \left\{ \begin{array}{l} \frac{1}{1 \cdot 2} - \frac{1}{3 \cdot 2^3} + \frac{1}{5 \cdot 2^5} - \frac{1}{7 \cdot 2^7} + \frac{1}{9 \cdot 2^9} - \&\text{c.} \\ \frac{1}{3} - \frac{1}{3 \cdot 3^3} + \frac{1}{5 \cdot 3^5} - \frac{1}{7 \cdot 3^7} + \frac{1}{9 \cdot 3^9} - \&\text{c.} \end{array} \right\}$ hoc ergo modo multo expeditius longitudo semicircumferentiæ [TRUNCATED]