Introductio in analysin infinitorum

EX CIRCULO ORTIS. 101 CAP. VIII. $+ \frac{m^{24}}{n^{24}} \cdot 0, 000000000000000000820675327$ $- \frac{m^{26}}{n^{26}} \cdot 0, 00000000000000000003115285$ $+ \frac{m^{28}}{n^{28}} \cdot 0, 0000000000000000000010165$ $- \frac{m^{30}}{n^{30}} \cdot 0, 00000000000000000000000026$ Cum igitur sufficiat Sinus & Cosinus angulorum ad $45^\circ$ nosse, fractio $\frac{m}{n}$ semper minor erit quam $\frac{1}{2}$, hincque etiam ob Potestates fractionis $\frac{m}{n}$, Series exhibitæ maxime convergent, ita ut plerumque aliquot tantum termini sufficiant, præcipue, si Sinus & Cosinus non ad tot figuras desiderentur. 135. Inventis Sinibus & Cosinibus inveniri quidem possunt Tangentes & Cotangentes, per analogias consuetas, at quia in hujusmodi ingentibus numeris multiplicatio & divisio vehementer est molesta, peculiari modo eas exprimere convenit. Erit ergo $tang. v = \frac{sin. v}{cos. v} = \frac{v - \frac{v^3}{1.2.3} + \frac{v^5}{1.2.3.4.5} - \frac{v^7}{1.2.3....7} + \&c.}{1 - \frac{v^2}{1.2} + \frac{v^4}{1.2.3.4} - \frac{v^6}{1.2.0....6} + \&c.}$ & $cot. v = \frac{cos. v}{sin. v} = \frac{1 - \frac{v^2}{1.2} + \frac{v^4}{1.2.3.4} - \frac{v^6}{1.2.3....6} + \&c.}{v - \frac{v^3}{1.2.3} + \frac{v^5}{1.2.3.4.5} - \frac{v^7}{1.2.3....7} + \&c.}$ N 3 fi