Introductio in analysin infinitorum

102 DE QUANTITATIBUS TRANSCENDENT. LIB. I. si jam fit Arcus $v = \frac{m}{n} 90^\circ$ erit eodem modo quo ante tang. A. $\frac{m}{n} 90^\circ =$ + $\frac{2mn}{nn-mm}$ 0, 6366197723675 + $\frac{m}{n}$ 0, 2975567820597 + $\frac{m^3}{n^3}$ 0, 0186886502773 + $\frac{m^5}{n^5}$ 0, 0018424752034 + $\frac{m^7}{n^7}$ 0, 0001975800714 + $\frac{m^9}{n^9}$ 0, 0000216977245 + $\frac{m^{11}}{n^{11}}$ 0, 0000024011370 + $\frac{m^{13}}{n^{13}}$ 0, 0000002664132 + $\frac{m^{15}}{n^{15}}$ 0, 0000000295864 + $\frac{m^{17}}{n^{17}}$ 0, 0000000032867 + $\frac{m^{19}}{n^{19}}$ 0, 0000000003651 + $\frac{m^{21}}{n^{21}}$ 0, 0000000000405 + $\frac{m^{23}}{n^{23}}$ 0, 0000000000045 + $\frac{m^{25}}{n^{25}}$ 0, 0000000000005 cot. A. $\frac{m}{n} 90^\circ =$ + $\frac{n}{m}$ 0, 6366197723675 − $\frac{4mn}{4nn-mm}$ 0, 3183098861837 − $\frac{m}{n}$ 0, 2052888894145 − $\frac{m^3}{n^3}$ 0, 0065510747882 − $\frac{m^5}{n^5}$ 0, 0003450292554 − $\frac{m^7}{n^7}$ 0, 0000202791060 − $\frac{m^9}{n^9}$ 0, 0000012366527 − $\frac{m^{11}}{n^{11}}$ 0, 0000000764959 − $\frac{m^{13}}{n^{13}}$ 0, 0000000047597 − $\frac{m^{15}}{n^{15}}$ 0, 0000000002969 − $\frac{m^{17}}{n^{17}}$ 0, 0000000000185 − $\frac{m^{19}}{n^{19}}$ 0, 0000000000011 quarum Serierum ratio infra fusius exponetur. 136. Ex superioribus quidem constat, si cogniti fuerint omnium angulorum semirecto minorum Sinus & Cosinus, inde simul omnium angulorum majorum Sinus & Cosinus haberi. Verum si tantum angulorum 30° minorum habeantur Sinus