20 6 Opuscula . 
Ut indoles feriei , quae ex hac methodo provenit , melius 
cognofcatur , fatis erit unam ex praediftis formulis evolvere ; 
feries enim in omnibus eodem palHi procedit . Hanc feligo 
S Cc . (p d(p . Habemus 
atqui 
s cT:^'"'" d(^=i~ c7:^'""'i'(?.(p + ^^y*sc7ri"'"* 
d<^\ ergo 
SC c .(o"* dCDr:: — C c .(d'*''"* Sc.to-^ — Cc .d)""^^ S c.c^ 
m — 1 . m ~ ^ — - m + 4 
H- fbCc.(p dp ; atqui 
J^; ergo 
SCc.qj dp=z-Cc.(p Sccp —:,__^r^Cc.<p Se.^ 
m — 1 . m —• i , ro— $ ^ m — i.w — — « ^ 
r^Cc.p Sc>p-^ ' 
m .m — 2.?w — 4 m . m •— 1, . m — 
m — 6 , , ^ . » 
SCc.cp J^p. Atque ita progrediens mvenies feriem , in 
qua oranes termini multiplicantur per Sc.(^% exponentes au- 
tem Cc.(^ procedunt per feriem m — i, m — 3, m-~5, 
m — 7 &c. ufque ad o, in quo tamquam in ultimo termino 
fiftes . Coefficientes vero terminorum funt — , — , 
m 7 
m — I . »3— ~3 .»72 — 5 
&c. Supple autem dimen- 
m , m — i.jjj — 4 m . m — z . m — . m — 6 
fiones per poteilates fmus totius z=. r . 
Si m lit numerus pofitivus , & par , duse primae formulae 
pendebunt ab hjperbolse quadratura , dujs ultimae a quadratu- 
ra circuli . Nam fafto eodem progreflii tandem pervenimus 
ad formulam S^/cp, quse in primis dat dupjum feftorem hy- 
perbolicum , in aliis duplum ft(florem circularem divifum 
per fmum totum . 
^ Si evolvas eamdem formulam S Cc.p'"d(Oi invenies 
eanv 
