III 



J. 2 2^ Simili modo denominatorem traflemus^ eritqiie 

 fa6la euolatione 



s{i -\-ss)-{-^sx-hss-{~x{i-hss)-\-xx, 



vbi termini folam s continentes funt 



s{i-i-ss)-i-ss-h^n(i-i-s^)~s(i-^ss)-hl(i-hssf 



~l,(l-hSs)(l-i-sf'^ 



termini vero litteram x continentes erunt 

 fisx-\-x(i-{-ss) — x(i-{- sf, 



ideoque denominator hanc induit formam : l(i -¥-sf(i x-+- i-hss). 

 Cum igitur numerator et denominator habeat communem 

 faflorem |(2x-f-i-|-<S'^), pars finiftra noftrae aequationis 

 fit l ^\=~l :^ 2 l ^-=^ , vti poftulabatur. 



5. 23. Supereft igitur, vt etiam aequalitatem inter 

 arcus circulares demonftremus , hoc eft vt lit 



i A t^"§- .-^x-ss — A tang. ^ — ^ A tang. -i-. 

 Transferamus hunc in fmem A tang. — in alteram partem^ 

 et cum fit 



A tang. a-\-A tang. b = A tang. ^^^ , 

 haec aequatio proueniet : 



A tang. ^sT. .-.-s^ — = 2 A tans;. s. 



c>x-+-xx— ssx — s s O 



At vero, fi loco xx fcribatur valor ^("^ -hs"^), denominator 

 euadet (i — ^ ^)[i(^ — .y^)-j-x], numerator vero : 



s(2x-\-i — ss) — 2sV^(^ — ss)-{-x], 



ficque adeft fa£lor communis 1(1 —ss)-hx, quo fublato fiet 

 A tang. p:^^ zz: 2 A tang. s. Sicque perfe6ta aequalitas rigide 



eft 



