22 1 



CA =: 1 , AP z=: a- , ei il PQ nz y 2 x -}- xx =z AU et CR =z 

 •j/CA- -+- AR"m 1 -f-a- :z3 CF. Tum vcro ob tnangula CPQ et 

 CAT , nec non CAR et CVS eiit : 



CP : CA=PO : AT, 



CR : es =: AR : SV , 



icicoque ob CP =z CR ; CA :=: CS ; PQ — AR , erit AT r= S V 

 Hinc igitur sequitur fore tag. ACT zzz sin. ACR, tum vero 



PC2 =z tag. ACR , 



CP zz: sec. ACR . 



§. 3. QuaeraiTiTis nunc superficlem Sectoris hj'-perbolici 

 CAQC pci- arcuni clrcularem AS , sive per angulnm ACR expres- 

 sum. A'ocetur hic angulus ACR :^ ^ et cum sif AR — PO — tng./ 

 et CP rz: CR izz sec. / erit area Iriançuli CPO zzz ^--^ ; a (lua 



-j o ,*., 2 COS. ç* * 



si auferatur area segmenti hjpeiboiici APQ , remanet area sectoris 

 CAQC. Posito autem AP =z a? , PQ z=: y , area segmenti est 

 APQ z=: y. ydx ; unde cum sit x :rz sec. ^ — 1 et 7 zn tag. ^, 



-•!' fu^- =/^,^ = .^, - i / • tg. (4 5° + i 0, --le fit 

 ai-ea sectoris quaesita : CAQC z:z 1 / . tag. (4 5 -}- l^). 



§. 4. Ponannis / . tg. (4 5° -|- | ^) z:z OJ, ita area sectoris sic 

 CAQC ;^ i w , eritque tag. (.i5° + ^ ^) zr: e" , hoc p-- 



unde porro deducitur 



V e" — 1 



tag.é^=:,o.-zpr 

 sicque habebimus 



'- . . y e" — e— w ,. 



sive tag. ,^ ::= ^ , hincque 



sec. ^ ZZ. 



