I50 Atti 



hypothcfes has omnes a nobis confiderari necenTe cfl, ut ea- 

 rum lingulis genuina Tua > & peculiaris conftriiftio accommo- 

 decur. 



XXIII. Sit primo u realis ac pofitiva , & quantirates AìB,(i 

 pofitivae . in hac hypotheiì tres ealus diilingaendi funr, quan- 

 doquidem fieri poteft, ut lit (^— ^ 5 v/w )*>(/?-+■ VVjS 



_ 4 32 



five ( A —i- B V 01 )* < (a —h vaT ) ^ , aut denique 



_4 _ 32 



( A-+B V u )^ = (a -H-v'w')J. Quoniatn in primo ca- 



4 pSL —_— 



fu quamitas 1/ ( A —^ B ^ u )' — (/i— (-v/«)^eft rcalis , 



4 32 



liquet > noflrae formulae coUationem infìitui oporrere ciim ea 

 )1~ , quae exprimit colinum logarithmi fubquiatupli , _unde 

 duae gignuntur aequationes C&. Mr'^—^Sb. Mr*=^A~*- B </ u -+■ 



l/{A^BV'Z)' — (a-^ V^^iCb. Mr^— Sb. Mr* = 



TJ" ____J1_^ 



^ -f 5 V/ w — / ( ^_2^ V u )' — ( g -H \/ ft) )^ , qua- 



^ 4 ^^ • r • 



rum additio > & deinde alterius a prima fubtra£lio , iufficiet 



Cb.M:^A-+BV'Z iS/j.M=l^(^^BV^y^^(a^V^. 

 Tr^ "^ 4 . 32 



Ex hyperbolae aequilaterae proprietate, quadratorum cofinus 

 & linus hyperbolici diiibrentia aequatur quadrato linus to- 



tius ; igitur CL^^ ~~Sb7M' = T^ -^ B ^ ^ ) ' — 



4 r^ 

 {A-^BVZy -^ {a-^\r Zy = r^hoc eft ( a^V «Y 



4 r* 3 2 r* - 3 ^ 



= r '° ; ac proinde r = V a -^ VV • Eric idcirco f = 



2 



Ch. 



