NOVI ALGORITHMI. 49 



S.2. Confideremus nunc fradionem fequentem: 



x^_ ( i>, a, 6, c ) _ c{v,a,b) -^lv, a) 

 y~ la,b,c) ~ c ( 0, 6 ) -+- a, 



ex qua colligitur : 



^i.zca{a,6) 



cuius pars media reducitur ad 

 zci^ir—aa-hv) 



vnde ob -uzA, aar A + B; pA = B4-C, Ytf=C+D 

 refultat xx—zjjzz^-i-c^C—D^^rzS 

 ita \t fit {v,a,b,cy-z{a,h,cyzz$f vnde per in- 

 dudionem fequentes valores facile colliguntur. 



23. Ne autem hic induftioni nimium videar 

 tribuiffc , fequenti modo haec inueftigatio inftitui 

 potcft : 



{n{vy -zi' -5t 



{v,ay -z{ay ==35 



{v,a,by -z{a,6y =(£ 

 [v,a,b,cy -z{a,b,cy =:© 

 {v,a,b,c,dy-z{a,b,c,dyz:z(l 

 etc. 

 vbi qtlidem iam \idimus effe 5( — "■« » S5— P, 

 ^ — -y etc. Cum vero fit 

 (v,a) —a{v)-^i [a) z=La 



{v,a,b) —b{v,a)-\-{v) {a,b) -b^a^-^-x 



\v,a,b,c) — c{v,a,b)-\-{v,a):,{a,b,c)-=:c{a,b;)-ir{a) 

 ( v,a,b,Cyd)—diV,a,byc)-i-{v,aJf) ; {a.b,c,d)—d,[a,b,c)-\-{a,b) 



etc. 

 Tom.XI.Nou.Comm. G habe- 



