NOVI ALGORITHMI. 47 



atqne ex his indicibus v , n ^ b ^ c , d etc. fmcftio- 

 nes ~ fbrmari poflriint , quac tam prope ad V z 

 accedunt, vt nonnifi maioribus numeris adhibendis, 

 eius valor accuratius exhibcri poflit. Hae fradiones 

 autem ita fbrmantur: 

 Indiccs T, ^, h c .... w, «, 



x_ , V av -t- t (ah -^ i)v -\- J} M N n N -4- W 



y 3>Ji» a » ab -\- i ••••PjQ.i n Q,-+--^ 



quae continuo propius valorcin irrationalera Vz 

 exprimunt. 



19. Nouus autem algorithmus fuccindura 

 modum fuppeditat, has fracftiones commode per in- 

 dices repraefentandi , quae ita fe habent : 



t iv) {v,a) {v,a-, b ^ ( T», q,6, c ) ( v, a, b,c,d ) 



BJ I ' (i) ' (0)6) ' (a>6, c) ' (a. 6,c, d) "^- 



Vbi cum ex natura progreflionis fit : 



(a)-ai + io;{a,b)-b(a)+i;(a,b,c)zcia,b)^r{a)i 

 erit ctiam ex natura harum formularum : . 



(a;,dr) — uC^)-!-! ; (.v,a,b{ — v(a,i?,)-{-/);(v,a.l>,c) 



:=:v(a,b,c)-h(b,c) 

 deinde etiam fequentes transformationes demonftraui : 

 {v,a,b,c,d,e) — v(a^b,c,d,^!) ^{b,c,d,e) 

 {v,a,b,c,d,e)=z('v,a)(b,c.,d,e)^v{c,d,e) ^H"»» 

 (<i;.^,^,r.(/,f)r:(c,^,^)(r,^,f)-4-('z?,^)(<!',^) 

 (v,a,b,c,d,e):z:{v.a,b,c),d,e)'+-{v,a,b)(e) 

 quas probe notaffe in fequentibus plurimum iuuabit. 



ao. 



