NOVI ALGORITHMI. 57 



erit xx — zyj>~^ij ideoque pro VeUiano problema- 

 tc ftatim habetur p — x et q:^y. Facilius autem 

 numcri x et y his transformationibus adhibitis iiiue- 

 Diciitur : 



Arrr(<?,^)('y,^,^,f)4-(«)('y,<7,^) et 



y-{a,b)[^,b,c) ^{a){a,b) 



vnde fi ex indicibus , «y , a ^ b ^ c, more expofito , 

 fraftioncs formentur: 



Ind, -y , ^ , ^ , c 



Fro/V , 3f ^ ff O 



rract. 3 , > b j c j b 

 fumi oportet 



^=CS)-+-b^ et jr^rCt^+bC. 

 At hic cafus locum habet, quoties pofito z^zvv-Vu 

 fuerit 



■nvzrm{a,b,c,b,a)-{b,c,b)(a,b,e,b) et 

 u=ztn{a,b, c ,b)-~{b,c,b){b,c,b) 



VIL CafuSj quo pronumero^indices (iint 

 i;^ ^5 Z», c^ c^ by a^ 2v etc. 



35. Hic iterum indicum numerus in qualibet 

 periodo e{\ impar , ideoque fi ponamus 



x — {v,ajb,c,c,b,a) et 

 y = {a,b,c,c,b,a) 



erit .wv — sj^j-i , ex quo vt fiat ppzzzqq-^i, 

 fumi oportet p— 2;fjL-H- I, et qz=:2xj. 



Tom.XI.Nou.Comm. H Pro 



