IRRATIONALIBVS. ifft 



quae pariter eft recurrens ad legem R — (s -}- iy)(^ 

 — y y P. Formata autem iiac ferie erit proxime 

 y (^ ^ _|- ^) ~ 2:^^! a , quac fcilicet fradio ex bi- 



nis termiais fe immediate fequentibus illius feriei fa.- 

 cillime formatur. 



Exemplum i. 



38. Radicem quadratam ex 2 proxime exhibere. 

 Cum fit aa-\-bz=:'2. erit a~x et ^— i, vnde 



-|_ — i— |-; ergo>'— I et s;z=4, atquc s + aj'^:^^. 

 Quare ex fcala relationis RzrSQ^— P formetur haec 

 feries recurrens : 



I,- (J; 35; 204; II 89; 5930; 4039I.-.-P, Q., R 

 et fradiones ?^p ad Va continuo magis appropia- 

 guantes funt : 



"1/5 — ^» *1 • V^ ' '_'?'• S"S." 47^51 

 ' ■* — — I) 29) J5S » 981 ? S7 + I? 3345f' 



Exemplum 2. 



39. Radicem quadmtam ex 3 proxime exhibere.- 

 Cum fit fffl-hZ' — 3, ftdtuntur a— i, erit ^—2; 



et -^ — I ~ 3 vnde fit ^ — i et 2 = 25 ergo 

 z-\-iy — ^. Quare ex fcala relationis R — 4Q— P 

 fbrmetur haec feries recurrens : 



i; 45 15; 5<?; 209; 780; 29 115 10864....P, Q, R 



eritque proxime V 3 — ^^p ; fiue 



"l/ n 5 . '9 ■ fl . 2fi5 , 9S9 . 55«l . T 5775 -*_ 



<i 3 7 »'1 41 ? '13 i I/X 1 5131 1 79S3 Cll,. 



.itf///m Vel ftatuamus o n: 2 ; vt fit ^ = — i ; erit 



J^^-rz-\^—l vndej — -i; 5;i=i(J et 2 + 2^^=14. 



Tom. XVIII. Nou.Comm. X Quare 



