204 MEblTATlO^ES DE QJANTrrJTIBJ-S 



Fiet nerhpe , attendendo id Regulnm de fignis mo- 

 do dMrh , 



in cafu I. c'=[Q_-f-y(Q^-P*)]'- » H-i<^-V(Q^-P*)]'- • 



II. r^-[Q-4-y ((^*_j-p^)].- ^ -f-[Q.-y(Q;+P*)^' ' 



III. ^'r:[-Q_+y(Q-P*)]'- ' ^-[-Q-y((^*_p^)]'- ' 



IV. i;-[-Q.+y(Q;4-p*)]*- ^+[-Q-y(Q;+p')]" ». 



§• 3 5- Quoninm luitcm in omnibiis his qiutuor 

 cafibus neqnatio cubica relpondens habcrc dcbct trc« nuli- 

 ces V ; valot qiioque pro v in §. XXXIV. inhentus , 

 qiii ( brcuitatis ^nttia ) dicatur A -j- B , icu -\- t . 

 ( A -h B ) , rc vcri triplex clfe debet , vt qunmcunquc 

 libct trium radicum aequ.uionis rcpncrcnt.irc pofllt. Qiioniam 

 tamen :idhuc dum defidcratur mcrhodus ektraheiVdi 

 wdicem ciibicam ex data quantitate irrationnli compofita 

 ( ea cnim , quae in Elemehtis Atgebrae commiinitcr tni- 

 di folct \ rem , vt erat , inconfccftam rclinquit ) , ita vt 

 in hoc diflicili ncgotio muitum induigcnduni fit diuiuatio- 

 nibus rcpctitis , ct cxnmini fiibicdlis ; ndnuidtim contcnti 

 funlus horum triilm valoruiVi vni/m fliltcm , quem piri- 

 mim radiccm nequationis , feii 1)1', dicimus , ex formu- 

 la dttcrminafle, cum , ex hoc cognito , reliquc vnlores, abs- 

 que vlla diuin-.uionc , ccrta mctliodo ,, pcr rcfolntioncrn 

 aeqnationis quadratic ic habcri poirmt. Tvlimirurn ad 'rcliquas 

 duas radiccs inucnicndas fiit fluflor fimplcx «y — (A -f- B) 

 ::n o , pcr qucm cum diuifibili^ effe dcbeat aequatio cu- 

 bica rcfpondcns , c. g. !•"■ a;* * — 3 P c — 2 'Q~ o , 

 diuifionc nftu iufiituta, erit rcfidutim diuifionis ^(A+A)*** 

 -3 P{A-hB)- ^Q^, 'h. c. —v*-z IV-^Q. 



— o. 



