V I B R A T R I O. 33S 



ex quibus elicitur : 



© =« ABCMP-«)(Q rZ )(R- 2 )-^(R-2)-^ M (P-2), 

 qui -valores in \ltima aequatione fubftituti ptaebent : 



ABO,cd(P-z)(Q_-z)(R-z)(S-z)-^{R-z)(S-z) 



-*-f'(P-*XS-*)-±?r- e (P-*)(<i-*) + sb= 

 quae per ABCk</ diuifa abit in hanc fbrmam : 



m ry /n ,vr ^vq ~\ (R-*Ks-*j (p-zXs— z) (p-zXQr-s? 



" t~ ABCD fcTdl -^ ° » 



cuius indoles clarius perfpitietur ex hac forma : 



i i i_ 



1 "~AB6*(P — 2)(a— s) "" BCcc(a— 2)(R— *) CDdd(R — »XS — *) 

 *+~ lEcDbbddiP^^y^zY^— zXS— a) " °- 



Verum fi ilki aequatio , reftituendis pro P, Q, R, S 

 valoribus, penitus euoiuatur 3 obtinebitur fequens aequatio 

 biquadratica : 



] ^-Mah^hS] f f ; , ^_ ' 



"A^-TfcM 4 -L.riJ_f^flJ_l) -ABC 5ftS-ra6a"Tacd"T"&cdi 



' | +&Q-H>GH*J)J -BCDW+««+6ie+c*)\ 

 j + cTD^ J d+ce+ai)J J 



*+" ABCD (aTcd "+" abce "+" cTde "+" ccdtf^" fccieV 



Inuentis autem huius aequationis quaternis radicibus z, 



z\ z" et z f/ \ ex illis totidem valores numeri n ha- 



Gg 2 bebun* 



