MifceUanea Curtoja. in 



+ q ^ 0, there is either one or three Nega- 

 tive Roots, under the very fame Conditions 5 

 but no Affirmative Root at all. So alfo in 

 the Equation z} -Y bz. 2 ~Y fz, — q n <?, there 

 are two Negatives and one Affirmative, if p 

 be lefs than f bb^ and i q lefs than \U 3 ~Y i> 

 b* \bp\ even as in the Equation *-*bk\ % 

 ~Y pz,'Y q z=z there were two Affirmatives 

 and one Negative : But the quantities p and 

 q exceeding thofe prefcrib'd Meafures, there 

 is here only one Affirmative Root, which there 

 was a Negative one. In like manner, in the 

 Equation ^ 3 -Y bz, 2 pz, + q ps 0, there are 

 either two Affirmatives and one Negative, or 

 one Negative only 



Laftly, For the fame reafons in the Equa- 

 tion z, 3 \ bz. 2 -* pz, < ci s=3 o 7 there are two 

 Negatives and one Affirmative, or one Af- 

 firmative only, for which, in the Equation 

 *, 3 r-H bz, 2 pz, "Y q s=a 0, there were two 

 Affirmatives and one Negative, or one Ne- 

 gative alone viz.. as i q is either greater 

 or lefs than Vd 2 -Y % f ^ ~Y i fy< 



If the third Term (or pz,) be wanting, the 

 Center R always falls in the Line IPEa, 

 wherefore if it be z 3 — » bz 2 . — < q or z. 3 

 bz, 2 . "Y there can be but one Root, 

 Affirmative if it be — • b, Negative, if + b< 

 But if it be z, 3 ~ bz 2 '. + q or z, 3 + bz 2 . 



-« q, there may be two Affirmatives and 

 one Negative in the former, or one Affir- 

 mative and two Negatives in the latter, the 

 Center falling in the Line Pa between P and 

 a, that is if %q be lefs than % j b 3 ; for if 

 it he greater, there can be but one Negative 

 in the former, or one Affirmative in the lat- 

 ter. Hitherto 



