1 1 o JMijceUanea Curtofa. 



Let the Equation zJ :=j bz. 2 *-*pz,>-*qzio ) be 

 propofed in the next place. That this Equati- 

 on may have three Roots, the Center of the 

 Circle mufi be found fomewhere in the inde^ 

 finite Space between the right Line D P D 

 and the Curve of the Paraboloid PX. The 

 quantity p is not here liable to Limitations 5 

 but i q ought always to be lefs than \/d 3 — 

 #7 b 31 ^ 6 fuppofing d to be sej £ 2 'b | p. 

 By this means, there are two Negative 

 Roots afforded, and one . Affirmative ; but 

 other wife, if f q be greater than \ld 3 — 2 X 7 

 & 5 6 % tne Equation is explicable by one 

 only (Affirmative) Root. 



Fourthly, Let the Equation z} ^ bz. — » 

 ^ 5=3 be propofed, which has two Affir- 

 mative Roots, and one Negative, if the Cen- 

 ter of the Circle be found in the indefi^ 

 nite Space between the right Lines Pa, PD* 

 and the Curve of the Paraboloid aL; that 

 is, (putting d^jbb~\~jp) \i\q be lefs 

 than \/d 3 ~\- 2 L 7 b 3 ~|-| bp\ but if | f be great- 

 er than this quantity, there is but one (Ne- 

 gative) Root. 



But the four remaining Equations in which 

 we have -V h\ do not differ from thofe that 

 have been mentioned already, as to the Limi- 

 tation of the Number of the Roots, if the Sign 

 of the laft Term be changed, keeping the 

 Sign of the third Term. But then them that 

 were the Affirmative Roots in the former, 

 will be the Negative ones here, and contra- 

 riwife. 



Thus in the Equation z) — bx> % -Yfz, *•* q 

 » <?, the Affirmative Roots were either one 

 or three j but in this Equation z} -\rbz 2 -Vpz, 



f. * H 



