9^ MifceUanea Curiofa. 



monftration of all which I leave to Cartefius 

 the Inventor. Let it be Noted, that I endea- 

 vour here that the Affirmative Roots, may 

 always be had on the Right fide of the Axis, 

 to avoid the Gonfufion that will necefTarily 

 arife from a multitude of Cautions, where the 

 reafon of them is not evident. 



Having premifed thefe things, in order to 

 make way for the conftru&ion of thefe Equa- 

 tions, even when the fecond Term is found 

 in them, we are to conftder the Rule it felf 

 for taking away the fecond Term, and redu- 

 cing jthe Equation to another, fuch as might, 

 be conftrueted by the foregoing Method. Now 

 all Cubick Equations of this Claffis, are re-* 

 duced to this form, z? bz.z,. apz,, aaq^o^ or to 

 this, z? . bz? < aaqzzo. Biquadratick ones 

 may be reduc'd to this, zs\ bz? . apz, z . aaqz,. 



a 3 ri=zo, or this, £ 4 . or this *, 4 . bz? . ^, daqz.. 

 a 3 rt=io 9 qrthis, *, + . bz, 3 . apz? . a 1 y r sba, or 

 laftly, to this Form, z^.bz? #. a 3 rzzo. 

 From all which there arifes a great Variety, 

 according as the Signs -V or — are diverfly 

 conne&ed together \ and hence the General 

 Rule ferving all thefe cafes, is rendred very 

 obfcure and difficult, unlefs (manag'd by the 

 help of the following Method) it be cleared 

 up and delivered from thofe Intricacies. 



The fecond Term in Biquadratic^! Equati- 

 ons, is taken away by putting xzzzrfab, if it 

 be "\~b in the Equation ; or x ^^—\b^ if it be 

 — b* Hence I b in the firft cafe, and 

 | b in the fecond, is ; and fb in any Equa- 

 tion propofed, fubftituting inftead of its 

 Equal, there will come forth a new Equation,' 

 wanting the fecond Term, all whole Roots x 



