Page:Philosophical Transactions - Volume 004.djvu/110

 may be reduc'd thereunto, by taking it away. More over, when such Æquations, wherein you are incumbred with Fractions or Surds, either in the Coefficents or Roots, are proposed, he goes on to find the Roots, sought in his own method, and when not explicable but by a quám proximè, according to the general method of Vieta, in the use of which method, he, determining the number of Figures in the Root, takes away the trouble of all the sub-gradual Punctations.

4. When he comes to Bi-quadratick Æquations, he intimates, that all such Æquations may be reduced into two Quadratick Æquations, but not without the aid of a Cubick Æquation: And first, when the second Term or Cubick Species is not wanting, he shews' how to find the said Adjutant Cubick Æquation, by placing the two highest Terms of the Æquation on one side, and the rest of the Termes on the other, and then finds such Quantities, which, added to either side, renders the same capable of a square Root; and this preparation being made, he thereby obtains the Cubick Æquation and the Root thereof; which serves for the purpose premised; to wit, to divide the Bi[quadratick Æquation propos'd into two Quadratick Æquations, and so solved.

Further, in regard that all Æquations are more easily solv'd, when some of their Terms are wanting, than when all are present; he proceeds to shew, how to take away the second Term, and, supposing it gone, gives easier Rules for finding the aforesaid Cubick-