Of the Indices or Expanents of Powers Part VI. Ol Surd-Roots. II. Reduction Part XII. Of several Methods of solving high ad- fected Equations. II. The Solution of Cabick Equations by Car- III. A Rule of Des Cartes for diffolving a Bi- quadratick into two Quadraticks IV. The Solution of Equations by Stephinus's V. The Solution of some Equations by Ker- How to raise Canons for finding the Sums of the Part XVIII. Of the Alternations and Combina: tions of Quantities. Part II. The Solution of Problems. Chap. I. Problems producing Simple Equations p. 363 II. A Problem producing a Simple Quadratick III. Of Problems producing adfected Quadra- IV. The Solution of several sorts of Pro- TREATISE OF BOOK Í. Definition. us, is derived from the first Word of AKA stions, in Arithmetick and Geometry, are Resolved and Demonstrated ; that is, it equally interferes with them both, and therefore it is promiscuously Nam'd, being some, times call'd Specious Arithmetick, as by Vieta, Harriot, Dr. Walls, &c. and sometimes Modern Geometry, as by Dr. Halley. This great Art may be Defined, or rather described to be ani Analytical way of Demonstration ; where, assuming the Quantity, or Quantities unknown, as if it, or they were known, we proceed by Consequences, in comparing it or them, and known, or given Quantities among themselves, untill the unknown Quan tity sought, or at least Tome Power or Powers thicreof, be found B equa! equal to some known Quantities, and so it self is, or may be, of Consequence made known. CHA P. I. Concerning the method of Poting down Quantities ; and Tracing their Steps, &c. Se&t. I. Potation. THE Quantity sought is called the Roor, which being une , known, cannot be really express’d; but may be design'd by any Symbol, or Character ar Pleasure. I commonly (with most others) use Vowels for unknown, and Consonants for known or given Quantities. But Des Cartes and his Followers, and most Foreign Writers, use the last Letters of the Alphabet, x,y, for unknown Quantities; and the first Letters, a, b, c, &c. for known ones. The advantage of thus expreffing known Quantities is, that the Numbers with their several Operations, which in Vulgar Arithmetick would be lost or swallowed up, in Algebraic Arithmetick are so ordered and managed, as to be preserved Distinct and in View ; and at last to produce a Canon or Rule for Resolving, not only the particular Question propos d, but in general, any other of the like Nature. Besides these Letters, there are certain Signs used, which are as follows. An Explanation of the Signs used in Algebra. More, or added to. Less, or Subftracted from, Disjunds Signifies |
