Part IV. Evolution, Chap. I. Of whole Quantiies II and III, Evoluton, and mixt Evolution of Numbers Pari V. Of the Indices or Exponents of Powers Part VI. Of Surd-Roots. V and VI. Additon and Subtraction Part XII. Of feveral Methods of folving high ad- Part II. The Solution of Problems. IV. The Solution of feveral forts of Pro- HE Name Algebra, Dr. Wallis acquaints us, is derived from the firft Word of Al giabr, Walmokabala, which Words in the Arabick Tongue, fignifie the Art of Reftitution and Comparison, or the Art of Refolution and Equation. It is a Science by which the most difficult and abftrufe Queftions, in Arithmetick and Geometry, are Refolved and Demonftrated; that is, it equally interferes with them both, and therefore it is promifcuoufly Nam'd, being fome times call'd Specious Arithmetick, as by Vieta, Harriot, Dr. Wallis, &c. and fometimes Modern Geometry, as by Dr. Halley. This great Art may be Defined, or rather defcribed to be an Analytical way of Demonftration; where, affuming the Quantity or Quantities unknown, as if it, or they were known, we proceed by Confequences, in comparing it or them, and known, or given Quantities among themselves, untill the unknown Quan tity fought, or at leaft fome Power or Powers thereof, be found B equal equal to fome known Quantities, and fo it felf is, or may be, of Consequence made known. CHAP. I. Concerning the Method of Poting down Quantities and Tracing their Steps, &c. Sect. 1. Dotation. THE Quantity fought is called the Root, which being unknown, cannot be really exprefs'd; but may be defign'd by any Symbol, or Character at Pleasure. I commonly (with moft others) ufe Vowels for unknown, and Confonants for known or given Quantities. But Des Cartes and his Followers, and moft Foreign Writers, use the laft Letters of the Alphabet, x, y, z for unknown Quantities; and the firft Letters, a, b, c, &c. for known ones. The advantage of thus expreffing known Quantities is, that the Numbers with their feveral Operations, which in Vulgar Arithmetick would be loft or swallowed up, in Algebraic Arithmetick are fo ordered and managed, as to be preferved Distinct and in View; and at laft to produce a Canon or Rule for Resolving, not only the particular Queftion propos'd, but in general, any other of the like Nature. Befides these Letters, there are certain Signs used, which are as follows. |