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TREATISE

OF
Algebra.

BOOK Í.

Definition.
HE Name Algebra, Dr. Wallis acquaints

us, is derived from the first Word of AKA
giabr; Walmokabala, which Words in the
Arabick Tongue, signifie the Art of Reftitu-
tion and Comparison, or the Art of Refolu-
tion and Aquation. It is a Science by
which the most difficult and abftrufe Que

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.

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An Explanation of the Signs used in Algebra.

More, or added to.

Less, or Subftracted from,
Múltiplied by, or Multiplying
Divided by, or Dividing.
Continually Divided by.
Equal'ro.
Continual Geometrical Proportion,
Disjunct Geometrical Proportion.
Continual Arithmetical Progression

Disjunds

Signifies

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