A Treatise of Algebra.

3

Moreover a -f- b X c denotes the Product of the com-pound Quantity a-\-b by the simple Quantity r; anda - b c Xa — b c x a c represents the Productwhich arises by multiplying the three compound Quanti-ties a-\- b c> a — b-\-c, and ac conti nually tug e-ther ; as if a was s , b 4 and c 3, then would s+i + txa — bc x a -{■ c be 12X4x8 or 3 84.

But when simple Quantities (or such as are denotedby single Letters) are to be multiply’d together, theSign x is generally omitted, or only understood : And soab is made to signify the same as axb j and abc , thesame as a xbxc.

It is likewise to be observed that, when a Quantityis to be multiply’d by itself, or raised to any Power, theusual Method of Notation is to draw a Line over thegiven Quantity, and at the End thereof place the Indexof the Power. Thus a -f- b ^ 1 denotes the same as a-^-bX a -f- b, viz. the second Power for Squa re) of a -f- bconsider ed as o ne Quanti ty ; also ab b? 1 denotes thesame as ab 4- be x ab -j- be x ab -\-bc, viz. the third Power(or Cube) of the Quantity ab-\-bc.

But in expressing the Powers of simple Quantitieswhich are represented by single Letters, the Line overthe Top is commonly omitted ; and so a 2 comes to sig-nify the same as aa or ax a, and b J the same as bbb orbxbxb: Whence, also, it appears, that a 2 b l will signifythe same as aabbb ; and a S c* the same as aaaaace ; andso of others.

The Note . (or a Full Point) and the Word into arealso sometimes used instead of X, or as Marks of Multi-plication.

Thus a 4- b . a -s-r a nd a b into a -j- c both signifythe fame thing as a -j-b x a-\- c.

The Sign 4- is used by some Authors to signify thatthe Quantity preceding it is to be divided by the Quan-tity which comes after it; as c-~b signifies that c isto be divided by b\ and a-^-b~a — c, that a-\-b isto be divided by a — c.

B 2.

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