Page:The method of fluxions and infinite series.djvu/28

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4
The Method of Fluxions,

8. In the same manner for aa/xaab/x2 + aab2/x3 , &c. may be wrote

9. And thus instead of aaxx may be wrote aaxx|1/2; and aaxx|2 instead of the Square of aaxx; and abby3/by + yy|1/3 instead of 3ab2y3/by + yy: And the like of others.

10. So that we may not improperly distinguish Powers into Affirmative and Negative, Integral and Fractional.

Examples of Reduction by Extraction of Roots.

11. The Quantity aa + xx being proposed, you may thus extract its Square-Root.

So that the Root is found to be a + x2/2ax4/8a3 + x6/16a5 , &c. Where it may be observed, that towards the end of the Operation I neglect all those Terms, whose Dimensions would exceed the Dimensions of the last Term, to which I intend only to continue the Root,

suppose to x12/ a11

12.