Page:The method of fluxions and infinite series.djvu/35

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and Infinite Series.
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of one Dimension only is affected, without the other indefinite Species, and by writing the Result in the Quote. So in the following Example, the Terms , , , &c. are produced by dividing , , , &c. by .

36. These things being premised, it remains now to exhibit the Praxis of Resolution. Therefore let the Equation be proposed to be resolved. And from its Terms , being a fictitious Equation, by the third of the foregoing Premises, I obtain , and therefore I write in the Quote. Then because is not the compleat Value of , I put , and instead of , in the Terms of the Equation written in the Margin, I substitute , and the Terms resulting (, &c.) I again write in the Margin; from which again, according to the third of the Premises, I select the Terms for a fictitious Equation, which giving , I write in the Quote. Then because is not the accurate Value of , I put , and in the marginal Terms for I substitute , and the resulting Terms (, &c.) I again write in the Margin, out of which, according to the foregoing Rule, I again select the Terms for a fictitious Equation, which giving , I write in the Quote. Again, since is not the accurate Value of , I make , and instead of I substitute in the marginal Terms. And thus I continue the Process at pleasure, as the following Diagram exhibits to view.

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