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SECTION III.

The XJse of Fluxions in drawing Tangentsto Curves.

Illustration.

48. T ET ACG be a Curve of any kind, and C1 j the given Point from whence the Tangent isto be drawn.

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Conceive a Right-line mg to be carried along uni-formly, parallel to itself, from A towards Q_, and let,at the fame time, a Point p so move in that Line,as to describe, or trace out, the given Curve ACG:Also let mm, or C n (equal and parallel to mm) expressthe Fluxion of Am, or the Celerity wherewith the Linemg is carried; and let «S express the correspondingFluxion of ?np , in the Position mCg, or the Celerity ofthe Point/), in the Line mg. Moreover, through thePoint C let the Right-line SF be drawn, meeting theAxis of the Curve (AQJ in F.

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Now,