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The Analyst.
XXI. In order therefore to clear up this Point, we will ſuppoſe for inſtance that a Tangent is to be drawn to a Parabola, and examine the progreſs of this Affair, as it is performed by infiniteſimal Differences.
Let AB be a Curve, the Abſciſſe AP = x, the ordinate PB = y, the Difference of the Abſciſſe PM = dx the Difference of the Ordinate RN = dy. Now by ſuppoſing the Curve to be a Polygon, and conſequently BN, the Increment or Difference of the Curve, to be a ſtraight Line coincident
with
