Descartes' method to find the tangent line to a curve

This is an example of how Descartes approach the tangent line problem, although this curve was not to deal with in his time.
The semi-cubical parabola was discovered by William Neile in 1657. It was the first algebraic curve to have its arc length computed. Wallis published the method in 1659 giving Neile the credit. The Dutch writer Van Heuraet used the curve for a more general construction. (St-Andrews University history resource)