Early Tangent Constructions

Abstract

In modern calculus courses the treatment of differentiation and the construction of tangent lines to curves usually precede the treatment of integration and the calculation of areas under curves. This is a reversal of the historical sequence of discovery; as we have seen in the preceding chapters, the calculation of curvilinear areas dates back to ancient times. However, apart from simple constructions of tangent lines to conic sections (with the static Greek view of a tangent line as a line touching the curve in only one point), and the isolated example of Archimedes’ construction of the tangent to his spiral, tangent lines were not studied until the middle decades of the seventeenth century.