Newton on Quadratures: A Brief Outline

When Newton began his mathematical career in the mid-1660s, the problem of determining the tangent to a plane curve was basically solved, either by kinematic methods à la Roberval (and this was often the case with “mechanical lines,” what we call transcendental curves) or by pre-calculus methods à la Hudde (and this was the case with “geometrical lines”, what we call algebraic curves) (Malet 1996). True: the formulation of an effective notation and the identification of a basic set of rules was yet to come.