 Isaac  Barrow[17]  (1630–77) was one of the first mathematicians to grasp the reciprocal relation between the problem of quadrature and that of finding tangents to curves—in modern parlance, between integration and differentiation. In his Lectiones Geometricae of 1670, Barrow observes, in essence, that if the quadrature of a curve \(y = f(x)\) is known, with the area up to \(x\) given by \(F(x)\), then the subtangent to the curve \(y = F(x)\) is measured by the ratio of its ordinate to the ordinate of the original curve.