"[Isaac Barrow's] lectures delivered in 1664, 1665, and 1666, were published in 1683 under the title Lectiones mathematicae: these are mostly on the metaphysical basis for mathematical truths. His lectures for 1667 were published in the same year and suggest the analysis by which Archimedes was led to his chief results. In 1669 he issued his Lectiones opticae et geometricae, which is his most important work. ...The geometrical lectures contain some new ways of determining the areas and tangents of curves. The latter is solved by a rule exactly analogous to the procedure of the differential calculus, except that a separate determination of what is really a had to be made for every curve to which it was applied. Thus he took the equation of the curve between the coordinates x and y, gave x a very small decrement e and found the consequent decrement of y, which he represented by a. The limit of the ratio a/e when the squares of a and e were neglected was defined as the angular coefficient of the tangent at the point, and completely determined the tangent there."