Fermat’s method of quadrature
The of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, , or under a higher hyperbola, —with the appropriate limits of integration in each case—has a second part which was mostly unnoticed by Fermat’s contemporaries. This second part of the is obscure and difficult to read. In it Fermat reduced the quadrature of a great number of algebraic curves in implicit form to the quadrature of known curves: the higher parabolas and hyperbolas...