III. The Method of Fluxions is the general Key, by help whereof the modern Mathematicians unlock the ſecrets of Geometry, and conſequently of Nature. And as it is that which hath enabled them ſo remarkably to outgo the Ancients in diſcovering Theorems and ſolving Problems, the exerciſe and application thereof is become the main, if not ſole, employment of all thoſe who in this Age paſs for profound Geometers. But whether this Method be clear or obſcure, conſiſtent or repugnant, demonſtrative or precarious, as I ſhall inquire with the utmoſt impartiality, ſo I ſubmit my inquiry to your own Judgment, and that of every candid Reader. Lines are ſuppoſed to be generated[1] by the motion of Points, Plains by the motion of Lines, and Solids by the motion of Plains. And whereas Quantities generated in equal times are greater or leſſer, according to the greater or leſſer Velocity, wherewith they increaſe and are generated, a Method hath been found to determine Quantities from the Velocities of their generating Motions.
