in the firſt place, it is ſuppoſed that the Abſciſſes z and x are unequal, without which ſuppoſition no one ſtep could have been made; and in the ſecond place, it is ſuppoſed they are equal; which is a manifeſt Inconſiſtency, and amounts to the ſame thing that hath been before confidered[1]. And there is indeed reaſon to apprehend, that all Attempts for ſetting the abſtruſe and fine Geometry on a right Foundation, and avoiding the Doctrine of Velocities, Momentums, &c. will be found impracticable, till ſuch time as the Object and End of Geometry are better underſtood, than hitherto they ſeem to have been. The great Author of the Method of Fluxions felt this Difficulty, and therefore he gave into thoſe nice Abſtractions and Geometrical Metaphyſics, without which he ſaw nothing could be done on the received Principles; and what in the way of Demonſtration he hath done with them the Reader will judge. It muſt, indeed, be acknowledged, that he uſed Fluxions, like the Scaffold of a building, as things to be laid aſide or got rid of, as ſoon as finite Lines were found proportio-
