Sure: the line tangent to any point on a smooth curve approximates a sufficiently small bit of the curve surrounding the point arbitrarily well.
Newton's contribution wasn't this, however, but the extension of Descartes' algebraic tangent-finding methods to curves represented by "infinite polynomials", which he neither uses nor explains in the Principia. If you're looking to learn Newton's flavor of calculus "from the master", here it is:
Newton's contribution wasn't this, however, but the extension of Descartes' algebraic tangent-finding methods to curves represented by "infinite polynomials", which he neither uses nor explains in the Principia. If you're looking to learn Newton's flavor of calculus "from the master", here it is:
http://archive.org/details/methodoffluxions00newt