What did Newton and Leibniz actually discover? Most popular sources credit Newton and Leibniz with the creation and the discovery of calculus. However there are many things that are normally regarded as a part of calculus (such as the notion of a limit with its $\epsilon$-$\delta$ definition) that seem to have been developed only much later (in this case in the late $18$th and early $19$th century).
Hence the question - what is it that Newton and Leibniz discovered?  

from my understanding, Newton's binomial said that the delta x should always have lim -> 0 because it's in the denominator, but once you got rid of it down there, delta x=0 is possible (and then you got rid of all the delta x in the numerator), thus, making the computation of derivatives systematic and easy.
