"In doing this he makes use of a Table of Products (...he calls Speculum Analyticum,) by which he computes the Coefficients in the new Equation for finding the Difference mentioned. This Table, I observed, was formed in the same Manner from the Equation propos'd, as the s are, taking the Root sought for the only flowing Quantity, its Fluxion for Unity, and after every Operation dividing the Product successively by the Numbers 1, 2, 3, 4, etc."
January 1, 1970
https://en.wikiquote.org/wiki/Brook_Taylor