Taylor didn't invent Taylor series -- others, first Gregory,
then Newton (independently) and others, had
used them before. His contribution was Taylor's theorem, which
justified them (I think...)

Taylor did invent integration by parts
  (which allows one to prove Taylor's theorem)
...
"1772 when Lagrange proclaimed it [Taylor's Theorem] the basic principle
of the differential calculus"
...which I suppose is why we have `C' quarter of calculus.

Taylor apparently was quite deep and influential, but his work was terse.
He introduced many major concepts but didn't elaborate on them,
due often to health/family/wealth/etc.