There are numerous proofs for Taylor's theorem, but
What's the original proof for Taylor's theorem (by Taylor?)?
In Wikipedia it says:
Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1712. Yet an explicit expression of the error was not provided until much later on by Joseph-Louis Lagrange. An earlier version of the result was already mentioned in 1671 by James Gregory.1
So if Taylor's was incomplete (or was it?), then what was the first "complete" one?