"Swallow". A verb that means to push food through your pharynx would be to "Swallow".
I'm not completely sure whether it was used in a way to be passive aggressive towards Hamilton himself. I completely understand why it can be seen this way though I'm not entirely sure whether or not it's made to sound that way towards him.
To put the actual question into light though, Jefferson is an opponent of Hamilton. They constantly fought over the ideals of America and both voiced their opinions loudly. Even in the song The Election of 1800 it can be quoted that Hamilton "[had] never agreed with Jefferson once", which in itself shows their relationship with one another.
Answer:
To make the writing smoother
Explanation:
The purpose of transitions make the writer flow easier and allows the audience to be able to read the essay more easily. This allows them to focus on the argument at hand