Why did Thomas Paine use both "hath" and "has" in the same sentence?

My understanding is that "hath" is archaic, but has exactly the same meaning as "has".

But then why would an educated writer use both in the same sentence when writing a formal article?

Example from Common Sense (1776):

"... but it hath so far happened that the first has failed, and the second has withdrawn her influence."

He uses both words throughout the text, often in the same sentence, causing me to think that he must perceive some distinction between the two in style or connotation, if not denotation.

Google Ngrams for hath,has is interesting: Unsurprisingly, as hath declined, has grew in popularity. The crossover point was c. 1693. By 1799 – the publication date – the frequency of hath was 0.02% and has was 0.17% - a ratio of approximately 1:8.

It is remarkable to see so many "haths", but nevertheless, if we look at a similar phenomenon, the periphrastic “do”, we can see that it is currently possible to say “Has he any money?”, or “Does he have any money?” and the same person might say either or both, even in the same sentence without any significance.