Isaiah Hoag - Quaker dates

Google search says: After 1752 all months were referred to by Quakers by their number. September became "Ninth Month" and so on. Today some researchers find it useful to write down the old style numbers as in the original text, but add the new style names in square brackets, such as: 27 iv [June] 1731 or 29 4mo.

But also:

What is 12th month of Quaker calendar?
Thus, under the Julian Calendar, first month meant March, and twelfth month was February. Thus, the Quaker usage has led to a lot of confusion -- e.g., until 1752, "8th month" was October, not August. At least, with the "pagan" months, you know August means August, regardless of the year. Dec 20, 2019

I just want to be sure his date is correct.

Thank you