Now forasmuch as in January, in which month the beginning of Gamelion is observ’d to have fallen, there happened a new Moon in the Attick Horizon, by the Tables of Celestiall Motions, the fourth day, in the morning, (or the third day, according to the Athenians, who as [31]Censorinus saith, reckon their day from Sun-set to Sun-set) and therefore the twentieth day of the Moon is co-incident with the three and twentieth of January
I point to this excerpt here to illustrate what we're up against. "The fourth day... Or the third day, according to the Athenians..." Do we calculate sunset to sunset? Sunrise to sunrise? New moon to New moon?
That "Athenian" calculation could make the difference between Sunday or Monday easily; however, I realize Gassendi is trying to say they were the same day just arrived at by two different calculations.
Gassendi's calculation strikes me as similar to the Usher's attempt to calculate the day of Creation
at least Gassendi was trying to calculate a real person's birthday.