After the Metonic cycle had been in use about a century, a correction was proposed by Calippus.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4" by Various
The Metonic cycle, presently mentioned, must have been used by many, perhaps most, churches.
"A Budget of Paradoxes, Volume I (of II)" by Augustus De Morgan
They compiled a calendar, in complete accord with the Metonic cycle, which modern science must declare faultless.
"Jewish Literature and Other Essays" by Gustav Karpeles
It is fair, however, to conclude that Daniel was aware of the Metonic cycle.
"The Astronomy of the Bible" by E. Walter Maunder