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5.4.20

The known calendar seems to be based on Meton from Athens, and was not mentioned in the gemara. Nor is there anywhere mentioned in the Gemara that Hillel II sanctified the calendar.

I think Passover ought to be on the 15th day after the new moon. That is,- if you think of the day of the "molad" [when the moon and sun are joined at the same longitude], as the new moon, then 15 days from that ought to be Passover. But why think this? Mainly because of Tosphot in Sanhedrin page 10 side b at the top.
The known calendar seems to be based on Meton from Athens, and was not mentioned in the gemara. Nor is there anywhere mentioned in the Gemara that Hillel II sanctified the calendar. That is thought to be the case, but in fact it is no where in Shas.
There are in fact many examples of basic things in the Gemara that people are not aware of.
[One more reason to get through Shas yourself.]