Summary

Translation:Talmud, Seder MoedTractate Rosh Hashana…

“ Therefore we learn this. [So a date can be stated in two ways, one based on the year of the reign of the first king and one based on the second. (RASHI) ]
"If a king died in Nisan and another was appointed in Nisan, the year can be counted by both." [Is this not] obvious? One may [mistakenly] think that a single day can count as a year only if the king took the throne in the beginning of the year and not the end. Therefore we learn this.
If a kind died in Adar and another was appointed in Nisan, the first year is counted by the first [king] and the second year by the second [king] ."
”
Source: Wikisource

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