Sanhedrin 13B

איכא בינייהו יום תקופה מתחיל ויום תקופה גומר. ולא מסיימי.

The Talmud answers: Also here, the difference between them concerns the question of whether the day of the equinox begins the season or whether the day of the equinox concludes the season, but their opinions are not defined. Although it is apparent from the baraita that these two tanna’im disagree about this issue, it is not clear from their words which tanna ascribes to which of these opinions.

אחרים אומרים: מיעוטו, וכמה מיעוטו? ארבעה עשר יום. מאי קסברי? אי קסברי יום תקופה גומר, וכוליה חג בעינן ⁠– האיכא! אמר רב שמואל בר רב יצחק: אחרים בתקופת ניסן קיימי, דכתיב: ״שמור את חדש האביב״⁠ – שמור אביב של תקופה שיהא בחדש ניסן.

The baraita teaches: The tanna referred to as Aḥerim says: The year is intercalated even on account of a minority of the month, and how much is a minority of the month? 14 days. The Talmud asks: What do Aḥerim hold? If they hold that the day of the equinox concludes the season, and also that we require all of the Festival to take place in the new season, this condition is fulfilled even if the season is lacking 15 days. Rav Shmuel bar Rav Yitzḥak says: Aḥerim are standing in, i.e., discussing, the season of Nisan. As it is written: “Observe the month of spring and keep the Pesaḥ” (Deuteronomy 16:1), from which it is inferred: Preserve the day of the equinox of the spring, to ensure that it will be in the month of Nisan, meaning that the equinox must occur during the first part of the month of Nisan, by the 14th, the day the Paschal offering is sacrificed.

וליעבריה לאדר? אמר רב אחא בר יעקב: תנא מלמעלה למטה קחשיב, והכי קאמר: עד מיעוטו מעברין. וכמה מיעוטו? ארבעה עשר יום.

The Talmud asks: In a situation like this, why is it necessary to intercalate the year? But let them intercalate the month of Adar by adding a day to it, and this will cause the day of the equinox to occur during the first half of Nisan. Rav Aḥa bar Ya’akov said: The tanna whom the baraita here refers to as Aḥerim calculated from the top, meaning the maximum number of days downward, and this is what he is saying: Up to a minority of the month, meaning, if the equinox would occur during the final days of Nisan, the court would intercalate the year and would also do so if the equinox would occur earlier in the month, unless it would be early enough that only a minority of the month would be in the previous season. And how much is a minority? 14 days. But if the equinox would occur on the 14th, the year is not to be intercalated, but instead a day should be added to the month of Adar.