Commentary for Pesachim 5:2

אמרו (להן) בית הלל לבית שמאי מאי שנא אור שמנים ואחד מיום שמנים ואחד אם שיוה לו לטומאה לא ישוה לו לקרבן מדקאמר ב"ה לב"ש מאי שנא אור שמונים ואחד מיום שמונים ואחד שמע מינה אור אורתא הוא שמע מינה

This proves it. New Moon was fixed by direct observation, not calculation, and communities at a distance from Jerusalem were informed by bonfires. These were lit only if the New Moon appeared 'in its (due) time,' i.e.,it was fixed for the thirtieth day, the previous month thus consisting of twenty-nine days only; in that case too Beth Din formally sanctified this day. But if observation fixed it for the thirty-first day, no bonfires were li since the absence of bonfires on the previous day would be a sufficient signal; further, New Moon was not formally sanctified by Beth Din (Rashi.)

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