Related for Rosh Hashanah 38:4

על אלול מפני ר"ה ועל תשרי מפני תקנת המועדות: כיון דנפקי להו אאלול אתשרי למה להו

OF ELUL ON ACCOUNT OF NEW YEAR, OF TISHRI FOR THE ADJUSTMENT OF THE FESTIVALS. Once the messengers have gone forth to report [the new moon of] Elul, why should they be required to do so for Tishri?

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