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Google.com can become your friend. From eudict.com the simple translation of discipules(discipulus) est prioris posterior dies is: each day succeeding is the student of the one preceding (Publilius Syrus)
Breaking it down: discipulus --> student est --> is prioris --> of the former (or previous or prior) posterior --> latter or next or subsequent dies --> day
You already have the Latin, so . . . The next day is the student of the previous. . . . would be the literal English translation.