Step 1: Break down the Latin phrase.
The legal maxim "De die in diem" is a Latin expression used in legal documents and proceedings. Breaking it down: "de" means "from," "die" means "day," and "in diem" means "to the day."
Step 2: Interpret the meaning.
Together the phrase means "from day to day," indicating something that continues or accumulates on a daily basis. In legal contexts it is used to describe obligations, interest, or proceedings that carry forward from one day to the next continuously.
Step 3: Match with options.
Option (1) correctly translates the maxim.
\[ \boxed{\text{from day-to-day}} \]