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This quote is commonly known as 'seize the day', probably made more famous through Robin Williams' film, 'The Dead Poet's Society'.
The original source for the Latin phrase is the lyric poet Quintus Horatius Flaccus (65 BC – 8 BC), more widely known as Horace. The term is first found in Odes Book I:
Dum loquimur, fugerit invida
Aetas: carpe diem, quam minimum credula postero
Aetas: carpe diem, quam minimum credula postero
which translates as:
While we're talking, envious time is fleeing:
pluck the day, put no trust in the future.