The two distinct meanings of "parabolic" trace back to the development of Late Latin and New Latin. Late Latin is the Latin language used by writers in the third to sixth centuries. In that language, the word for "parable" was "parabola" - hence, the "parable" sense of "parabolic." New Latin refers to the Latin used since the end of the medieval period, especially in regard to scientific description and classification. In New Latin, "parabola" names the same geometrical curve as it does in English. Both meanings of "parabola" were drawn from the Greek word for "comparison": "parabolē."
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(sense 1) Middle English parabolik, borrowed from Late Latin parabolicus, borrowed from Greek parabolikós "figurative," from parabolḗ "comparison, parable" + -ikos-ic entry 1; (sense 2) borrowed from New Latin parabolicus, from parabolaparabola + -icus-ic entry 1