In Modern English, Greek is the usual adjective meaning of or pertaining to Greece. Grecian is an earlier construction, with an adjective-forming -an suffix (American, Norwegian, Virginian), which is now pretty much relegated to stylistic and fixed phrase duty. It's common in the following expressions, among others: Grecian Formula Grecian urn Grecian style or Grecian dress Grecian sandals But ...
Hornblower is only 17 at the time of this exchange, so it must be something pre-university, but I cannot find any more information to suggest what being a Grecian actually meant in the late 18th century in England.
education - What did it mean to be a Grecian in late-18th Century ...
Keats, over a millennium and a half later, wrote an Ode to a Grecian Urn, in which the urn itself is the recipient/addressee. Thou still unravish'd bride of quietness, Thou foster-child of silence and slow time, Sylvan historian, who canst thus express A flowery tale more sweetly than our rhyme: What leaf-fring'd legend haunts about thy shape ...
Those contortions resembled a pose affected by fashionable people of that time and earlier. The pose was known as the "Grecian Bend" (evidence in print from 1820). The evening world, New York, .
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