Pate

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Middle English: of unknown origin.

wiktionary

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From Middle English pate, of uncertain origin. Perhaps a shortened form of Old French patene or Medieval Latin patena, both from Latin patina(“pan, dish”). Alternatively, perhaps akin to Old Frisian pote(“skull”).

Attested since circa 1700, from French pâté, from Old Frenchpaste, pastée. Doublet of pâté.

etymonline

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pate (n.1)

"top of the head," early 14c. (late 12c. in surnames), of unknown origin; perhaps a shortened form of Old French patene or Medieval Latin patena, both from Latin patina "pan, dish" (see pan (n.)). "[U]sually employed in a trivial or derogatory sense" [Century Dictionary].