early 15c., "the giving of medicine (in a specified amount or at a stated time)," from Old French dose (15c.) or directly from Medieval Latin dosis, from Greek dosis "a portion prescribed," literally "a giving," used by Galen and other Greek physicians to mean an amount of medicine, from stem of didonai "to give" (from PIE root *do- "to give").
Meaning "quantity of medicine given or prescribed" is from c. 1600. Extended sense, in reference to anything given to be "swallowed," literal or figurative, is from c. 1600. Slang meaning "a case of venereal disease" is by 1914.
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