In Shakespeare’s day, physic was used to mean “medicine” and physician was used as we still do today, meaning “one who practices medicine”:

This Physicke but prolongs thy sickly days (Hamlet)

More needs she the divine than the physician. (Macbeth)

Medicine was a synonym for this “remedy for disease” use of physic, and the two words co-existed for centuries:

“Thus did they all things that were contrary to their safety, as if no physic or medicine had been bestowed upon the world by the true physician of all”
—William Camden, Britain, or A chorographicall description of the most flourishing kingdomes, 1637

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