Feed a Cold, Starve a Fever
"The old advice to eat well if you have a cold, but cut back on food if you have a fever."
The idea traces to Hippocratic-era medical theory, when fever itself was thought to be the disease rather than a symptom of one, meaning starving the sick person would starve the fever out. John Withals's 1574 dictionary records exactly this logic: "fasting is a great remedy of fever." Modern medicine disagrees with both halves. Doctors now agree that proper nutrition and fluids matter whether you have a cold or a fever, and that deliberately eating too little during either can weaken your immune response rather than help it.
Myth vs. FactNeither half of the advice holds up medically. Starving yourself during a fever isn't recommended, and 'starving' was never good advice to begin with, it just reflected a genuinely different, outdated theory of how fevers worked.
Sources: John Withals's dictionary (1574); modern medical consensus per Cleveland Clinic and Johns Hopkins Medicine.