While the Greeks made simple thermometers as early as the first century b.c., it wasn't until Galileo (1564-1642) that a real thermometer was invented. It was an air thermometer, in which a colored liquid was driven down by the expansion of air, so that as the air got warmer (and expanded), the liquid dropped. This is unlike ordinary thermometers in use today, which rely on the colored liquid of mercury to rise as it gets warmer.
In 1612 Italian physician Santorio Santorio (1561-1636), a friend of Galileo, adapted the device to measure the body's change in temperature due to illness. (The clinical thermometer wasn't Santorio's only invention: As the first doctor to use precision instruments in the practice of medicine, Santorio also developed the pulse clock.)
It was a full century though before thermometers had a fixed scale. This was provided by German physicist Daniel Fahrenheit (1686-1736), who in 1714 invented the mercury thermometer.
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