gage
An old spelling of gauge, meaning a tool for measuring.
A gage is sometimes used as an old-fashioned spelling of gauge, which means a measuring instrument or a standard of measurement. You might see a fuel gage in a car showing how much gas is left, or a pressure gage on a bicycle pump. When someone gauges the temperature of bath water with their hand, they're trying to measure or estimate it.
The word also appears in older English writings and historical contexts with this spelling. For example, knights in medieval times would sometimes throw down a gage, like a glove, as a challenge to fight. Throwing down the gage meant you were daring someone to prove themselves in combat. This dramatic gesture was a way of saying “I challenge you” without words.
Today, most people spell it gauge for the measuring-instrument meaning, but you'll still see gage in older books and historical writing.