Looking for "batter" in the forum, I found several threads, all from more than a year ago (some about Galileo, and some about Galileo Gen 2):
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As you already saw, there are several threads about this topic. In general, powering the Galileo with a battery is not recommended unless you are using a battery with enough capacity to provide power to the board.
Besides the threads you have checked, I'm not aware of any project that uses a battery to power the Galileo board. I'd add, however, a recommendation to use an extra circuit to monitor the battery status and switch the power source once the battery reaches certain level that might not be enough to keep the board working properly.