To speak or write about something in a highly eloquent or verbose manner. Comes from "wax" meaning "grow" or "become" as in the waxing and waning of the moon, thus "to wax poetic" is equivalent to "to grow poetic." Thus "to wax poetically" doesn't really make sense, as it would mean "to grow poetically," which isn't the same as "to grow poetic."
All you can do is wax poetic on your new computer -- let me talk for a change!
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