From the archives...

Sphincter was first used by Galen in the 2nd century, probably as an allusion to the talented constrictor that was the Sphinx of Greek mythology. A chimera with the head of a woman and the body of a winged-lion, and who received her name from the Greek sphingo, "I strangle", the Sphinx sat outside Thebes and demanded that all passersby answer her riddle: "Which creature travels in the morning on four feet, at noon on two, and in the evening upon three?" She strangled anyone unable to answer. Oedipus finally provided the correct response.

A fourth century BC kylix from the Vatican Museum showing Oedipus with the Sphinx wikipedia.org

Note that the Grecian Sphinx is not the same as the sphinxes of Egypt: The Greek name "sphinx" was inexplicably applied some 2600 years ago to an Egyptian chimeric lion, even though it is wingless and has the head of a man not a woman. The original Egyptian name of this creature is unknown. The most famous of the Egyptian sphinxes is the Great Sphinx of Giza.