The meaning of Eunuch in the Bible
(From Easton's Bible Dictionary)

literally bed-keeper or chamberlain, and not necessarily in all cases one who was mutilated, although the practice of employing such mutilated persons in Oriental courts was common (II Kings 9:32; Esther 2:3). The law of Moses excluded them from the congregation (Deuteronomy 23:1). They were common also among the Greeks and Romans. It is said that even to-day there are some in Rome who are employed in singing soprano in the Sistine Chapel. Three classes of eunuchs are mentioned in Matthew 19:12.

See more on the meaning of Eunuch in the Bible:
Eunuch {International Standard Bible Encyclopedia}

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