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late 12c. (in plural, giwis), from Anglo-French iuw, Old French giu, from Latin Iudaeum (nominative Iudaeus), from Greek Ioudaios, from Aramaic jehudhai (Hebrew y'hudi) "Jew," from Y'hudah "Judah," literally "celebrated," name of Jacob's fourth son and of the tribe descended from him. Replaced Old English Iudeas "the Jews." Originally, "Hebrew of the kingdom of Judah."
Jews' harp "simple mouth harp" is from 1580s, earlier Jews' trump (1540s); the connection with Jewishness is obscure. Jew-baiting first recorded 1853, in reference to German Judenhetze. In uneducated times, inexplicable ancient artifacts were credited to Jews, based on the biblical chronology of history: e.g. Jews' money (1570s) "Roman coins found in England." In Greece, after Christianity had erased the memory of classical glory, ruins of pagan temples were called "Jews' castles," and in Cornwall, Jews' houses was the name for the remains of ancient tin-smelting works.
"to cheat, to drive a hard bargain," 1824, from Jew (n.) (cf. gyp, welsh, etc.). The campaign to eliminate it in early 20c. was so successful that people began to avoid the noun and adjective, too, and started using Hebrew instead.
Now I'll say 'a Jew' and just the word Jew sounds like a dirty word and people don't know whether to laugh or not. [Lenny Bruce (1925-1966)]
The Israelites, particularly after their return from captivity in Babylon about five hundred years before the birth of Jesus; at that time, the Israelites were established as a religious group, founded on the Mosaic law, not simply a national group.
Note: When the Jewish nation was destroyed by the Romans in the year a.d. 70 and the Jews were scattered throughout the world, their religious beliefs and customs allowed them to remain one people.
Adherents of Judaism.
the name derived from the patriarch Judah, at first given to one belonging to the tribe of Judah or to the separate kingdom of Judah (2 Kings 16:6; 25:25; Jer. 32:12; 38:19; 40:11; 41:3), in contradistinction from those belonging to the kingdom of the ten tribes, who were called Israelites. During the Captivity, and after the Restoration, the name, however, was extended to all the Hebrew nation without distinction (Esther 3:6, 10; Dan. 3:8, 12; Ezra 4:12; 5:1, 5). Originally this people were called Hebrews (Gen. 39:14; 40:15; Ex. 2:7; 3:18; 5:3; 1 Sam. 4:6, 9, etc.), but after the Exile this name fell into disuse. But Paul was styled a Hebrew (2 Cor. 11:22; Phil. 3:5). The history of the Jewish nation is interwoven with the history of Palestine and with the narratives of the lives of their rulers and chief men. They are now  dispersed over all lands, and to this day remain a separate people, "without a king, and without a prince, and without a sacrifice, and without an image [R.V. 'pillar,' marg. 'obelisk'], and without an ephod, and without teraphim" (Hos. 3:4). Till about the beginning of the present century  they were everywhere greatly oppressed, and often cruelly persecuted; but now their condition is greatly improved, and they are admitted in most European countries to all the rights of free citizens. In 1860 the "Jewish disabilities" were removed, and they were admitted to a seat in the British Parliament. Their number in all is estimated at about six millions, about four millions being in Europe. There are three names used in the New Testament to designate this people, (1.) Jews, as regards their nationality, to distinguish them from Gentiles. (2.) Hebrews, with regard to their language and education, to distinguish them from Hellenists, i.e., Jews who spoke the Greek language. (3.) Israelites, as respects their sacred privileges as the chosen people of God. "To other races we owe the splendid inheritance of modern civilization and secular culture; but the religious education of mankind has been the gift of the Jew alone."