Conclusion
From the information included in this paper, I have attempted to demonstrate that the word 'Arab' has had a wide variety of uses over the centuries. Despite this wide use, it is my opinion that the majority of ancient historians who wrote, or gleanded their material from the period that the Nabataeans were at the height of their power, considered the Nabataeans to be Arabs and the Arabs to be Nabataeans.
Bibliography
Ammianus Marcellinus, The Roman History of Ammianus Marcellinus During the reigns of The Emperors Constantius, Julian, Jovianus, Valentinian, and Valens, trans. C. D. Yonge (London: G. Bell & Sons, 1911), pp. 11-12
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Procopius, History of the Wars, 7 vols., trans. H. B. Dewing (Cambridge, Mass., and London: Harvard University Press & Wm. Heinemann, 1914; reprint ed., 1953-54), I.179-195. Scanned by: J. S. Arkenberg, Dept. of History, Cal. State Fullerton. Prof. Arkenberg has modernized the text and added the annotations.
Strabo, The Geography of Strabo: Literally Translated, with Notes, trans. by H. C. Hamilton & W. Falconer (London: H. G. Bohn, 1854-1857), pp. 185-215
Many of ancient texts quotes in this paper come from the Internet Ancient History Sourcebook. The Sourcebook is a collection of public domain and copy-permitted texts related to medieval and Byzantine history, and permission is granted to use their texts for educational purposes.
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http://nabataea.net/arabia.html