Etymology
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pax (n.)

late 14c., "kiss of peace," from Latin pax (genitive pacis) "peace," in Ecclesiastical Latin, "kiss of peace" (see peace). Capitalized, Pax was the name of the Roman goddess of peace. Used with adjectives from national names, on model of Pax Romana (such as Pax Britannica, 1872); Pax Americana was used by 1884 in reference to the union of the states:

The great state of New York, stronger already in population than Sweden, Portugal, the Dominion of Canada, or any South American state, except Brazil, is surrounded by smaller states, Vermont, Connecticut, New Jersey, Delaware. But these last have no anxieties: no standing armies breed taxes and hinder labor; no wars or rumors of wars interrupt trade; there is not only profound peace, but profound security, for the Pax Americana of the Union broods over all. ["Cyclopaedia of Political Science,: John J. Lalor, ed., vol. III, 1884]

The phrase typically meant that at first, but by 1898 was used of theoretical influence of U.S. power beyond its borders, and by 1920 as a practical reality with reference to Latin America. 

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Definitions of pax

pax (n.)
(Roman Catholic Church) a greeting signifying Christian love for those assisting at the Eucharist;
Synonyms: kiss of peace
From wordnet.princeton.edu