The term middle east as a noun and adjective was common in the 19th century in nearly every context except diplomacy and archaeology. An uncountable number of places appear to have had their middle easts from gardens to regions, including the United States. The innovation of the term "Near East" to mean the holdings of the Ottoman Empire as early as the Crimean War had left a geographical gap. The East Indies, or "Far East," derived ultimately from Ptolemy's "India Beyond the Ganges." The Ottoman Empire ended at the eastern border of Iraq. "India This Side of the Ganges" and Iran had been omitted. The archaeologists counted Iran as "the Near East" because Old Persian cuneiform had been found there. This usage did not sit well with the diplomats; India was left in an equivocal state. They needed a regional term.
Where did the "Far East" derive from?
Ptolemy's "India Beyond the Ganges."