1814, coined by English polymath Thomas Young (1773-1829) and first used in an article in the "Quarterly Review," from Indo- + European. "Common to India and Europe," specifically in reference to the group of related languages and to the race or races characterized by their use. William Dwight Whitney ("The Life and Growth of Language," 1875) credits its widespread use to Franz Bopp.
The alternative Indo-Germanic (1835) was coined in German in 1823 (indogermanisch), based on the two peoples then thought to be at the extremes of the geographic area covered by the languages, but this was before Celtic was realized also to be an Indo-European language. After this was proved, many German scholars switched to Indo-European as more accurate, but Indo-Germanic continued in use (popularized by the titles of major works) and the predominance of German scholarship in this field made it the popular term in England, too, through the 19c. See also Aryan and Japhetic.
Indo-Aryan (1850) seems to have been used only of the Aryans of India. Indo-European also was used in reference to trade between Europe and India or European colonial enterprises in India (1813).
the hypothetical reconstructed ancestral language of the Indo-European family, by 1905. The time scale of the "language" itself is much debated, but a recent date proposed for it is about 5,500 years ago.
c. 1600, as a term in classical history, from Latin Arianus, Ariana, from Greek Aria, Areia, names applied in classical times to the eastern part of ancient Persia and to its inhabitants. Ancient Persians used the name in reference to themselves (Old Persian ariya-), hence Iran. Ultimately from Sanskrit arya- "compatriot;" in later language "noble, of good family."
Also the name Sanskrit-speaking invaders of India gave themselves in the ancient texts. Thus it was the word early 19c. European philologists (Friedrich Schlegel, 1819, who linked it with German Ehre "honor") applied to the ancient people we now call Indo-Europeans, suspecting that this is what they called themselves. This use is attested in English from 1851. In German from 1845 it was specifically contrasted to Semitic (Lassen).
German philologist Max Müller (1823-1900) popularized Aryan in his writings on comparative linguistics, recommending it as the name (replacing Indo-European, Indo-Germanic, Caucasian, Japhetic) for the group of related, inflected languages connected with these peoples, mostly found in Europe but also including Sanskrit and Persian. The spelling Arian was used in this sense from 1839 (and is more philologically correct), but it caused confusion with Arian, the term in ecclesiastical history.
The terms for God, for house, for father, mother, son, daughter, for dog and cow, for heart and tears, for axe and tree, identical in all the Indo-European idioms, are like the watchwords of soldiers. We challenge the seeming stranger; and whether he answer with the lips of a Greek, a German, or an Indian, we recognize him as one of ourselves. [Müller, "History of Ancient Sanskrit Literature," 1859]
Aryan was gradually replaced in comparative linguistics c. 1900 by Indo-European, except when used to distinguish Indo-European languages of India from non-Indo-European ones. From the 1920s Aryan began to be used in Nazi ideology to mean "member of a Caucasian Gentile race of Nordic type." As an ethnic designation, however, it is properly limited to Indo-Iranians (most justly to the latter) and has fallen from general academic use since the Nazis adopted it.