From Bill Bryson's The Mother Tongue--An Englishman, Sir William Jones, was sent to India in 1783, and taught himself Sanskrit--an odd thing to do, since it had been a dead language for centuries. He noticed a lot of similarities between that and European languages: bhurja was birch, for ex., and Sanskrit for ten was dasa, similar to the Latin decem. He proposed a theory that many of the classical languages--among them Sanskrit, Greek, Latin, Gothic, Celtic, and Persian--must spring from the same source.(p. 30.) Linguists delved eagerly into this theory over the next century, and this source language came to be called Indo-European.
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I had not known how this came by its name, and thought there might be others who would also like to know. And thanks again to you folks who led me to this book.