The central insight of modern historical scholarship came from Sir William Jones, a British jurist posted to Calcutta in 1783. Jones noted similarities among Sanskrit, Latin, and Greek, proposing to the Asiatic Society in 1786 that “no philologer could examine them all three, without believing them to have sprung from some common source.”
A century of linguistic detective work followed, working out the correspondences among the sounds, words, and grammar of Indo-European languages. Donald Ringe’s From Proto-Indo-European to Proto-Germanic gives a detailed account of the development of Germanic, including an extensive discussion of the famous Grimm’s Law, which states correspondences between Germanic consonants and those of other Indo-European languages. The American Heritage Dictionary of Indo-European Roots, revised and edited by Calvert Watkins, lists more than 1,300 reconstructed Indo-European roots (such as *bhē “to warm”) and their reflexes in English (bath, bake, zwieback), and Orrin Robinson’s Old English and Its Closest Relatives surveys early Germanic languages and cogently describes the comparative method.
 Sir William Jones, “The Third Anniversary Discourse, on the Hindus,” Asiatick Researches 1 (1788): 415-31, 422 (repr. in Winfred P. Lehmann, comp., A Reader in Nineteenth Century Historical Indo-European Linguistics [Bloomington: Indiana Univ. Press, 1967], 10-20). Jones added that there were reasons to suppose that Gothic, Celtic, and Persian might be added to that common mother tongue. Jones’s story is told in Garland Cannon and Kevin Brine, Objects of Enquiry: The Life, Contributions and Influences of Sir William Jones, 1746-1794 (New York: New York Univ. Press, 1995), which places Jones in the context of the Orientalism of the early period of British rule in India.