Similarities between Sanskrit and some European languages, ancient and modern, had been noticed earlier. In 1786 Sir William Jones, a judge in the British court in India, read his presidential address to the Asiatic Society of Bengal. In this paper he established the historical kinship of Sanskrit with Latin, Greek, Celtic and the Germanic languages (Gothic being the oldest surviving among them) and proposed that they must have a common source which perhaps no longer existed. This paper led to the development of historical linguistics; 1786 is thus considered to mark the start of contemporary linguistic science. Though its immediate effect was the rise of historical linguistics, the Western study of Sanskrit also, over a longer time period, influenced modern descriptive linguistics.
Western linguistics Before Chomsky took a strictly empiricist approach - study language data to discern regularities in observed utterances.
Historical Linguistics (Late-18th to 19th C)
Reconstruction of the proto Indo-Europian language was attempted (the Ursprache) and its divergences traced to contemporary languages of India, Iran and Europe. Branches - etymology, dialectology, phonology, morphology, syntax.
Philology = German school of comparative and historical linguistics - studied evolution and interrelations of languages; led to the establishment of language families and geneologies.
German philologists like Adam Muller tried to find the original Ursprache, to see how modern Indo-European languages differed from them (the geneologies). This research however had a political agenda - trying to infer a hierarchy of races, to prove ``Aryan superiority'', via proximity to the Ursprache.
Descriptive Linguistics (Early to mid-20th C) was concerned with the description of single languages at a particular point in time.