The common ancestor of PIE has been reconstructed by projecting backwards from Greek and Sanskrit. The chart below shows the earliest date for which written sources have been found.
German philologists had worked out systematic relationships between their own language and Greek and Latin. Grimm’s law is the best-known rule for change from PIE to Germanic, summarised as a chain:
bʰ > b > p > f *bʰréh₂tēr → E: brother, Persian → barádar Latin → → frāter
dʰ > d > t > θ *médʰu → G: met E: mead, Greek: → → μέθυ (methu)
gʰ > g > k > x *ǵʰans- → G: gans E: goose, Latin: anser, Sanskrit hamsa
gʷʰ > gʷ > kʷ > xʷ *gʷih₃wós → E: quick, G: keck, Russian: → živoj, Sanskrit: → jīvá-
Academia Prisca have comprehensive dictionaries, syntax and a modern version of PIE