About 5,000 years ago people along the Dnepr River in what is now the Ukraine, spoke a language from which virtually all the languages of present-day Europe and India developed. Linguists call it 'Proto-Indo-European' or simply 'PIE'—and, boy, is it a linguistic dessert!
As the original tribe expanded, various segments of it moved farther and farther away from the central mother language, developing their own accents or 'dialects', much like those in the northern and southern US states. Without TV and cell phones to keep everyone in contact, eventually those dialects changed so much that they became different languages, usually called things like 'Proto-Slavic', 'Proto-Germanic', 'Proto-Indo-Iranian'. The same process repeated itself over and over in these languages until we reached modern English, French, German, Russian, etc, illustrated in the abbreviated table below. (Click here for a complete list of Indo-European languages.)
PIE contained a word with three variants: pt-, pet-, pot-, which meant something like "fly" or "flow" or both (note the fl- in both English words—they share the same origin, too). The forms probably corresponded to tenses such as are found in English grow : grew. We don't know for sure but that relation broke down in the dialects where they became separate words. When they became separate words, their meanings began to change in the various languages they were used in. In the Greek dialect, the pot- variant became the word for "river": pot-amos from the sense "that which flows". The English word hippopotamus is taken from the Greek hippo "horse" + pot-amos "river" = "river horse".
In the Germanic languages, to which English belongs, the pet- variant of the same word attracted the suffix -er, something like pet-er-. But as the Old Germanic dialects continued to develop into the modern Germanic languages, both the pronunciation and meaning of this word changed. Jakob Grimm, the famous linguist who collected fairy tales on the side, figured out the rules by which Germanic sounds differed from those of Indo-European. According to Grimm's Law, Proto-Indo-European [p] became Germanic [f] and Indo-European [t] became Germanic [th], and Indo-European [k] became Germanic [kh] (the now unpronounced [gh] in many English words like night).
|p > f||Greek pod (tri-pod)||English foot|
|Latin pre- (pre-dict)||English fore- (fore-tell)|
|Greek pter-on "wing"||English feather|
|t > th||Latin pater||English father|
|k > gh||Latin lux (luk-s)||English ligh-t|
|Latin rect-us "straight"||English right|
Thus the "pot-" of hippopotamus and the feath- of "feather" share a common origin. By the way, the suffix -er has played an interesting role in these words. This suffix derives agents (someone who does something) and instruments (the means by which something is done) from verbs, e.g. bake > bak-er (agent), slice > slic-er (instrument). Russian placed its own suffix, -ica, on the pt- stem and guess what the result was: pt-ica "bird, one that files". Greek also used this vowelless form with the suffix -er : pt-er-on "wing, the means of flying" (pter-o-dactyl = "wing-fingered one").
Remember, the magic word is linguistics, a very new science. Etymology is the study of the historical development of words, part of historical linguistics. Check with the Linguistics Program at the university nearest you for the courses you can take next semester.