First of all, I’d like to give a bit of background information. English is part of the Indo-European (IE) language group, the origins of which stretch back over 6000 years. Although we can never know exactly how words were pronounced in IE, we can postulate their likely forms and pronunciations based on the words that have come down from it into ancient written languages, like Latin, Greek, Sanskrit, Hittite and Avestan, and also modern IE languages, which range over most of Europe and through Iran into the Indian sub-continent. Based on the recorded forms in all these languages, the likely ancient forms can be postulated, albeit with some variation and uncertainty. Postulated forms are always written with an asterisk. IE also gave rise to the Germanic language group by way of Proto-Germanic (PG) some 3000 years ago. This group is made up of West Germanic (Dutch, English, German and Frisian) and North Germanic (Swedish, Norwegian, Danish, Icelandic and Faroese). There was also East Germanic, the most well-known of which was Gothic, the oldest written Germanic language, but the last remnants of that group finally died out over three hundred years ago.
Now for the good part. Firstly, let’s look at two words in modern English which are probably the closest we can find to identical twins, growing up and going their own ways, but keeping pretty well the same meanings over all that time despite being sundered for so long, and then meeting up and saying: “Gosh, you look different, well, actually, not really”. IE had a form which is rendered as *peḱu, probably pronounced something like “peck-you”. This root had a variety of derivations, but only two interest us here: Latin pecus and PG *feHu. We can see here that the original p was preserved in Latin, but was changed to f in PG, and the original ḱ sound became c in Latin, but H (pronounced like ch in “loch”) in PG. The meaning of both these forms was “cattle, livestock” and by extension “property, money”. These associations are fairly unsurprising given that livestock has always been a basis of wealth in many societies, and the people who spoke the original IE language were almost certainly nomadic herders. The Latin pecus produced pecū, “cattle”, then pecūnia, “money, property”, and then pecūniārius, “pertaining to money”, from which we derive pecuniary. In the meantime, Proto-Germanic produced OE feoh, “money, property, cattle”. So far so good.
However, feoh did not come down to us in modern English. Instead, we inherited a similar form, from another Germanic language, Frankish, which had the form *fehu, from which *fehu-od was formed, meaning “payment-estate”. The Franks, of course, settled in the Roman province of Gaul in the 3rd century and gave the country its new name – yes, the French are actually Germans, in a sense, and around 10% of French words come from Frankish. This word was also borrowed into Medieval Latin in the form of feudum, which gives us feudal. After the Norman conquest, thousands of OE words were replaced by French words, one of which was the Anglo-French fee, which came into Middle English with the meaning of “an estate belonging to a feudal lord”. It soon came to mean “payment for services provided”, hence our modern fee. Not content with borrowing it once as fee, English later borrowed it again from French as fief. It’s fascinating to think that the French word, borrowed from a Germanic language, replaced the lost OE word and kept not only the same basic meaning of the original, but also the meaning of its Latin-derived twin, pecuniary, after being separated for thousands of years. Just a word of warning: if you want to pay your university fees, I don’t think they accept cows any more - it's not the dung thing.
Now I’d like to turn to the second set of words passing through Latin and OE into modern English, but with such different meanings that it’s surprising that they once had any connection at all. These are the unruly siblings that refuse to acknowledge the resemblance they once had. When they all met up again in modern English, they all asked: “Do I know you from somewhere?” The IE root probably had three forms, *leis-/lois-/lis-, and the meaning was something like “trace, track”. Now, the idea of tracing or tracking could lead to a number of developments, in this case three. Firstly, and most basically, tracking is something done on foot, so the idea of a path or walkway, or even tracks left in the ground, is a likely development. This also stretched to the modes of tracking, namely, the feet themselves. Secondly, tracing and tracking can lead to finding out about something, gaining knowledge. Thirdly, tracking may lead to persistence in following. Let’s look at the second development first, as it’s the most important one. The IE root gave rise to the PG verb *liznōjanan (PG j is pronounced like y), “follow along a track”, which eventually developed into OE leornian, which gives us learn. Another form, *laizijanan, developed into the modern German lehren, “teach”, but the related word in OE didn’t reach modern English. However, a third form, *laizō, became OE lār, “learning, knowledge, doctrine”, giving us modern English lore. Clearly, in the minds of the early Germanic peoples, tracking and tracing were good ways of gaining knowledge. I hope you’re keeping track.
Another derivation from the IE root which came down to us via PG involves tracking and following of a different kind, not with the mind but with persistence, the third development given above. PG *laistjanan developed the meaning of “follow, perform, carry out” and OE inherited it as lǣstan, “accomplish, carry out”, with the meaning developing into “continue, endure”, which is the meaning of the modern verb last. The final Germanic derivation from the same IE root in modern English, albeit a highly specialised and little used one, retains the use of the foot as opposed to the track itself, as outlined in the first development given above. PG also inherited the root word *laistaz from IE and this became lāst in OE, meaning “track, footprint”. This found its way into modern English as last, which is a foot-shaped block used by shoemakers to model their wares. Incidentally, the most common word with this spelling, the adjective last, is actually a contraction of latest, and has nothing to do with this root. If you’ve lasted to this point, I hope you can keep on the right track.
Now we come to the final (last?) derivation in modern English from this IE root, though this came to us courtesy of Latin, and in a rather strange way. The IE root turned up in Latin as līra, denoting a rather specialised type of track, namely “furrow”, as in the long, straight line produced by a plough. If a Roman ploughman couldn’t stay on a straight line, he would literally veer “off the furrow”, or dē līrā. This produced a verb dēlīrāre, “go off the furrow”, with the extended meaning of “go mad, rave”, and a noun dēlīrium, which modern English then borrowed as delirium, subsequently creating the adjective delirious and the medical term delirium tremens, which describes the effects of losing a dependency on alcohol. This also begs the question of whether Roman ploughmen were frequently drunk. I hope you can last out, though, without going delirious.
The concluding set of examples shows how a root can separate into different strands which can still remain true to the original meaning in their own ways, while showing clear divergence and different interpretations of that original meaning, sort of identical twins going their own ways but staying true to mum in some way. IE had a root *al-, with the basic meaning of “grow, nourish”. This produced a variety of derivations in Latin, including these: almus/alma, “nourishing”, as in the expression alma mater, literally “nourishing mother”, the institution where a graduate studied; adolēscere (with the prefix ad- and the change from a to o), “grow up”, which gives us adolescent and adult; alimentum, “nourishment”, from which we get alimentary and alimentation; and alimōnia, “nourishment, sustenance”, from which we get alimony. The IE *al- root was also extended in another way, *al-d-/ *al-dh-, which produced two types of growing, one in Latin altus and a different one in PG *alđáz. The Latin form focused on the aspect of growing in height, while the PG form did the same for age. Hence, altus produced altitude and altimeter, while *alđáz produced OE ald and eald, which give us old, elder and alderman, among other words. French has also bequeathed us more derivations from Latin after altus became haut, namely haute cuisine, oboe (originally haut bois, “high wood”, via Italian), and haughty, with the spelling mistakenly changed. For good measure, we also got alto from Italian. I can just imagine the reactions of quarrelling teenagers 6000 years ago when their parents shouted: “I wish you lot would just grow up!” – “which way?”
So, there we have it – three ways to get two or more words from the same root, but with widely varying results. There are a lot more of these out there as well – you just have to look for them. Or maybe I’ll bring them to you. Let me summarise this discussion in this way: for pecuniary reasons, you need to pay your fees when you learn in your alma mater, especially when you’re old enough, but don’t get haughty or you may find yourself suffering from delirium. Have fun word-hunting.