Origins
The Latin word 'caput' — meaning 'head' — is one of the most consequential nouns in the history of the English vocabulary. Through direct borrowing, through Old French, and through Medieval Latin, it has given English an extraordinary range of words that collectively illustrate how a single concrete body-part term can ramify into the domains of leadership, finance, architecture, law, anatomy, geography, and religion.
Caput traces to the Proto-Indo-European root *kaput-, meaning simply 'head.' This root has cognates across the family: Greek κεφαλή (kephalē, 'head,' the source of 'encephalitis' and 'cephalopod'), Germanic *haubudam (giving German Haupt, Dutch hoofd, and English 'head' via a separate PIE variant *kaput- > Proto-Germanic *haubudą). The Latin form preserved the original consonants most faithfully.
In Latin, caput was a third-declension neuter noun with the oblique stem capit-. The Romans used it with dazzling metaphorical range. Caput meant the physical head, but also a person's life or civil existence (in Roman law, 'capitis dēminūtiō' was the reduction of a person's legal status — the loss of one's metaphorical 'head' in society). It meant the top or summit of anything, the source of a river ('caput flūminis'), a main point or heading (giving us 'chapter,' from 'capitulum,' the diminutive 'little head'), and the principal sum of money (as opposed to interest — still the meaning of 'capital' in finance).
Latin Roots
The most direct English borrowing is 'capital,' from Latin capitālis ('of the head'). A 'capital' crime is one punishable by loss of the head. A 'capital' city is the head city. 'Capital' as money is the head sum, the principal. 'Capitalism' — coined in the mid-nineteenth century — builds on this financial sense. The 'Capitol' (the Roman temple of Jupiter on the Capitoline Hill, literally the 'head hill') gives its name to legislative buildings worldwide.
'Captain' arrived through Old French capitaine, from Late Latin capitāneus ('chief'), from caput. The parallel French development produced 'chief' (from Old French chief, 'head') and 'chef' (the modern French form of the same word, borrowed into English to mean 'head cook'). 'Chieftain' blends the French chief with the Latin -tāneus ending. 'Achieve' comes from Old French achever ('to come to a head, to finish'), from à chef venir — literally 'to come to a head.'
The diminutive capitulum ('little head, heading, chapter') gave English 'chapter' through Old French chapitre. A 'chapter' of a book is literally a 'heading' — a little head marking a division. 'Capitulate' originally meant 'to draw up under headings or chapters' (as in the terms of a treaty), and only later acquired its modern sense of 'to surrender (on stated terms).'
French Influence
Some of the most surprising descendants arrive through metaphorical extensions in medieval economics. 'Cattle' comes from Anglo-Norman catel, from Medieval Latin capitāle ('property, stock'), from caput — because livestock was the primary form of movable wealth, counted 'by the head.' 'Chattel' is a doublet of 'cattle,' arriving through a different Old French dialectal form, and retaining the broader sense of 'movable property.' The legal phrase 'goods and chattels' preserves this. 'Capital' in its financial sense traveled the same path but kept its Latin form.
'Decapitate' (from de- + caput, 'to remove the head') is transparent. 'Precipice' and 'precipitate' come from praeceps (stem praecipit-), meaning 'head-first' (prae- 'before, forward' + caput), hence 'steep, headlong.' To 'precipitate' something is to throw it headlong. 'Biceps' and 'triceps' contain caput in the sense of 'head' or 'end' — a biceps is a muscle with 'two heads' (two points of origin).
Even words that look nothing like 'caput' descend from it. 'Kerchief' comes from Old French couvrechief ('cover-head'). 'Handkerchief' is thus a 'hand-cover-head' — etymologically redundant but historically layered. 'Mischief' comes from Old French meschever ('to come to a bad head,' to come out badly). 'Cadet' comes from Gascon French capdet, a dialectal form of capitellum (diminutive of caput), meaning 'little head' or 'little chief' — applied to younger sons of noble families who sought military careers.
Figurative Development
The journey from a PIE word for 'head' to the concepts of capital, capitalism, cattle, chapters, chiefs, and achievement is one of the most remarkable semantic radiations in any language, illustrating how deeply metaphor shapes the evolution of vocabulary.