Origins
The Proto-Indo-European root *per- is not a single root so much as a constellation of closely related forms — *per- (forward, through), *pro- (before, in front), *preh₂- (before, from the front), and extended forms like *prH-wo- (first) — all orbiting the same spatial concept: forward motion, priority, and being in front. Together, this family constitutes one of the largest and most important root clusters in Indo-European, generating prepositions, prefixes, adverbs, adjectives, and nouns across every attested branch.
The basic form *per- carried the sense of 'going forward, passing through.' In Latin, it became the preposition and prefix 'per' (through, completely), yielding an enormous English vocabulary: 'percent' (per centum, through a hundred), 'perfect' (per + facere, done thoroughly), 'perform' (par + fournir, to furnish thoroughly, through Old French), 'period' (via Greek períodos, a going around), 'permit' (per + mittere, to send through, to allow passage), 'persist' (per + sistere, to stand through), 'person' (per + sonāre, to sound through — originally a theatrical mask through which an actor speaks), 'perspective' (per + specere, to look through), 'perhaps' (per + hap, through chance), and 'peril' (from Latin perīculum, a trial, a risk — literally 'a going through danger').
The variant *pro- (before, in front of, forward) became Latin prō (for, in front of, on behalf of), generating another vast family: 'provide' (prō + vidēre, to see ahead), 'produce' (prō + dūcere, to lead forward), 'project' (prō + iacere, to throw forward), 'progress' (prō + gradī, to step forward), 'promise' (prō + mittere, to send forward), 'promote' (prō + movēre, to move forward), 'protect' (prō + tegere, to cover in front), 'prove' (probāre, to test, from probus, tested and found good), 'problem' (from Greek próblēma, something thrown forward), 'process' (prō + cēdere, to go forward), 'program,' 'prophet' (from Greek prophḗtēs, one who speaks before/forth), 'protein' (from Greek prôtos, first, via proteios), and 'protocol' (from Greek prōtókollon, the first sheet glued to a manuscript). The prefix 'pro-' remains fully productive in English.
Proto-Indo-European Roots
The extended form *preh₂- or *prai- (before) gave Latin prae- (before), producing 'prefix,' 'predict,' 'prepare,' 'present,' 'preserve,' 'president,' 'prevent,' 'previous,' and 'premier' (from Latin prīmārius, of the first rank). Latin prīmus (first, from *prH-wo-mo-s, the most forward) yielded 'prime,' 'primary,' 'primitive,' 'prince' (prīnceps, one who takes first), 'principal,' and 'prior' (earlier, from prī-). The word 'privacy' descends from Latin prīvātus (withdrawn from public life, from prīvus, one's own — the individual 'put first' or 'set apart').
In Ancient Greek, *per- produced the preposition and prefix περί (perí, around, about), yielding 'perimeter' (a measuring around), 'period' (a going around, a cycle), 'peripheral,' 'peripatetic' (walking around — the Aristotelian philosophers who walked and talked). The Greek *pro- became πρό (pró, before, forward), generating 'prognosis,' 'prologue,' 'program,' and the combining form 'proto-' (from prôtos, first) in 'prototype,' 'protocol,' and 'proton.'
In the Germanic branch, *per- underwent Grimm's Law (*p > *f), producing Proto-Germanic *fur (before, for). Old English 'for' (on behalf of, because of) descends directly from this. 'Fore' (in front) and 'before' (in front of) are related formations. 'First' comes from Proto-Germanic *furista (the most forward, superlative of *fur). 'Former' is the comparative. 'From' descends from Proto-Germanic *fram (forward, away from — what is in front recedes as you approach it, yielding the sense of origin and departure). 'Forth' (forward, onward) and 'further' (more forward) continue the spatial sense. 'Far' derives from Proto-Germanic *ferro (at a distance ahead). 'Frame' (originally 'to go forward, to benefit, to make progress') and 'furnish' (from Old French fournir, originally a Germanic loanword meaning 'to provide, to advance') also connect.
Latin Roots
In Sanskrit, pári (around) and prá (forward, forth) are direct cognates of Greek perí and pró. The adjective pūrva (former, first, eastern — the direction one faces, hence 'forward') shows the same development as Latin prīmus. In Old Persian, the prefix pairi- (around) combined with daēza (wall) to form 'pairidaēza' (an enclosed park, a walled garden), which passed through Greek parádeisos into English as 'paradise' — etymologically, a place 'walled around.'
The Russian prefix 'пере-' (pere-, through, across) and Lithuanian 'per' (through) confirm the root's pan-IE distribution. The Slavic prefix 'про-' (pro-, through, forward) parallels the Latin and Greek forms exactly.
Few roots demonstrate the organizational power of spatial metaphor as clearly as *per-. The idea of 'going forward' extends naturally to being first (priority), being in front (protection), passing through (completion, permission, danger), going beyond (surpassing), and being set apart (privacy). From a single directional concept articulated on the Pontic steppe, the Indo-European languages built much of their spatial, temporal, and conceptual vocabulary.