peroration (n.)

late 14c., oratour, "an eloquent or skilled speaker; one who pleads or argues for a cause," from Anglo-French oratour (Modern French orateur) and directly from Latin orator "speaker," from ōrare "to speak, speak before a court or assembly, pray to, plead."

This is sometimes said to be  from PIE root *or- "to pronounce a ritual formula" (source also of Sanskrit aryanti "they praise," Homeric Greek are, Attic ara "prayer," Hittite ariya- "to ask the oracle," aruwai- "to revere, worship").  But according to de Vaan, the Latin word is rather from Proto-Italic *ōs- "mouth," from PIE *os- "mouth" (see oral). He writes:

The chronology of the attestations shows that 'to plead, speak openly' is the original meaning of orare .... The alternative etymology ... seems very unlikely to me: a connection with Skt. a-aryanti 'they acknowledge' and Ru. orat' 'to shout', since nothing suggests a meaning 'to shout' for the Latin verb, nor does it seem onomatopoeic.

The general meaning "public speaker," is attested from early 15c. Fem. forms were oratrice (early 15c., from Anglo-French); oratrix (mid-15c., from Latin); oratress (1580s).

"to make a speech," especially a grandiloquent one, c. 1600, a colloquial back-formation from peroration (q.v.), or else from Latin peroratus, past participle of perorare. Related: Perorated; perorating.

Proto-Indo-European root forming prepositions, etc., meaning "forward," and, by extension, "in front of, before, first, chief, toward, near, against," etc.

It forms all or part of: afford; approach; appropriate; approve; approximate; barbican; before; deprive; expropriate; far; first; for; for-; fore; fore-; forefather; foremost; former (adj.); forth; frame; frau; fret; Freya; fro; froward; from; furnish; furniture; further; galore; hysteron-proteron; impervious; improbity; impromptu; improve; palfrey; par (prep.); para- (1) "alongside, beyond; altered; contrary; irregular, abnormal;" paradise; pardon; paramount; paramour; parvenu; pellucid; per; per-; percent; percussion; perennial; perestroika; perfect; perfidy; perform; perfume; perfunctory; perhaps; peri-; perish; perjury; permanent; permeate; permit; pernicious; perpendicular; perpetual; perplex; persecute; persevere; perspective; perspire; persuasion; pertain; peruse; pervade; pervert; pierce; portray; postprandial; prae-; Prakrit; pre-; premier; presbyter; Presbyterian; preterite; pride; priest; primal; primary; primate; primavera; prime; primeval; primitive; primo; primogenitor; primogeniture; primordial; primus; prince; principal; principle; prior; pristine; private; privilege; privy; pro (n.2) "a consideration or argument in favor;" pro-; probably; probe; probity; problem; proceed; proclaim; prodigal; produce; profane; profess; profile; profit; profound; profuse; project; promise; prompt; prone; proof; proper; property; propinquity; prophet; prose; prostate; prosthesis; protagonist; Protean; protect; protein; Proterozoic; protest; proto-; protocol; proton; protoplasm; Protozoa; proud; prove; proverb; provide; provoke; prow; prowess; proximate; Purana; purchase; purdah; reciprocal; rapprochement; reproach; reprove; veneer.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pari "around, about, through," parah "farther, remote, ulterior," pura "formerly, before," pra- "before, forward, forth;" Avestan pairi- "around," paro "before;" Hittite para "outside of," Greek peri "around, about, near, beyond," pera "across, beyond," paros "before," para "from beside, beyond," pro "before;" Latin pro "before, for, on behalf of, instead of," porro "forward," prae "before," per "through;" Old Church Slavonic pra-dedu "great-grandfather;" Russian pere- "through;" Lithuanian per "through;" Old Irish ire "farther," roar "enough;" Gothic faura "before," Old English fore (prep.) "before, in front of," (adv.) "before, previously," fram "forward, from," feor "to a great distance, long ago;" German vor "before, in front of;" Old Irish air- Gothic fair-, German ver-, Old English fer-, intensive prefixes.