Etymology
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royal (adj.)

mid-13c., "fit for a king;" late 14c., "pertaining to a king," from Old French roial "royal, regal; splendid, magnificent" (12c., Modern French royal), from Latin regalis "of a king, kingly, royal, regal," from rex (genitive regis) "king," from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."

Of institutions, "founded under the patronage of a sovereign" (c. 1500). The meaning "splendid, first-rate" is by 1853. The U.S. colloquial use as an emphasizer, "thorough, total" is attested from 1940s. Battle royal (1670s) preserves the French pattern of adjective after noun (as in attorney general); the sense of the adjective here is "on a grand scale" (compare pair-royal "three of a kind in cards or dice," c. 1600). Royal Oak was the name given to the tree in Boscobel in Shropshire after Charles II hid himself in it during flight from the Battle of Worcester in 1651. Sprigs of oak were worn to commemorate his restoration in 1660.

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royal (n.)

"royal person," c. 1400, from royal (adj.). Specifically "member of the royal family" from 1774, colloquial.

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royale (adj.)
French, "royal" (see royal (adj.)).
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royally (adv.)

late 14c., "regally, in a manner befitting a sovereign, with royal pomp and splendor;" 1836, "gloriously" (colloquial), from royal (adj.) + -ly (2).

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royalist (n.)

"supporter or adherent of a sovereign" (especially in times of civil war), "a monarchist," 1640s, from royal + -ist. In England, a partisan of Charles I and II during the Civil War; in the U.S., an adherent of British government during the Revolution; in France, a supporter of the Bourbons.

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Port Royal 

name of a convent near Versailles, in 17c. the home of a lay community notorious for Jansenism; hence Port-Royalist.

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pennyroyal (n.)

perennial herb of the mint family, formerly cultivated for medicinal purposes, 1520s, alteration by folk etymology of Anglo-French puliol real; for second element see royal; the first element ultimately is from Latin puleium "thyme," a word of unknown origin. Later also applied to an American plant.

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royalty (n.)

c. 1400, "office or position of a sovereign, royal power or authority," also "magnificence," from or modeled on Old French roialte (12c., Modern French royauté), from Vulgar Latin *regalitatem (nominative *regalitas), from Latin regalis "royal, kingly; of or belonging to a king, worthy of a king" (see royal (adj.)).

The meaning "royal persons collectively" is from late 15c. From the notion of prerogatives of a sovereign the sense expanded to "prerogatives or rights granted by a sovereign to an individual or corporation" (late 15c.). From that evolved more general senses, such as "payment to a landowner for use of a mine" (1839), and ultimately "payment to an author, composer, etc." for sale or use of his or her work (1857). Compare realty.

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loyal (adj.)

"true or faithful in allegiance," 1530s, in reference to subjects of sovereigns or governments, from French loyal, from Old French loial, leal "of good quality; faithful; honorable; law-abiding; legitimate, born in wedlock," from Latin legalem, from lex "law" (see legal).

Identical with legal, which maintains the Latin form; in most uses it has displaced Middle English leal, which is an older borrowing of the French word. For the twinning, compare royal/regal. Sense development in English is feudal, via notion of "faithful in carrying out legal obligations; conformable to the laws of honor." In a general sense (of dogs, lovers, etc.), from c. 1600. As a noun meaning "those who are loyal" from 1530s (originally often in plural).

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*reg- 

Proto-Indo-European root meaning "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."

It forms all or part of: abrogate; address; adroit; Alaric; alert; anorectic; anorexia; arrogant; arrogate; bishopric; correct; corvee; derecho; derogate; derogatory; Dietrich; direct; dress; eldritch; erect; ergo; Eric; Frederick; Henry; incorrigible; interregnum; interrogate; maharajah; Maratha; prerogative; prorogue; rack (n.1) "frame with bars;" rail (n.1) "horizontal bar passing from one post or support to another;" Raj; rajah; rake (n.1) "toothed tool for drawing or scraping things together;" rake (n.2) "debauchee; idle, dissolute person;" rakish; rank (adj.) "corrupt, loathsome, foul;" real (n.) "small Spanish silver coin;" realm; reck; reckless; reckon; rectangle; rectify; rectilinear; rectitude; recto; recto-; rector; rectum; regal; regent; regicide; regime; regimen; regiment; region; regular; regulate; Regulus; Reich; reign; resurgent; rex; rich; right; Risorgimento; rogation; royal; rule; sord; source; subrogate; subrogation; surge; surrogate; viceroy.

It is the hypothetical source of/evidence for its existence is provided by:

Sanskrit raj- "a king, a leader," rjyati "he stretches himself," riag "torture" (by racking); Avestan razeyeiti "directs," raštva- "directed, arranged, straight;" Persian rahst "right, correct;" Latin regere "to rule, direct, lead, govern," rex (genitive regis) "king," rectus "right, correct;" Greek oregein "to reach, extend;" Old Irish ri, Gaelic righ "a king," Gaulish -rix "a king" (in personal names, such as Vircingetorix), Old Irish rigim "to stretch out;" Gothic reiks "a leader," raihts "straight, right;" Lithuanian raižytis "to stretch oneself;" Old English rice "kingdom," -ric "king," rice "rich, powerful," riht "correct;" Gothic raihts, Old High German recht, Old Swedish reht, Old Norse rettr "correct."

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