Online Etymology Dictionary

compendious (adj.): "concise," late 14c., from Old French compendieux, from Latin compendiosus "advantageous, abridged, brief," from compendium (see compendium).
compendium (n.): 1580s, from Latin compendium "a shortening, saving," literally "that which is weighed together," from compendere "to weigh together," from com- "together" (see com-) + pendere "to weigh" (see pendant). Borrowed earlier as compendi (mid-15c.).
compensable (adj.): 1660s, from French compensable (16c.), from compenser, from Latin compensare (see compensate).
compensate (v.): 1640s, "to be equivalent;" 1650s, "to counterbalance, make up for," from Latin compensatus, past participle of compensare "to weigh one thing (against another)," thus, "to counterbalance," from com- "with" (see com-) + pensare, frequentative of pendere "to weigh" (see pendant). Meaning "to recompense, remunerate" is from 1814. Related: Compensated; compensating.
compensation (n.): late 14c., "action of compensating," from Latin compensationem (nominative compensatio) "a weighing one thing against another, a balancing," noun of action from past participle stem of compensare (see compensate). Meaning "what is given in recompense" is from c. 1600; meaning "amends for loss or damages" is from 1804; meaning "salary, wages" is attested from 1787, American English. The psychological sense is from 1914.
compensatory (adj.): c. 1600, from French compensatoire, from Latin compensatus, past participle of compensare (see compensate). Psychological sense is from 1921.
compere (n.): 1738, from French compère "a godfather," from Old French compere (13c., from Medieval Latin compater) "godfather," also a friendly greeting, "friend, brother," hence "fellow, familiar, intimate" (see compadre).
compete (v.): 1610s, " to enter or be put in rivalry with," from Middle French compéter "be in rivalry with" (14c.), or directly from Late Latin competere "strive in common," in classical Latin "to come together, agree, to be qualified," later, "strive together," from com- "together" (see com-) + petere "to strive, seek, fall upon, rush at, attack" (see petition (n.)).

Rare 17c., revived from late 18c. in sense "to strive (alongside another) for the attainment of something" and regarded early 19c. in Britain as a Scottish or American word. Market sense is from 1840s (perhaps a back-formation from competition); athletics sense attested by 1857. Related: Competed; competing.
competence (n.): 1590s, "rivalry" (based on compete); c. 1600 "adequate supply;" 1630s, "sufficiency of means for living at ease," from French compétence, from Latin competentia "meeting together, agreement, symmetry," from competens, present participle of competere, especially in its earlier sense of "fall together, come together, be convenient or fitting" (see compete). Meaning "sufficiency to deal with what is at hand" is from 1790.
competency (n.): 1590s, "rivalry;" c. 1600, "sufficiency to satisfy the wants of life," from Latin competentia "meeting together, agreement, symmetry," from competens, present participle of competere (see compete). Meaning "sufficiency of qualification" is recorded from 1797.
competent (adj.): late 14c., "suitable," from Old French competent "sufficient, appropriate, suitable," from Latin competentem (nominative competens), present participle of competere "coincide, agree" (see compete). Meaning "able, fit" is from 1640s. Legal sense is late 15c.
competition (n.): c. 1600, "action of competing," from Latin competitionem (nominative competitio) "agreement, rivalry," noun of action from past participle stem of competere (see compete). Meaning "a contest for something" is from 1610s. Sense of "rivalry in the marketplace" attested from 1793; that of "entity or entities with which one competes" is from 1961, especially in business.
competitive (adj.): 1826, from Latin competit-, past participle stem of competere (see compete) + -ive. Related: Competitively; competitiveness.
competitor (n.): 1530s, from Middle French compétiteur (16c.), or directly from Latin competitor "rival," agent noun from competere (see compete).
compilation (n.): early 15c., "that which is compiled," also "action of compiling," from Middle French compilation, from Latin compilationem (nominative compilatio) "a compilation," literally "a pillaging," noun of action from compilare (see compile).
compile (v.): early 14c., from Old French compiler "compile, collect" (13c.), from Latin compilare "to plunder, rob," probably originally "bundle together, heap up;" hence "to pack up and carry off," from com- "together" (see com-) + pilare "to compress, ram down." Related: Compiled; compiling.
compiler (n.): early 14c., from Anglo-French compilour, Old French compileur "author, chronicler," from Latin compilatorem, agent noun from compilare (see compile). Another form of the word current in early Modern English was compilator, directly from the Latin.
complacence (n.): mid-15c., "pleasure," from Medieval Latin complacentia "satisfaction, pleasure," from Latin complacentem (nominative complacens), present participle of complacere "to be very pleasing," from com-, intensive prefix (see com-), + placere "to please" (see please). Sense of "pleased with oneself" is 18c.
complacency (n.): 1640s, from same source as complacence but with the later form of the suffix (see -cy).
complacent (adj.): 1650s, "pleasing," from Latin complacentem (nominative complacens) "pleasing," present participle of complacere "be very pleasing" (see complacence). Meaning "pleased with oneself" is from 1767. Related: Complacently.
complain (v.): late 14c., "find fault, lament," from stem of Old French complaindre "to lament" (12c.), from Vulgar Latin *complangere, originally "to beat the breast," from Latin com-, intensive prefix (see com-), + plangere "to strike, beat the breast" (see plague (n.)). Older sense of "lament" died out 17c. Related: Complained; complaining.
complainant (n.): early 15c., from Old French complaignant, present participle of complaindre (see complain). The present participle also was used as a noun in Middle French.
complaint (n.): late 14c., "lamentation, grief," from Old French complainte (12c.) "complaint, lament," noun use of fem. past participle of complaindre (see complain). Meaning "bodily ailment" is from 1705 (often in U.S. colloquial use generalized as complaints).
complaisance (n.): 1650s, from French complaisance (14c.), in Middle French "care or desire to please," from Medieval Latin complacentia (see complacence).
complaisant (adj.): 1640s, from French complaisant (16c.), in Middle French, "pleasing," present participle of complaire "acquiesce to please," from Latin complacere "be very pleasing" (see complacent, with which it overlapped till mid-19c.). Possibly influenced in French by Old French plaire "gratify."
compleat (adj.): archaic spelling of complete (adj.).
complected (adj.): 1806, American English, "complexioned," a variant derivation from complexion, which, intentionally or not, shows the Latin root.
complement (n.): late 14c., "that which completes," from Old French compliement "accomplishment, fulfillment" (14c., Modern French complément), from Latin complementum "that which fills up or completes," from complere "fill up" (see complete (adj.)). Originally also having senses which were taken up c. 1650-1725 by compliment.
complement (v.): 1610s, "exchange courtesies," from complement (n.). Meaning "make complete" is from 1640s. Related: Complemented; complementing.
complementarity (n.): 1908, a term in physics, from complementary + -ity.
complementary (adj.): 1620s, "ceremonious," from complement + -ary. Sense "forming a complement" attested from 1829, earliest in complementary colors.
complete (adj.): late 14c., from Old French complet "full," or directly from Latin completus, past participle of complere "to fill up, complete the number of (a legion, etc.)," transferred to "to fill, to fulfill, to finish (a task)," from com-, intensive prefix (see com-), + plere "to fill" (see pleio-).
complete (v.): late 14c.; see complete (adj.). Related: Completed; completing.
completely (adv.): 1520s, from complete (adj.) + -ly (2).
completion (n.): late 14c., from Latin completionem (nominative completio), noun of action from past participle stem of complere "to fill up, complete" (see complete (adj.)).
complex (adj.): 1650s, "composed of parts," from French complexe "complicated, complex, intricate" (17c.), from Latin complexus "surrounding, encompassing," past participle of complecti "to encircle, embrace," in transferred use, "to hold fast, master, comprehend," from com- "with" (see com-) + plectere "to weave, braid, twine, entwine," from PIE *plek-to-, from root *plek- "to plait" (see ply (v.1)). The meaning "not easily analyzed" is first recorded 1715. Complex sentence is attested from 1881.
complex (n.): 1650s, "a whole comprised of parts," from complex (adj.). Psychological sense of "connected group of repressed ideas" was established by C.G. Jung, 1907.
complexion (n.): mid-14c., "bodily constitution," from Old French complexion, complession "combination of humors," hence "temperament, character, make-up," from Latin complexionem (nominative complexio) "combination" (in Late Latin, "physical constitution"), from complexus (see complex (adj.)). Meaning "appearance of the skin of the face" is first recorded mid-15c. In medieval physiology, the color of the face indicated temperament or health.
complexity (n.): 1721, "composite nature," from complex (adj.) + -ity. Meaning "intricacy" is from 1790. Meaning "a complex condition" is from 1794.
compliance (n.): 1640s, from comply + -ance. Related: Compliancy.
compliant (adj.): 1640s, from comply + -ant.
complicate (v.): 1620s, "to intertwine" (as a past participle adjective, early 15c.), from Latin complicatus "folded together; confused, intricate," past participle of complicare (see complication). Meaning "to make more complex" is recorded from 1832, from earlier sense "to combine in a complex way" (17c.). Related: Complicated; complicating.
complicated (adj.): 1640s, "tangled," from past participle adjective from complicate. Figurative meaning "not easy to solve, intricate, confused, difficult to unravel" is from 1650s.
complication (n.): early 15c., from Middle French complication, from Latin complicationem (nominative complicatio), noun of action from past participle stem of complicare "to fold together, fold up, roll up," from com- "together" (see com-) + plicare "to fold, weave" (see ply (v.1)). Meaning "something that complicates" first recorded 1903.
complicity (n.): 1650s, from French complicité, from Old French complice "accomplice, comrade, companion" (14c.), from Late Latin complicem, accusative of complex "partner, confederate," from Latin complicare "to fold together" (see complicate; also compare accomplice).
compliment (n.): "An act, or expression of civility, usually understood to include some hypocrisy, and to mean less than it declares" [Johnson], 1570s, complement, via French compliment (17c.), from Italian complimento "expression of respect and civility," from Vulgar Latin *complire, for Latin complere "to complete" (see complete (adj.)), via notion of "complete the obligations of politeness." Same word as complement but by a different etymological route; differentiated by spelling after 1650.
compliment (v.): 1610s, from French complimenter, from compliment (see compliment (n.)). Related: Complimented; complimenting.
complimentary (adj.): 1620s, "conveying a compliment," from compliment (n.) + -ary. In later use loosely meaning "free of charge."
compline (n.): the last canonical service of the day, early 13c., cumplie, compelin, from Old French complie (12c.), from Latin completa (hora), from completus (see complete (adj.)); with unexplained -n-.
comply (v.): early 14c., "to fulfill, carry out," from Old French compli, past participle of complir "to accomplish, fulfill, carry out," from Vulgar Latin *complire, from Latin complere "to fill up" (see complete (adj.)). Meaning influenced by ply (v.2). Sense of "to consent" began c. 1600 and might have been a reintroduction from Italian, where complire had come to mean "satisfy by 'filling up' the forms of courtesy."