Etymology
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towel (n.)
mid-13c., from Old French toaille (12c.), from Frankish *thwahlja, from Proto-Germanic *thwahlijan (source also of Old Saxon thwahila, Middle Dutch dwale "towel," Dutch dwaal "altar cloth," Old High German dwehila "towel," German dialectal Zwehle "napkin"); related to German zwagen, Old English þwean "to wash." Spanish toalla, Italian tovaglia are Germanic loan-words. To throw in the towel "admit defeat" (1915) is from boxing.
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admission (n.)
Origin and meaning of admission

early 15c., "acceptance, reception, approval," from Latin admissionem (nominative admissio) "a letting in," noun of action from past-participle stem of admittere "admit, give entrance; grant an audience," of acts, "let be done, allow, permit," from ad "to" (see ad-) + mittere "let go, send" (see mission). Meaning "an acknowledging" is from 1530s. Literal sense of "act of allowing to enter, admittance," is from 1620s. As short for admission price, by 1792.

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suppose (v.)
early 14c., "to assume as the basis of argument," from Old French suposer "to assume" (13c.), probably a replacement (influenced by Old French poser "put, place") of *suppondre, from Latin supponere "put or place under; to subordinate, make subject," from assimilated form of sub "under" (see sub-) + ponere "put, place" (past participle positus; see position (n.)). Meaning "to admit as possible, to believe to be true" is from 1520s.
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allow (v.)

early 14c., allouen, "to commend, praise; approve of, be pleased with; appreciate the value of;" also, "take into account or give credit for," also, in law and philosophy, "recognize, admit as valid" (a privilege, an excuse, a statement, etc.). From late 14c. as "sanction or permit; condone;" in business use from early 15c.

The Middle English word is from Anglo-French alouer, Old French aloer, alloiier (13c.) "place, situate, arrange; allot, apportion, bestow, assign," from Latin allocare "allocate" (see allocate). This word in Old French was confused and ultimately merged with aloer; alloer "to praise, commend, approve," from Latin allaudare, adlaudare, compound of ad "to" (see ad-) + laudare "to praise" (see laud).

Between the two primary significations there naturally arose a variety of uses blending them in the general idea of assign with approval, grant, concede a thing claimed or urged, admit a thing offered, permit, etc., etc. [OED].

From the first word came the sense preserved in allowance "money granted;" from the second came allowance "permission based on approval." Meaning "assert, say," 19c. U.S. colloquial, also was in English dialect and goes back to 1570s. Related: Allowed; allowing.

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ordain (v.)

c. 1300, ordeinen, "to appoint or admit to the ministry of the Church," also "to decree, enact," from stem of Old French ordener "place in order, arrange, prepare; consecrate, designate" (Modern French ordonner) and directly from Latin ordinare "put in order, arrange, dispose, appoint," from ordo (genitive ordinis) "row, rank, series, arrangement" (see order (n.)). The notion is "to confer holy orders upon." Sense of "establish, set (something) that will continue in a certain order" is from early 14c. Related: Ordained; ordaining.

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own (v.)

c. 1200, ounen, ahnen, "to possess, have; rule, be in command of, have authority over;" from Old English geagnian, from root agan "to have, to own" (see owe), and in part from the adjective own (q.v.). It became obsolete after c. 1300, but was revived early 17c., in part as a back-formation of owner (mid-14c.), which continued. From c. 1300 as "to acknowledge, concede, admit as a fact," said especially of things to one's disadvantage. To own up "make full confession" is from 1853. Related: Owned; owning.

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demur (v.)

c. 1200, demuren, "to linger, tarry, delay," a sense now obsolete, from variant stem of Old French demorer "delay, retard," from Latin demorari "to linger, loiter, tarry," from de- (see de-) + morari "to delay," from mora "a pause, delay" (see moratorium).

Modern sense of "raise objections, take exception, have scruples" is by 1630s, from a legal sense attested from the 1620s: "admit provisionally the facts of the opponent's proceeding but deny he is entitled to legal relief," a verb from demurrer. Such a pleading effectively stops the action until the point is settled. Related: Demurred; demurring.

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petitio principii 

Latin, from petitio "petition" (see petition (n.)) + genitive of principium (see principle (n.)). It translates Greek to en arkhē aiteisthai "an assumption at the outset."

In logic, the assumption of that which in the beginning was set forth to be proved; begging the question: a fallacy or fault of reasoning belonging to argumentations whose conclusions really follow from their premises, either necessarily or with the degree of probability pretended, the fault consisting in the assumption of a premise which no person holding the antagonistic views will admit. [Century Dictionary]
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grant (v.)
in early use also graunt, early 13c., "to allow, permit (something); consent to (a prayer, request, etc.)," from Old French graanter, variant of creanter "assure, promise, guarantee, swear; confirm, authorize, approve (of)," from Latin credentem (nominative credens), present participle of credere "to believe, to trust" (see credo). From c. 1300 as "transfer possession of in any formal way." Meaning "admit to be true, acknowledge" in English is from c. 1300; hence to take (something) for granted "regard as not requiring proof" (1610s). The irregular change of -c- to -g- in Old French is perhaps from influence of garantir. Related: Granted; granting.
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chancellor (n.)

early 12c., from Old French chancelier (12c.), from Late Latin cancellarius "keeper of the barrier, secretary, usher of a law court," so called because he worked behind a lattice (Latin cancellus) at a basilica or law court (see chancel).

In the Roman Empire, a sort of court usher who stood at the latticed railing enclosing the judgment seat to keep the crowd out and admit those entitled to enter. The post gradually gained importance in the Western kingdoms as an intermediary between the petitioners and the judges as a notary or scribe. In England eventually he prepared all important crown documents and became keeper of the great seal and highest judicial officer of the crown. A variant form, canceler, existed in Old English, from Old North French, but was replaced by this central French form.

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