Etymology
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Words related to subtle

sub- 
word-forming element meaning "under, beneath; behind; from under; resulting from further division," from Latin preposition sub "under, below, beneath, at the foot of," also "close to, up to, towards;" of time, "within, during;" figuratively "subject to, in the power of;" also "a little, somewhat" (as in sub-horridus "somewhat rough"), from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo "under," also "up from under." The Latin word also was used as a prefix and in various combinations.

In Latin assimilated to following -c-, -f-, -g-, -p-, and often -r- and -m-. In Old French the prefix appears in the full Latin form only "in learned adoptions of old Latin compounds" [OED], and in popular use it was represented by sous-, sou-; as in French souvenir from Latin subvenire, souscrire (Old French souzescrire) from subscribere, etc.

The original meaning is now obscured in many words from Latin (suggest, suspect, subject, etc.). The prefix is active in Modern English, sometimes meaning "subordinate" (as in subcontractor); "inferior" (17c., as in subhuman); "smaller" (18c.); "a part or division of" (c. 1800, as in subcontinent).
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*teks- 

Proto-Indo-European root meaning "to weave," also "to fabricate," especially with an ax," also "to make wicker or wattle fabric for (mud-covered) house walls."

It forms all or part of: architect; context; dachshund; polytechnic; pretext; subtle; technical; techno-; technology; tectonic; tete; text; textile; tiller (n.1) ""bar to turn the rudder of a boat;" tissue; toil (n.2) "net, snare."

It is the hypothetical source of/evidence for its existence is provided by: *teks- "to weave, to fabricate, to make; make wicker or wattle framework" (source also of Sanskrit taksati "he fashions, constructs," taksan "carpenter;" Avestan taša "ax, hatchet," thwaxš- "be busy;" Old Persian taxš- "be active;" Latin texere "to weave, fabricate," tela "web, net, warp of a fabric;" Greek tekton "carpenter," tekhnē "art;" Old Church Slavonic tesla "ax, hatchet;" Lithuanian tašau, tašyti "to carve;" Old Irish tal "cooper's ax;" Old High German dahs, German Dachs "badger," literally "builder;" Hittite taksh- "to join, unite, build."

subtile (adj.)

c. 1300, sotil; modern form from late 14c., "clever, dexterous, crafty; not dense, thin, rarefied," from Old French subtil (14c.), a learned Latinized reformation of earlier sotil (12c.), source of subtle (q.v.). Still used in some Bible translations in Genesis iii.1, and it survived after 17c. as a parallel formation to subtle in some material senses ("fine, delicate, thin"). Related: Subtilly.

subtlety (n.)
c. 1300, sotilte, "skill, ingenuity," from Old French sotilte "skillfulness, cunning" (Modern French subtilité), from Latin subtilitatem (nominative subtilitas) "fineness; simplicity, slenderness," noun of quality from subtilis "fine, thin, delicate" (see subtle). From late 14c. as "cleverness, shrewdness; trickery, guile, craftiness," also "thinness, slenderness, smallness; rarity." The -b- begins to appear late 14c. in English, in imitation of Latin.
subtly (adv.)
early 14c., sotylleche; see subtle + -ly (2).
*upo 

Proto-Indo-European root meaning "under," also "up from under," hence "over."

It forms all or part of: above; assume; Aufklarung; eave; eavesdropper; hyphen; hypo-; hypochondria; hypocrisy; hypotenuse; hypothalamus; hypothesis; hypsi-; hypso-; opal; open; oft; often; resuscitate; somber; souffle; source; soutane; souvenir; sub-; subject; sublime; subpoena; substance; subterfuge; subtle; suburb; succeed; succinct; succor; succubus; succumb; sudden; suffer; sufficient; suffix; suffrage; suggestion; summon; supine; supple; supply; support; suppose; surge; suspect; suspend; sustain; up; up-; Upanishad; uproar; valet; varlet; vassal.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit upa "near, under, up to, on," Greek hypo "under," Latin sub "under, below," Gothic iup, Old Norse, Old English upp "up, upward," Hittite up-zi "rises."