"turned in the opposite direction, having an opposite course or tendency," in early use also enverse, mid-15c., from Latin inversus, past participle of invertere "turn about, turn upside-down, upset, reverse, invert" (see invert). Related: Inversely. As a noun, "inverted state or condition," 1680s, from the adjective.

1590, one of the three fundamental functions of trigonometry, from tangent (adj.). From 1650s as "a tangent line." Figurative use of **on a tangent** is from 1771.

in trigonometry, "the tangent of the complement of a given angle," a contraction of co. tangent, abbreviation of complement + tangent (n.).

late 15c., "with subtraction of," from Latin minus "less," neuter of minor "smaller" (from PIE *mi-nu-, suffixed form of root *mei- (2) "small").

According to OED, this mathematical prepositional use in expressions of calculation was not in the classical Latin word and probably is from North Sea medieval commercial usage of Latin plus and minus to indicate surplus or deficiency of weight or measure.

The origin and original signification of the "minus sign" is disputed. As "deprived of, not having," by 1813. Of temperature, etc., "below 0 or the lowest point of positive reckoning, belonging to the inverse or negative side," by 1811.

late 14c., divisioun, "act of separating into parts, portions, or shares; a part separated or distinguished from the rest; state of being at variance in sentiment or interest," from Old French division and directly from Latin divisionem (nominative divisio), noun of action from past-participle stem of dividere "to divide" (see divide (v.)).

Military sense "portion of an army, fleet, or ship's company" is from 1590s. Mathematical sense of "operation inverse to multiplication" is from late 14c. The mathematical division sign supposedly was invented by British mathematician John Pell (1611-1685) who taught at Cambridge and Amsterdam.

1930, from newspaper comic "Out Our Way" by U.S. cartoonist J.R. Williams (1888-1957), in which Worry Wart is attested by 1929. Worry Wart was a generic nickname or insult for any character who caused others to worry, which is the inverse of the current colloquial meaning. For example, from the comic printed in the Los Angeles Record, Dec. 5, 1929: One kid scolds another for driving a screw with a hammer "You doggone worry wart! Poundin' on a nut till it's buried inta th' table!" (etc.).

It forms all or part of: attain; contact; contaminate; entire; intact; integer; integrate; integrity; noli me tangere; tact; tactics; tactile; tangent; tangible; task; taste; tax; taxis.

It is the hypothetical source of/evidence for its existence is provided by: Latin tangere "to touch," taxare "to touch, assess," tactus "touch," integer "intact, whole, complete, perfect; honest;" Greek tassein "to arrange," tetagon "having seized;" Old English þaccian "stroke, strike gently."