Etymology
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sixtieth (adj., n.)

"next in order after the fifty-ninth; an ordinal numeral; being one of sixty equal parts into which a whole is regarded as divided;" Old English sixteogoða "sixtieth;" see sixty + -th (1).

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sexagesimal (adj.)

"composed of or produced by sixties; pertaining to division into sixty," 1680s, from Medieval Latin sexagesimalis, from Latin sexagesimus "the sixtieth," from sexaginta "sixty." Sexagisema, "second Sunday before Lent" (eighth before Easter), is from late 14c. (Sexagesime), from Medieval Latin sexagesima (dies) "the sixtieth (day)."

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second (n.1)

"one-sixtieth of a minute of degree," also "sixtieth part of a minute of time," late 14c. in geometry and astronomy, seconde, from Old French seconde, from Medieval Latin secunda, short for secunda pars minuta "second diminished part," the result of the second division of the hour by sixty (the first being the "prime minute," now simply the minute), from Latin secunda, fem. of secundus "following, next in time or order" (see second (adj.)).

The second hand of a clock, the pointer indicating the passage of seconds, is attested by 1759.

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minute (n.)

"sixtieth part of an hour or degree of a circle," late 14c., from Old French minut (13c.) or directly from Medieval Latin minuta "minute of time; short note," from Latin minuta "a small portion or piece," noun use of fem. of minutus "little, small, minute," past participle of minuere "to lessen, diminish" (from PIE root *mei- (2) "small").

In Medieval Latin, pars minuta prima "first small part" was used by mathematician Ptolemy for one-sixtieth of a circle, later one-sixtieth of an hour (next in order was secunda minuta, which became second (n.)). German Minute, Dutch minuut also are from French. Used vaguely for "short time" from late 14c. As a measure expressing distance (travel time) by 1886. Minute hand "hand which indicates the minutes on a clock or watch" is attested from 1726. Minute-jumper (1890) was the name for the kind of electric clock on which the hands move only at the end of each minute.

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tierce (n.)
old unit of liquid measure equal to one-third of a pipe (42 gallons), 1530s, from Anglo-French ters, Old French tierce (11c.). used in the sense "one-third" in various ways, from Latin tertia, fem. of tertius "a third," from PIE *tri-tyo-, from root *trei- (see three). Also used in Middle English for "a third part" (late 15c.), "the third hour of the canonical day" (ending at 9 a.m.), late 14c., and, in astronomy and geometry, "sixtieth part of a second of an arc."
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*sekw- (1)

Proto-Indo-European root meaning "to follow."

It forms all or part of: associate; association; consequence; consequent; dissociate; ensue; execute; extrinsic; intrinsic; obsequious; persecute; persecution; prosecute; pursue; second (adj.) "next after first;" second (n.) "one-sixtieth of a minute;" sect; secundine; segue; sequacious; sequel; sequence; sequester; sociable; social; society; socio-; subsequent; sue; suit; suite; suitor; tocsin.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sacate "accompanies, follows;" Avestan hacaiti, Greek hepesthai "to follow;" Latin sequi "to follow, come after," secundus "second, the following;" Lithuanian seku, sekti "to follow;" Old Irish sechim "I follow."

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