Etymology
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Words related to fortnight

fourteen (adj., n.)

"1 more than thirteen; the number which is one more than thirteen; a symbol representing this number;" c. 1300, from Old English feowertyne; see four + -teen. Compare Old Saxon fiertein, Old Frisian fiuwertine, Dutch veertien, Old High German fiorzehan, German vierzehn, Danish fjorten, Gothic fidwortaihun.

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night (n.)

late Old English niht (West Saxon neaht, Anglian næht, neht) "the dark part of a day; the night as a unit of time; darkness," also "absence of spiritual illumination, moral darkness, ignorance," from Proto-Germanic *nahts (source also of Old Saxon and Old High German naht, Old Frisian and Dutch nacht, German Nacht, Old Norse natt, Gothic nahts).

The Germanic words are from PIE *nekwt- "night" (source also of Greek nyx "a night," Latin nox, Old Irish nochd, Sanskrit naktam "at night," Lithuanian naktis "night," Old Church Slavonic nosti, Russian noch', Welsh henoid "tonight"), according to Watkins, probably from a verbal root *neg- "to be dark, be night." For spelling with -gh- see fight.  The vowel indicates that the modern English word derives from oblique cases (genitive nihte, dative niht).

The fact that the Aryans have a common name for night, but not for day (q.v.), is due to the fact that they reckoned by nights. [Weekley]

Thus in Old English combinations night was "the night before (a certain day or feast day);" compare German Weihnachten "Christmas," literally "holy night." In early times, the day was held to begin at sunset, so Old English monanniht "Monday night" was the night before Monday, or what we would call Sunday night. The Greeks, by contrast, counted their days by mornings.

To work nights preserves the Old English genitive of time. Night soil "excrement" (1770) is so called because it was removed (from cesspools, etc.) after dark. Night train is attested from 1838; night-school from 1520s; night-life "habitual nocturnal carousing" is attested from 1852.

*kwetwer- 
Proto-Indo-European root meaning "four."

It forms all or part of: cadre; cahier; carillon; carrefour; catty-cornered; diatessaron; escadrille; farthing; firkin; fortnight; forty; four; fourteen; fourth; quadrant; quadraphonic; quadratic; quadri-; quadrilateral; quadriliteral; quadrille; quadriplegia; quadrivium; quadroon; quadru-; quadruped; quadruple; quadruplicate; quarantine; quarrel (n.2) "square-headed bolt for a crossbow;" quarry (n.2) "open place where rocks are excavated;" quart; quarter; quarterback; quartermaster; quarters; quartet; quarto; quaternary; quatrain; quattrocento; quire (n.1) "set of four folded pages for a book;" squad; square; tessellated; tetra-; tetracycline; tetrad; tetragrammaton; tetrameter; tetrarch; trapezium.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit catvarah, Avestan čathwaro, Persian čatvar, Greek tessares, Latin quattuor, Oscan petora, Old Church Slavonic četyre, Lithuanian keturi, Old Irish cethir, Welsh pedwar.
sennight (n.)
"period of seven days, a week" (archaic), c. 1200, contracted from Old English seofon nihta; see seven + night. Also compare fortnight.