"1 more than fifty-nine, twice thirty; the number which is one more than fifty-nine; a symbol representing this number;" Old English sixtig, from siex (see six) + -tig (see -ty (1)). Similar formation in Old Norse sextugr, sextögr, sextigir, Old Frisian sextich, Middle Dutch sestig, Dutch zestig, Old High German sehszug, German sechzig. Phrase sixty-four dollar question is attested from 1942, from a radio quiz show where that was the top prize.
1827, "period or term of six months," specifically, a half-year course in a German or other Continental university, from German Semester "half-year course in a university," from Latin semestris, in cursus semestris "course of six months," from semestris, semenstris "of six months, lasting six months, half-yearly, semi-annual," from assimilated form of sex "six" (see six) + mensis "month" (see moon (n.)). The word, and the idea, were picked up in the U.S., where the German higher education system served as a model. Related: Semestral; semestrial (1701).
"1 more than fifteen, twice eight; the number which is one more than fifteen; a symbol representing this number;" Old English sixtyne, from siex (see six) + -teen. Similar formation in Old Frisian sextine, Middle Dutch sestien, Dutch zestien, German sechzehn, Old Norse sextan.
The age of the gods is always sixteen. Sixteen represents the number of perfection, of plenitude. In man it is after the sixteenth year that the first elements of decay begin to appear, and when the moon reaches the sixteenth digit it begins to decrease. [Alain Daniélou, "The Myths and Gods of India"]
From Latin contracted form sexdecim, sedecim come Italian sedici, French seize.
"next in order after the fifth; an ordinal numeral; being one of six equal parts into which a whole is regarded as divided;" 1520s, replacing Middle English sixte (c. 1200), from Old English syxte, from siex (see six). Compare Old Frisian sexta, Middle Dutch seste, Old High German sehsto, German sechste, Gothic saihsta. With ending conformed to -th (1). Related: Sixthly. The noun meaning "a sixth part" is from 1550s. As a music tone, from 1590s. Sixth sense "supernatural perception of objects" is attested from 1712; earlier it meant "titillation, the sense that apprehends sexual pleasure" (1690s, from Scaliger).
Then said Peter, That is false; for there is a sixth Sense, that of Prescience : for the other five Senses are capable only of Knowledg ; but the Sixth of Foreknowledg ; which Sense the Prophets had. [William Whitson, "Primitive Christianity Reviv'd," vol. v, London, 1712]
1841, also sextette, "work for six voices," altered (by influence of German Sextett) from sestet (q.v.). As "company or group of six persons or things" by 1873.
1944, in reference to the Holocaust, probably translating German Todeslager; they also were known as extermination camps (German Vernichtungslager); historians usually count six of them: Auschwitz-Birkenau, Chełmno, Bełżec, Majdanek, Sobibór, Treblinka.