word-forming element meaning "always, ever," from Latin semper "always, ever, at all times, continuously" (literally "once for all"), from PIE *semper-, from root *sem- (1) "one; as one, together with" + *per- "during, for."
before vowels heter-, word-forming element meaning "other, different," from Greek heteros "the other (of two), another, different; second; other than usual." It is a compound; the first element means "one, at one, together," from PIE root *sem- (1) "one; as one, together with;" the second is cognate with the second element in Latin al-ter, Gothic an-þar, Old English o-ðer "other."
Compounds in classical Greek show the range of the word there: Heterokretes "true Cretan," (that is, of the old stock); heteroglossos "of foreign language;" heterozelos "zealous for one side;" heterotropos "of a different sort or fashion," literally "turning the other way;" heterophron "raving," literally "of other mind."
word-forming element forming nouns meaning "rule or government by," from French -cratie or directly from Medieval Latin -cratia, from Greek -kratia "power, might; rule, sway; power over; a power, authority," from kratos "strength," from PIE *kre-tes- "power, strength," suffixed form of root *kar- "hard." The connective -o- has come to be viewed as part of it. Productive in English from c. 1800.
before vowels, xen-, word-forming element meaning "strange, foreign; stranger, foreigner," from Greek xenos "a guest, stranger, foreigner, refugee, guest-friend, one entitled to hospitality," cognate with Latin hostis, from PIE root *ghos-ti- "stranger, guest, host." "The term was politely used of any one whose name was unknown" [Liddell & Scott].
word-forming element meaning "beyond" (ultraviolet) or "extremely" (ultramodern), from Latin ultra- from ultra (adv. and prep.) "beyond, on the other side, on the farther side, past, over, across," from PIE *ol-tero-, suffixed form of root *al- "beyond." In common use from early 19c., it appears to have arisen from French political designations. As its own word, a noun meaning "extremist" of various stripes, it is first recorded 1817, from French ultra, shortening of ultra-royaliste "extreme royalist."
word-forming element meaning usually "one half more" than the indicated unit, from Latin sesqui-, sesque- "one and a half; one-half more," contraction of *semis-que- "a half in addition," from *semis "a half" (see semi-) + -que "and" (from PIE root *kwe "and, -ever," for which see ubiquity). Latin semi- had a tendency to get partly swallowed in compounds; compare these derivatives listed in de Vaan: selibra "half a libra," semodius "half a modius," sestertius "having the value of two-and-a-half" (as a noun, the name of a silver Roman coin, short for sestertius nummus), contracted from *semistertius; simbella "coin worth half a libella;" sincipitis "a half-head."
word-forming element meaning "more than one, several, many," from Latin pluri-, from stem of plus (genitive pluris); see plus.
before vowels hapl-, word-forming element meaning "simple, single; simply, once," from Greek haploos, haplous "single, simple" (as opposed to "compound"); "natural, plain," from PIE compound *sm-plo-, from root *sem- (1) "one; as one, together with" + *-plo- "-fold" (from PIE root *pel- (2) "to fold"). Compare simple, which represents the same compound in Latin.