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after [after 词源字典]: after: [OE] In the first millennium AD many Germanic languages had forms cognate with Old English æfter (Gothic aftra, for example, and Old Norse aptr), but, with the exception of Dutch achter, none survive. It is not clear what their ultimate origin is, but the suffix they share may well be a comparative one, and it is possible that they derive from a Germanic base *af- (represented in Old English æftan ‘from behind’).

It has been suggested that this goes back to Indo-European *ap- (source of Latin ab ‘away, from’ and English of(f)), in which case after would mean literally ‘more off’ – that is, ‘further away’. Nautical aft is probably a shortening of abaft, formed, with the prefixes a- ‘on’ and be- ‘by’, from Old English æftan.
=> of, off[after etymology, after origin, 英语词源]
lavatory: lavatory: [14] The notion of ‘washing’ was represented in prehistoric Indo-European by *lou-, which produced Greek loúein ‘wash’, English lather, and Latin lavāre ‘wash’. This last has been a fruitful source of English words, not all of them as obvious as lavatory, which originally meant simply ‘place or vessel for washing’ (its use for a ‘room containing a water closet’ appears to date from the 19th century).

Among its relatives are deluge [14], latrine [17] (from a contraction of Latin lavātrīna), laundry, lava [18] (from Italian lava, which originally denoted a ‘stream caused by sudden rain’), lavish [15] (from the metaphorical notion of an ‘outpouring’), and lotion [14]. And from Latin luere, the form taken on by lavāre after prefixes, we get ablution [14] and dilute [16]. Lavender [15] looks as though it should belong to the same family, but no actual connection has ever been demonstrated.
=> ablution, deluge, dilute, lather, latrine, laundry, lava, lavish, lotion
up: up: [OE] Up is part of a widespread family of Germanic adverbs which also includes German auf, Dutch and Danish op, and Swedish upp. It goes back ultimately to Indo-European *up-, which also produced English over and the prefixes hyper- and super- and may lie behind English evil. To open something is etymologically to put it ‘up’.
=> open, over
a- (1): in native (derived from Old English) words, it most commonly represents Old English an "on" (see a (2)), as in alive, asleep, abroad, afoot, etc., forming adjectives and adverbs from nouns; but it also can be Middle English of, as in anew, abreast (1590s); or a reduced form of Old English past participle prefix ge-, as in aware; or the Old English intensive a-, as in arise, awake, ashame, marking a verb as momentary, a single event. In words from Romanic languages, often it represents Latin ad- "to, at."
[I]t naturally happened that all these a- prefixes were at length confusedly lumped together in idea, and the resultant a- looked upon as vaguely intensive, rhetorical, euphonic, or even archaic, and wholly otiose. [OED]
cablese (n.): 1895, from cable in the telegraphic sense + -ese as a language name suffix. "Since cablegrams had to be paid for by the word and even press rates were expensive the practice was to affix Latin prefixes and suffixes to make one word do the work of several" [Daniel Schorr], such as exLondon and Londonward to mean "from London," "to London" (non-Latin affixes also were used). Hence the tale, famous in the lore of the United Press International, of the distinguished but harried foreign correspondent who reached his breaking point and wired headquarters UPSTICK JOB ASSWARD. Its economy and expressive power fascinated Hemingway in his newspapering days.
ir-: assimilated form of Latin prefixes in- (see in-) before -r-.
over-: word-forming element meaning "above; highest; across; too much; above normal; outer," from Old English ofer (see over). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."
per (prep.): 1580s (earlier in various Latin and French phrases), from Latin per "through, during, by means of, on account of, as in," from PIE root *per- (1) "Base of prepositions and preverbs with the basic meanings of 'forward,' 'through,' and a wide range of extended senses such as 'in front of,' 'before,' 'early,' 'first,' 'chief,' 'toward,' 'against,' 'near,' 'at,' 'around'" [Watkins]. Cognates: Sanskrit pari- "around, about, through," pura "before, formerly;" Avestan pairi- "around," paro "before;" Old Persian pariy; Hittite para- "on, forth;" Greek peri "around, about, near, beyond," paros "before," para "from beside, beyond," pro "before;" Latin pro "before, for, on behalf of, instead of," porro "forward," prae "before;" Old English fore (prep.) "before, in front of;" (adv.) "before, previously;" German vor "for;" Old Church Slavonic pra-dedu "great-grandfather;" Russian pere- "through;" Lithuanian per "through;" Old Irish air- Gothic fair-, German ver-, Old English fer-, intensive prefixes.
privative (adj.): 1580s, "expressing negation" (as do the prefixes un-, a- (2), etc.), from Latin privativus "denoting privation, negative," from privatus, past participle of privare (see private).
suspicion (n.): c. 1300, "act of suspecting; unverified conjecture of wrongdoing; mistrust, distrust," from Anglo-French suspecioun, corresponding to Old French suspicion, sospeçon "mistrust, suspicion" (Modern French soupçon), from Late Latin suspectionem (nominative suspectio) "mistrust, suspicion, fear, awe," noun of state from past participle stem of Latin suspicere "look up at" (see suspect (adj.)). Spelling in English influenced 14c. by learned Old French forms closer to Latin suspicionem. Used as a verb meaning "to suspect," it figures in literary representations of U.S. Western (Kentucky) slang from 1830s.

"Suspicion" words in other Indo-European languages also tend to be words for "think" or "look" with prefixes meaning "under, behind;" such as Greek hypopsia (hypo "under," opsis "sight"), hyponoia (noein "to think"); Lettish aizduomas (aiz "behind," duomat "think"); Russian podozrenie (Slavic podu "under," Old Church Slavonic zireti "see, look"); Dutch achterdocht (achter "behind," denken "to think").
un- (1): prefix of negation, Old English un-, from Proto-Germanic *un- (cognates: Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), comb. form of PIE root *ne "not" (cognates: Avestan na, Old Church Slavonic and Lithuanian ne "not," Latin ne "that not," Greek ne- "not," Old Irish ni, Cornish ny "not"). Often euphemistic (such as untruth for "lie").

The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
up-: prefix with various senses, from Old English up (adv.), corresponding to similar prefixes in other Germanic languages.