Etymology
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-er (3)
suffix used to make jocular or familiar formations from common or proper names (soccer being one), first attested 1860s, English schoolboy slang, "Introduced from Rugby School into Oxford University slang, orig. at University College, in Michaelmas Term, 1875" [OED, with unusual precision].
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-yl 

chemical suffix used in forming names of radicals, from French -yle, from Greek hylē "wood," also "building stuff, raw material" (from which something is made), of unknown origin. The use in chemistry traces to the latter sense (except in methylene, where it means "wood").

It was introduced into chemical nomenclature by Liebig and Wohler when, in 1832, they used the term benzoyle for the radical which appeared to be the "essential material" of benzoic acid and related compounds. [Flood]
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-ary 
adjective and noun word-forming element, in most cases from Latin -arius, -aria, -arium "connected with, pertaining to; the man engaged in," from PIE relational adjective suffix *-yo- "of or belonging to." The neuter of the adjectives in Latin also were often used as nouns (solarium "sundial," vivarium, honorarium, etc.). It appears in words borrowed from Latin in Middle English. In later borrowings from Latin to French, it became -aire and passed into Middle English as -arie, subsequently -ary.
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-a (1)
word-forming element which in English is characteristic of fem. nouns and adjectives of Latin or Greek origin (such as idea, coma, mania, basilica, arena, formula, nebula). From Latin -a (plural -ae) and Greek -a, (plural -ai, Latinized as -ae). The Latin suffix also became Italian -a (plural -e), Spanish -a (plural -as). It is represented in Old English by -u, -e, but even then the suffix was fading and by the time of modern English was totally lost or swallowed into silent final -e-.

It also appears in Romanic words from Latin that have been borrowed into English, such as opera, plaza, armada. It figures in scientific names coined in Modern Latin (amoeba, soda, magnolia, etc.) and is common in geographical names formed according to Latin or Greek models (Asia, Africa, America, Arabia, Florida, etc.)

In English it marks sex only in personal names (Julia, Maria, Alberta) and in a few words from Italian or Spanish where a corresponding male form also is in use (donna, senora).
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-ish 
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.

The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.
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-ic 

Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).

In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.

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-ade 

word-forming element denoting an action or product of an action, via French, Spanish, or Italian, ultimately from Latin -ata, fem. past participle ending used in forming nouns. The usual form in French is -ée. The parallel form, -ade, came into French about the 13c. via southern Romanic languages (Spanish, Portuguese, and Provençal -ada, Italian -ata), hence grenade, crusade, ballad, arcade, comrade, balustrade, lemonade, etc.

This foreign suffix ade has been so largely imported, and at a time when the French language had still a certain plastic force, that it has been adopted as a popular suffix, and is still employed to form a crowd of new words, such as promenade, embrassade, glissade, bourrade, &c. [Brachet, "Etymological Dictionary of the French Language," Kitchin transl., Oxford, 1882]

Latin -atus, past-participle suffix of verbs of the 1st conjugation, also became -ade in French (Spanish -ado, Italian -ato) and came to be used as a suffix denoting persons or groups participating in an action (such as brigade, desperado).

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