Etymology
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-ate (3)

in chemistry, word-forming element used to form the names of salts from acids in -ic; from Latin -atus, -atum, suffix used in forming adjectives and thence nouns; identical with -ate (1).

The substance formed, for example, by the action of acetic acid (vinegar) on lead was described in the 18th century as plumbum acetatum, i.e. acetated lead. Acetatum was then taken as a noun meaning "the acetated (product)," i.e. acetate. [W.E. Flood, "The Origins of Chemical Names," London, 1963]
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-ory 
adjective and noun suffix, "having to do with, characterized by, tending to, place for," from Middle English -orie, from Old North French -ory, -orie (Old French -oir, -oire), from Latin -orius, -oria, -orium.

Latin adjectives in -orius, according to "An Etymological Dictionary of the French Language," tended to "indicate a quality proper to the action accomplished by the agent; as oratorius from orator; laudatorius from laudator. The neuter of these adjectives was early employed as a substantive, and usually denoted the place of residence of the agent or the instrument that he uses; as praetorium from praetor; dormitorium from dormitor; auditorium, dolatorium.

"These newer words, already frequent under the Empire, became exceedingly numerous at a later time, especially in ecclesiastical and scholastic Latin; as purgatorium, refectorium, laboratorium, observatorium, &c." [transl. G.W. Kitchin, Oxford, 1878]
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-ster 

Old English -istre, from Proto-Germanic *-istrijon, feminine agent suffix used as the equivalent of masculine -ere (see -er (1)). Also used in Middle English to form nouns of action (meaning "a person who ...") without regard for gender.

The genderless agent noun use apparently was a broader application of the original feminine suffix, beginning in the north of England, but linguists disagree over whether this indicates female domination of weaving and baking trades, as represented in surnames such as Webster, Baxter, Brewster, etc. (though spinster probably carries an originally female ending).

Also compare whitester "one who bleaches cloth;" kempster (c. 1400; Halliwell has it as kembster) "woman who cleans wool." Chaucer ("Merchant's Tale") has chidester "an angry woman." In Modern English, the suffix has been productive in forming derivative nouns (gamester,roadster, punster, rodster "angler," etc.; the 17c. had scoldster).

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-er (1)

English agent noun ending, corresponding to Latin -or. In native words it represents Old English -ere (Old Northumbrian also -are) "man who has to do with," from Proto-Germanic *-ari (cognates: German -er, Swedish -are, Danish -ere), from Proto-Germanic *-arjoz. Some believe this root is identical with, and perhaps a borrowing of, Latin -arius (see -ary).

Generally used with native Germanic words. In words of Latin origin, verbs derived from past participle stems of Latin ones (including most verbs in -ate) usually take the Latin ending -or, as do Latin verbs that passed through French (such as governor); but there are many exceptions (eraser, laborer, promoter, deserter; sailor, bachelor), some of which were conformed from Latin to English in late Middle English.

The use of -or and -ee in legal language (such as lessor/lessee) to distinguish actors and recipients of action has given the -or ending a tinge of professionalism, and this makes it useful in doubling words that have a professional and a non-professional sense (such as advisor/adviser, conductor/conducter, incubator/incubater, elevator/elevater).

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