Etymology
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-ency 

word-forming element denoting quality or state, from Latin -entia. Derivatively identical with -ence; also see -ancy. The slight difference of sense is that -ence can and -ency cannot mean "an act of ____."

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-machy 

word-forming element meaning "battle, war, contest, fighting, warfare," from Latinized form of Greek -makhia, from makhe "a battle, fight," related to makhesthai "to fight." Beekes suspects it is from an isolated root, perhaps Pre-Greek: "In the domain of fighting and battle, old inherited expressions can hardly be expected."

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-able 

common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).

A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."

To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]

In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.

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-ate (1)

word-forming element used in forming nouns from Latin words ending in -atus, -atum (such as estate, primate, senate). Those that came to English via French often arrived with -at, but an -e was added after c. 1400 to indicate the long vowel. The suffix also can mark adjectives formed from Latin past participles in -atus, -ata (such as desolate, moderate, separate); again, they often were adopted in Middle English as -at, with an -e appended after c. 1400.

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-ette 
diminutive word-forming element, from Old French -ette (fem.), used indiscriminately in Old French with masculine form -et (see -et). As a general rule, older words borrowed from French have -et in English, while ones taken in since 17c. have -ette. In use with native words since late 19c., especially among persons who coin new product names, who tend to give it a sense of "imitation, a sort of" (for example flannelette "imitation flannel of cotton," 1876; leatherette, 1855; linenette, 1894). Also in such words as lecturette (1867), sermonette, which, OED remarks, "can scarcely be said to be in good use, though often met with in newspapers."
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