late 14c., "set (one's eyes or mind) on something" (a figurative use), probably from Old French verb *fixer, from fixe "fixed," from Latin fixus "fixed, fast, immovable; established, settled," past-participle adjective from figere "to fix, fasten, drive, thrust in; pierce through, transfix," also figurative, from PIE root *dheigw- "to pierce, stick in;" hence "to fix, fasten."
Sense of "fasten, attach" is c. 1400; that of "to make (colors, etc.) fast or permanent" is from 1660s. The meaning "settle, assign" evolved into "adjust, arrange" (1660s), then "to repair" (1737), but this sometimes was objected to (see below). Sense of "tamper with" (a fight, a jury, etc.) is from 1790. As euphemism for "castrate a pet" it dates from 1930. Related: Fixed; fixing.
To fix is to make fast, or permanent; to set immoveably, &c.: hence, to fix a watch, is to stop it, or prevent it from 'going;' which, it must be admitted, is a very unsatisfactory mode of repairing that article. [Seth T. Hurd, "A Grammatical Corrector; or, Vocabulary of the Common Errors of Speech," 1847]
-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.