-able Look up -able at Dictionary.com
word-forming element expressing ability, capacity, fitness, from French, from Latin -ibilis, -abilis, forming adjectives from verbs, from PIE *-tro-, a suffix used to form nouns of instrument.

In Latin, infinitives in -are took -abilis, others -ibilis; 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 has contributed to its survival as a living suffix. It is related to the second syllable of rudder and saddle.