reliable adj.

mid-14c., relien, "to gather, assemble" an army, followers, a host, etc. (transitive and intransitive), from Old French relier "assemble, put together; fasten, fasten again, attach, rally, oblige," from Latin religare "fasten, bind fast," from re-, here perhaps an intensive prefix (see re-), + ligare "to bind" (from PIE root *leig- "to tie, bind").

The older sense now are obsolete. The meaning "depend on with full trust and confidence, attach one's faith to" a person or thing is from 1570s, perhaps via the notion of "rally to, fall back on." Typically used with on, perhaps by influence of unrelated lie (v.2) "rest horizontally." Related: Relied; relying.

The verb rely, in the orig. sense 'fasten, fix, attach,' came to be used with a special reference to attaching one's faith or oneself to a person or thing (cf. 'to pin one's faith to a thing,' 'a man to tie to,' colloquial phrases containing the same figure); in this use it became, by omission of the object, in transitive, and, losing thus its etymological associations (the other use, 'bring together again, rally,' having also become obsolete), was sometimes regarded, and has been by some etymologists actually explained, as a barbarous compound of re- + E. lie (1) rest, .... But the pret. would then have been *relay, pp. *relain. [Century Dictionary]

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.