discoverable adj.

c. 1300, discoveren, "divulge, reveal, disclose, expose, lay open to view, betray (someone's secrets)," senses now obsolete, from stem of Old French descovrir "uncover, unroof, unveil, reveal, betray," from Medieval Latin discooperire, from Latin dis- "opposite of" (see dis-) + cooperire "to cover up, cover over, overwhelm, bury" (see cover (v.)).

At first with a sense of betrayal or malicious exposure (discoverer originally meant "informant"). Also in Middle English used in literal senses, such as "to remove" (one's hat, the roof from a building). The meaning "to obtain the first knowledge or sight of what was before not known," the main modern sense, is by 1550s.

Discover, Invent, agree in signifying to find out; but we discover what already exists, though to us unknown; we invent what did not before exist: as, to discover the applicability of steam to the purposes of locomotion, and to invent the machinery necessary to use steam for these ends. ... Some things are of so mixed a character that either word may be applied to them. [Century Dictionary]

Sense of "make famous or fashionable" is by 1908. Related: Discovered; discovering.

That man is not the discoverer of any art who first says the thing; but he who says it so long, and so loud, and so clearly, that he compels mankind to hear him—the man who is so deeply impressed with the importance of the discovery that he will take no denial, but at the risk of fortune and fame, pushes through all opposition, and is determined that what he thinks he has discovered shall not perish for want of a fair trial. [Sydney Smith, in Edinburgh Review, June 1826]

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.