"that may be, capable of existing, occurring, or being done," mid-14c., from Old French possible and directly from Latin possibilis "that can be done," from posse "be able" (see potent).

The only kind of object which in strict propriety of language can be called possible is the truth of a proposition ; and when a kind of thing is said to be possible, this is to be regarded as an elliptical expression, meaning that it is of such a general description that we do not know it does not exist. So an event or act is said to be possible, meaning that one would not know that it would not come to pass. But it is incorrect to use possible meaning practicable ; possible is what may be, not what can be. [Century Dictionary]

"that which may take place or come into being," 1640s, from possible (adj.).

c. 1400, possibli, "by any existing power or means, in a possible manner," from possible (adj.) + -ly (2). By c. 1600 as "perhaps. perchance."

late 14c., "state, fact, or condition of being possible," from Old French possibilité (13c.) and directly from Latin possibilitatem (nominative possibilitas) "possibility," from possibilis (see possible (adj.)). Meaning "a possible thing or substance; that which may take place or come into being" is from c. 1400. Related: Possibilities.

late 14c., from Old French impossible (14c.), from Latin impossibilis "not possible," from assimilated form of in- "not, opposite of" (see in- (1)) + possibilis (see possible). Weakened sense of "unable to be accomplished or tolerated" is from mid-19c. Related: Impossibly.

Proto-Indo-European root meaning "powerful; lord." 

It forms all or part of: bashaw; compos mentis; despot; hospodar; host (n.1) "person who receives guests;" idempotent; impotent; omnipotent; pasha; plenipotentiary; posse; possess; possible; potence; potency; potent; potentate; potential; potentiate; potentiometer; power; totipotent. 

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit patih "master, husband;" Greek posis, Lithuanian patis "husband;" Latin potis "powerful, able, capable; possible." 

1759, "a possible occurrence," from eventual + -ity, on model of French éventualité.

late 14c., "possible" (as opposed to actual), "capable of being or becoming," from Old French potenciel and directly from Medieval Latin potentialis "potential," from Latin potentia "power, might, force;" figuratively "political power, authority, influence," from potens "powerful," from potis "powerful, able, capable; possible;" of persons, "better, preferable; chief, principal; strongest, foremost," from PIE root *poti- "powerful; lord."

The noun, meaning "that which is possible, anything that may be" is attested by 1817 (Coleridge), from the adjective. Middle English had potencies (plural) "a caustic medicine" (early 15c.).

"possible to achieve, obtainable," mid-15c., from procure + -able. Related: Procurability.

"lowest possible," 1884, from the noun phrase meaning "bedrock" (1815), also figurative, from rock (n.1) + bottom (n.).