1590s, "conception, mental scheme," from Late Latin theoria (Jerome), from Greek theōria "contemplation, speculation; a looking at, viewing; a sight, show, spectacle, things looked at," from theōrein "to consider, speculate, look at," from theōros "spectator," from thea "a view" (see theater) + horan "to see," which is possibly from PIE root *wer- (3) "to perceive." Philosophy credits sense evolution in the Greek word to Pythagoras.
Earlier in this sense was theorical (n.), late 15c. Sense of "principles or methods of a science or art" (rather than its practice) is first recorded 1610s (as in music theory, which is the science of musical composition, apart from practice or performance). Sense of "an intelligible explanation based on observation and reasoning" is from 1630s.
"demonstrable proposition in science or mathematics," 1550s, from French théorème (16c.) and directly from Late Latin theorema, from Greek theorema "spectacle, sight," in Euclid "proposition to be proved," literally "that which is looked at," from theorein "to look at, behold" (see theory).
1530s, "action, a thing performed, anything done, a deed," good or evil but in 16c.-17c. commonly "evil deed, crime;" from Latin factum "an event, occurrence, deed, achievement," in Medieval Latin also "state, condition, circumstance" (source also of Old French fait, Spanish hecho, Italian fatto), etymologically "a thing done," noun use of neuter of factus, past participle of facere "to do" (from PIE root *dhe- "to set, put").
An earlier adaptation of the Old French word that also became feat. The older senses are mostly obsolete but somewhat preserved in such phrases as after the fact, originally legal, "after the crime." Also compare matter-of-fact.
The modern, empirical, sense of "thing known to be true, a real state of things, what has really occurred or is actually the case," as distinguished from statement or belief, is from 1630s, from the notion of "something that has actually occurred." The particular concept of the scientific, empirical fact ("a truth known by observation or authentic testimony") emerged in English 1660s, via Hooke, Boyle, etc., in The Royal Society, as part of the creation of the modern vocabulary of knowledge (along with theory, hypothesis, etc.); in early 18c. it was associated with the philosophical writings of Hume. Middle English thus lacked the noun and the idea of it; the closest expression being perhaps thing proved (c.1500).
Hence facts "real state of things;" in fact "in reality" (1707). By 1729, fact was being used of "something presented as a fact but which might be or is false."
By fact is also often meant a true statement, a truth, or truth in general ; but this seems to be a mere inexactness of language .... Fact, as being special, is sometimes opposed to truth, as being universal ; and in such cases there is an implication that facts are minute matters ascertained by research, and often inferior in their importance for the formation of general opinions, or for the general description of phenomena, to other matters which are of familiar experience. [Century Dictionary]
Facts of life is by 1854 as "the stark realities of existence;" by 1913 it had also acquired a more specific sense of "knowledge of human sexual functions." The alliterative pairing of facts and figures for "precise information" is by 1727.
Facts and Figures are the most stubborn Evidences; they neither yield to the most persuasive Eloquence, nor bend to the most imperious Authority. [Abel Boyer, "The Political State of Great Britain," 1727]
Facts are stubborn things is in an 1822 translation of the popular novel "Gil Blas" (earlier English translations have facts speak for themselves).
variant of encase.
Theory of Incasement, an old theory of reproduction which assumed that when the first animal of each species was created, the germs of all other individuals of the same species which were to come from it were incased in its ova. The discovery of spermatozoa developed the theory in two opposite directions: the ovulists, or ovists, held still to the theory of incasement in the female while the animalculists, or spermists, entertained the theory of incasement in the male. [Century Dictionary]