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."
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).
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]