late 14c., "carried away in an ecstatic trance," from Latin raptus, past participle of rapere "seize, carry off" (see rape (v.)). A figurative sense, the notion is of being "carried up into Heaven" (bodily or in a dream), as in a saint's vision.
The Latin literal sense of "carried away" also was in English from 1550s. Essentially an alternative past participle of rape, in 15c.-17c. the word also sometimes could mean "raped." The sense of "engrossed" is recorded from c. 1500.
As a Latin past-participle adjective, in English it spawned unthinking the back-formed verb rap "to affect with rapture," which was common c. 1600-1750. Before that, there was a verb rapt "seize or grasp, seize and carry off; ravish" (1570s), also "enrapture, transport as with ecstasy" (1590s). There also was a noun rapt in 15c. meaning both "rapture" and "rape."
c. 1600, "act of carrying off" as prey or plunder, from rapt + -ure, or else from French rapture, from Medieval Latin raptura "seizure, rape, kidnapping," from Latin raptus "a carrying off, abduction, snatching away; rape" (see rapt). The earliest attested use in English is with women as objects and in 17c. it sometimes meant rape (v.), which word is a cognate of this one.
The sense of "spiritual ecstasy, state of mental transport or exaltation" is recorded by c. 1600 (raptures). The connecting notion is a sudden or violent taking and carrying away. The meaning "expression of exalted or passionate feeling" in words or music is from 1610s.
c. 1600, from French enthousiasme (16c.) and directly from Late Latin enthusiasmus, from Greek enthousiasmos "divine inspiration, enthusiasm (produced by certain kinds of music, etc.)," from enthousiazein "be inspired or possessed by a god, be rapt, be in ecstasy," from entheos "divinely inspired, possessed by a god," from en "in" (see en- (2)) + theos "god" (from PIE root *dhes-, forming words for religious concepts). It acquired a derogatory sense of "excessive religious emotion through the conceit of special revelation from God" (1650s) under the Puritans; generalized meaning "fervor, zeal" (the main modern sense) is first recorded 1716.
late 14c., "intelligent contemplation, consideration; act of looking," from Old French speculacion "close observation, rapt attention," and directly from Late Latin speculationem (nominative speculatio) "contemplation, observation," noun of action from speculatus, past participle of Latin speculari "observe," from specere "to look at, view" (from PIE root *spek- "to observe").
The meaning "pursuit of the truth by means of thinking" is from mid-15c. The disparaging sense of "mere conjecture" is recorded from 1570s. The meaning "buying and selling in search of profit from rise and fall of market value" is recorded from 1774; its short form spec is attested from 1794.
Protestant clergy were at least as bigoted as Catholic ecclesiastics, nevertheless there soon came to be much more liberty of speculation in Protestant than in Catholic countries, because in Protestant countries the clergy had less power. The important aspect of Protestantism was schism, not heresy, for schism led to national Churches were not strong enough to control the lay government. This was wholly a gain, for the Churches, everywhere, opposed as long as they could practically every invention that made for an increase of happiness or knowledge here on earth. [Bertrand Russell, "A History of Western Philosophy," 1945]