[extent] 1530s, "room to act, free play," also literal (1550s), "room to move in, space;" from Italian scopo "aim, purpose, object; thing aimed at, mark, target," from Latin scopus, from Greek skopos "aim, target, object of attention;" also "watcher, one who watches," which according to Watkins is from a metathesized form of PIE *spek-yo-, suffixed form of root *spek- "to observe." Beekes writes that the the old IE root noun (as in Latin haruspex) from *spek- apparently was replaced in Greek by skopos.
It is attested from 1550s as "that which is aimed at or desired," hence "ultimate aim;" the classical sense of "a mark to aim or shoot at" was in English by 1560s but now is obsolete. Hence "object a speaker or writer has in view" (1530s). The sense of "intellectual range, distance the mind can reach" is recorded from c. 1600. By 1590s as "extent in space." By 1830 as "sphere in which some activity operates." Elizabethan scopious "spacious, wide" did not stick.
[instrument for viewing] 1872, shortened from telescope, microscope, etc., in which the element (Latinized) is from Greek skopein "to look" (from PIE root *spek- "to observe"). Earlier used as a shortening of horoscope (c. 1600). Extended to radar screens, etc., by 1945 as a shortening of oscilloscope.
1910, "examination of the bladder with a cystoscope" (1889), from Latinized combining form of Greek kystis "bladder" (which is of unknown origin) + -scope. Related: Cystoscopic.