"telescope or opera glass with two tubes for use by both eyes at once," 1690s, from French binocle (17c.), from Latin bini- "two by two, twofold, two apiece" (see binary) + oculus "eye" (from PIE root *okw- "to see").
"dual, twofold, double," mid-15c., from Late Latin binarius "consisting of two," from bini "twofold, two apiece, two-by-two" (used especially of matched things), from bis "double" (from PIE root *dwo- "two"). Binary code in computer terminology was in use by 1952, though the idea itself is ancient. Binary star in astronomy is from 1802.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit akshi "the eye; the number two," Greek osse "(two) eyes," opsis "a sight;" Old Church Slavonic oko, Lithuanian akis, Latin oculus, Greek okkos, Tocharian ak, ek, Armenian akn "eye."
1738, "involving both eyes," earlier "having two eyes" (1713), from French binoculaire, from Latin bini "two by two, twofold, two apiece" (see binary) + ocularis "of the eye," from oculus "eye" (from PIE root *okw- "to see"). The double-tubed telescopic instrument (1871, short for binocular glass) earlier was called a binocle. Related: Binocularity; binocularly.