1510s, "by the day, in each day," Latin, "by the day," from per (see per) + diem, accusative singular of dies "day" (from PIE root *dyeu- "to shine"). As a noun from 1809, "amount or allowance of so much every day."
"through, by means of," 1580s (earlier in various Latin and French phrases, in the latter often par), from Latin per "through, during, by means of, on account of, as in," from PIE root *per- (1) "forward," hence "through, in front of, before, first, chief, toward, near, around, against."
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit deva "god" (literally "shining one"); diva "by day;" Avestan dava- "spirit, demon;" Greek delos "clear;" Latin dies "day," deus "god;" Welsh diw, Breton deiz "day;" Armenian tiw "day;" Lithuanian dievas "god," diena "day;" Old Church Slavonic dini, Polish dzień, Russian den "day;" Old Norse tivar "gods;" Old English Tig, genitive Tiwes, name of a god.
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Harper, D. (n.d.). Etymology of per diem. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/per diem
Harper Douglas, “Etymology of per diem,” Online Etymology Dictionary, accessed $(datetime), https://www.etymonline.com/word/per diem.
Harper, Douglas. “Etymology of per diem.” Online Etymology Dictionary, https://www.etymonline.com/word/per diem. Accessed $(datetimeMla).
D. Harper. “Etymology of per diem.” Online Etymology Dictionary. https://www.etymonline.com/word/per diem (accessed $(datetime)).