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."
we'll save 100 man-hours per diem
*per-
per-
per
per annum
per capita
per diem
per se
per stirpes
peradventure
perambulate
perambulation
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