An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

1) To divide into or mark with degrees or other divisions, as the scale of a thermometer.
2) To receive a degree or diploma on completing a course of study (often followed by from).
3) To confer a degree upon, or to grant a diploma to, at the close of a course of study, as in a university, college, or school.
4) A person who has received a degree or diploma on completing a course of study, as in a university, college, or school (Dictionary.com).

M.E., from M.L. graduatus, p.pa. of graduari "to take a degree," from L. gradus "step, → grade."

1, 3) Padâk dâdan, compound infinitive, padâkidan simple infinitive, both from padâk, → grade, + dâdan "to give, grant," → datum, and -idan, → -fy.
2) Padâk gereftan, from padâk + gereftan "→ take, hold."
4) Padâkmand, from padâk + -mand suffix of possession and ability, → -al; padâkidé, p.p. of padâkidan, as above.