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

1) To make evident or establish by arguments or reasoning; prove.
2) To describe, explain, or illustrate by examples, specimens, experiments, or the like.
3) To manifest or exhibit; show.
4) T display openly or publicly, as feelings (Dictionary.com).

From L. demonstratus, p.p. of demonstrare "to show, point out," from → de- + monstrare "to show," from monstrum "sign, portent."

Padišidan, from Sogd. padēš "to show," ultimately from Proto-Ir. *apa-dais-, from *dais- "to show," cf. Av. daēs- "to show," related to andiš, → think.