From Longman Dictionary of Contemporary Englishrun/cast your eye over somethingrun/cast your eye over somethingLOOK ATto look at something quickly She cast her eye over the front page of the paper. → eye
Examples from the Corpus
run/cast your eye over something• He also casts his eye over the proposed law changes.• And of course Prince also casts his eye over rock too.• Above him Cornelius ran his eye over a box of ancient cane carpet beaters.• I cast my eye over the front page of the Telegraph while Anne poured the coffee.• The customs officers run their eyes over us as if we weren't there.• They've even invited Michael Heseltine, care of Spitting Image, to cast his eyes over the exhibition.• A note from Mellowes instructed me to cast my eye over the draft, pronto, for inaccuracies. 