I saw him cross the road.
Is cross the road the object of saw? Or is it the complement of him?
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In this sentence,
to cross the road is an objective predicative complement within the sentence.
Such phrases take the general form:
SUBJECT + VERB + OBJECT + COMPLEMENT
The object here is clearly
As far as I'm aware, the "objective complement" is a rather peculiar construct to the English language. Other European languages (I can vouch for French and Spanish at least) require a separate clause, something akin to
I saw that he crossed the road. (Also perfectly grammatical English, but less natural.)