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Question

Are these adjective phrases of adverb phrases
1)From Ancient Egypt
2)WithComplex Patterns
3)about great people
4)From the bible
5)Of famous battles

Answer 1

They aren't absolutely one or the other. They are prepositional phrases, but whether they are adjectival or adverbial depends on the context and whether they are modifying a noun or a verb.

Examples:
He talks about great people. (adv.)
He tells stories about great people. (adj.)

Answer 2

adverb