Waḍaʿa is the verb; the teacher is subject; book the direct object; ʿalā + desk forms the prepositional complement.
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Integrated Analysis: Iḍāfah and Preposition
Comprehensive Review: Applied Arabic Parsing
Waḍaʿa is the verb; the teacher is subject; book the direct object; ʿalā + desk forms the prepositional complement.