Non Posset Componere
Non Posset Componere is a verb + infinitive. Posset is in the third person singular imperfect subjunctive active of the verb possum (posse, potui) which means to be able, to have power. It is in the subjunctive because it is part of the temporal subordinate clause that Cum signalled. It is made negative by non.
Componere is an present active infinitive that clarifies the action in posset. It is from the verb compono, -ere, composui, compositum, meaning to compose, to put together.
Putting it all together, you get: he was unable to compose
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