مُتَحَرِّكَ الْأَوْسَطِ concerns the vowel on the word’s middle letter, not the case ending imposed at the final position.
In شَتَر, the middle ت is vowelled; in نُوح, the middle و is sākin.
By contrast, the kasra on the final letter of بِنُوحٍ is a genitive ending. Keep these two concepts separate.
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Diptote Causes — Foreign Origin and Its Conditions
مُتَحَرِّكَ الْأَوْسَطِ concerns the vowel on the word’s middle letter, not the case ending imposed at the final position.
In شَتَر, the middle ت is vowelled; in نُوح, the middle و is sākin.
By contrast, the kasra on the final letter of بِنُوحٍ is a genitive ending. Keep these two concepts separate.