In «وَالصَّيْفِ», ṣād is a sun letter, so article lām assimilates. Its «صَيْ» contains a līn yāʾ; pausing makes the final fāʾ sākin, yielding madd al-līn.
In «الْبَيْتِ», bāʾ is a moon letter, so article lām is clear. Yet «بَيْ» also contains a līn yāʾ, and pausing on final tāʾ likewise gives madd al-līn.
The article-lām rule differs, but the cause of pausal lengthening is the same. Separate the two issues.
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Waṣ-ṣayf and al-bayt: compare the līn pauses
Al-Fīl and Quraysh: Applied Iẓhār, Ikhfāʾ, Idghām, Madd and Waqf
In «وَالصَّيْفِ», ṣād is a sun letter, so article lām assimilates. Its «صَيْ» contains a līn yāʾ; pausing makes the final fāʾ sākin, yielding madd al-līn.
In «الْبَيْتِ», bāʾ is a moon letter, so article lām is clear. Yet «بَيْ» also contains a līn yāʾ, and pausing on final tāʾ likewise gives madd al-līn.
The article-lām rule differs, but the cause of pausal lengthening is the same. Separate the two issues.