Al-`Awfi related that Ibn `Abbas said, "The people asked Allah's Messenger about the crescent moons. Thereafter, this Ayah was revealed:
﴿يَسْـَلُونَكَ عَنِ الأَهِلَّةِ قُلْ هِىَ مَوَاقِيتُ لِلنَّاسِ﴾
(They ask you (O Muhammad) about the crescents. Say, "These are signs to mark fixed periods of time for mankind...) so that they mark their acts of worship, the `Iddah (the period of time a divorced woman or a widow is required to wait before remarrying) of their women and the time of their Hajj (pilgrimage to Makkah).'' `Abdur-Razzaq reported that Ibn `Umar narrated that Allah's Messenger said:
«جَعَلَ اللهُ الْأَهِلَّةَ مَوَاقِيتَ لِلنَّاسِ، فَصُومُوا لِرُؤْيَتِهِ، وَأَفْطِرُوا لِرُؤْيَتِهِ، فَإِنْ غُمَّ عَلَيْكُمْ فَعُدُّوا ثَلَاثِينَ يَوْمًا»
(Allah has made the crescents signs to mark fixed periods of time for mankind. Hence, fast on seeing it (the crescent for Ramadan) and break the fast on seeing it (the crescent for Shawwal). If it (the crescent) was obscure to you then count thirty days (mark that month as thirty days).) WThis Hadith was also collected by Al-Hakim in his Mustadrak, and he said, "The chain is Sahih, and they (Al-Bukhari and Muslim) did not recorded it."