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The primary source of Islamic law is the Holy Quran and the Sahih Ahadith. If a problem arises which is not mentioned in these sources, ijma (consensus) and qiyas (analogy) are to be used. The Quran says in Surah ale-Imran, Chapter 3, Verse no. 32:
Obey Allah and Obey the Messenger so that you may obtain mercy.
In the case of the method of salat, we, therefore, have to analyse how the Prophet (S) offered it. He (S) said in Sahih al-Bukhari, Volume 1, Book of Adhan (Book 11), Hadith 604:
Narrated By Malik:
We came to the Prophet and stayed with him for twenty days and nights. We were all young and of about the same age. The Prophet was very kind and merciful. When he realized our longing for our families, he asked about our homes and the people there and we told him. Then he asked us to go back to our families and stay with them and teach them (the religion) and to order them to do good things. He also mentioned some other things which I have (remembered or) forgotten. The Prophet then added, "Pray as you have seen me praying and when it is the time for the prayer one of you should pronounce the Adhan and the oldest of you should lead the prayer.
From this again we come to know that we should analyse the method of prayer of the Prophet (S). Here are some ahadith concerning some actions in salat from Sahih al-Bukhari, Volume 1, Book of Characteristics of Prayer (Book 12).
Narrated Salim bin Abdullah
My father said, "Allah's Apostle used to raise both his hands up to the level of his shoulders when opening the prayer; and on saying the Takbir for bowing. And on raising his head from bowing he used to do the same and then say 'Sami a-l-lahu Liman hamida, Rabbana walaka-l-hamd.' And he did not do that (i.e. raising his hands) in prostrations."
Narrated Abdullah bin Umar
I saw that whenever Allah's Apostle stood for the prayer, he used to raise both his hands up to the shoulders, and used to do the same on saying the Takbir for bowing and on raising his head from it and used to say, "Sami a-l-lahu Liman hamida". But he did not do that (i.e. raising his hands) in prostrations.
Narrated Sahl bin Sad
The people were ordered to place the right hand on the left forearm in the prayer. Abu Hazim said, "I knew that the order was from the Prophet."
Narrated Abu Huraira
Allah's Apostle used to keep silent between the Takbir and the recitation of Qur'an and that interval of silence used to be a short one. I said to the Prophet "May my parents be sacrificed for you! What do you say in the pause between Takbir and recitation?" The Prophet said, "I say, 'Allahumma, ba'id baini wa baina khatayaya kama ba'adta baina-l-mashriqi wa-l-maghrib. Allahumma, naqqim min khatayaya kama yunaqqa-ththawbu-l-abyadu mina-ddanas. Allahumma, ighsil khatayaya bil-ma'i wa-th-thalji wal-barad (O Allah! Set me apart from my sins (faults) as the East and West are set apart from each other and clean me from sins as a white garment is cleaned of dirt (after thorough washing). O Allah! Wash off my sins with water, snow and hail.)"
Narrated Abu Mamar
We asked Khabbab whether Allah's Apostle used to recite (the Qur'an) in the Zuhr and the 'Asr prayers. He replied in the affirmative. We said, "How did you come to know about it?" He said, "By the movement of his beard."
Narrated Ubada bin As Samit
Allah's Apostle said, "Whoever does not recite Al-Fatiha in his prayer, his prayer is invalid."
Narrated Abu Huraira
The Prophet said, "Say 'Amin' when the Imam says it and if the Amin of any one of you coincides with that of the angels then all his past sins will be forgiven." Ibn Shihab said, "Allah's Apostle used to say 'Amin.' "
The Prophet used to say in his bowing and prostrations, "Subhanaka-Allahumma Rabbana wa-bihamdika Allahumma-ighfirli. (I honor Allah from all what (unsuitable things) is ascribed to Him. O Allah Our Lord! And all the praises are for You. O Allah! Forgive me)."
Abu Qilaba said, "Malik bin Huwairith used to demonstrate to us the prayer of the Prophet at times other than that of the compulsory prayers. So (once) he stood up for prayer and performed a perfect Qiyam (standing and reciting from the Holy Qur'an) and then bowed and performed bowing perfectly; then he raised his head and stood straight for a while." Abu Qilaba added, "Malik bin Huwairith in that demonstration prayed like this Sheikh of ours, Abu Yazid." Abu Yazid used to sit (for a while) on raising his head from the second prostration before getting up.
Narrated Malik bin Huwairith Al Laithi
I saw the Prophet praying and in the odd Rakat, he used to sit for a moment before getting up.
Narrated Ibn Abbas
The Prophet was ordered (by Allah) to prostrate on seven parts and not to tuck up the clothes or hair (while praying). Those parts are: the forehead (along with the tip of nose), both hands, both knees, and (toes of) both feet.
Narrated Anas bin Malik
The Prophet said, "Be straight in the prostrations and none of you should put his forearms on the ground (in the prostration) like a dog."