The account of the building of the House and its rebuilding several times

It is narrated from Khalid bin Ar'arah that he said: When Sayyiduna Uthman (may Allah be pleased with him) was martyred, the people were greatly frightened that day, and the drawing of swords among us became a very serious matter, so I stayed sitting in my house. Then I had some business in the market, so I went out, and I saw some people sitting in the shade of the palace, about forty men, and there was a chain placed across the door. I wanted to enter, but the doorkeeper stopped me. Those people said: "Let the man in." So I entered, and there were the nobles and dignitaries of the people. Then a handsome man came, dressed in a suit of garments, with neither a shirt nor a turban on him, and he sat down; he was Sayyiduna Ali bin Abi Talib (may Allah be pleased with him). Then he said: When Sayyiduna Ibrahim (peace be upon him) intended to build the House of Allah, he felt some difficulty (in the matter of its plan), so Allah Almighty sent the "Sakinah", which was a strong wind. It coiled up (over the foundations of the House of Allah) in a circle, and he began to lay one course (a layer of the wall) upon it every day, while Makkah was intensely hot. When he reached the place of the Black Stone, he said to Sayyiduna Isma'il (peace be upon him): Go and look for a stone so that I may place it here. So he went roaming about the mountains. Meanwhile, Jibril (peace be upon him) brought the Black Stone and placed it. When Isma'il (peace be upon him) came, he asked: Who brought this? Ibrahim (peace be upon him) said: It was brought by the One who did not rely on my building nor on yours. In short, he built it. Then it collapsed, and the Amalekites built it; then it fell down, and the tribe of Jurhum built it; then it collapsed, and the tribe of Quraysh built it. When they were about to place the Black Stone, they quarrelled among themselves, and they said: The first person to come out of this door will place it. Then the Messenger of Allah (peace and blessings be upon him) came out from the direction of the Gate of Banu Shaybah. He (peace and blessings be upon him) ordered that a cloth be spread out and placed the Black Stone in its middle. Then he ordered one man from every branch of Quraysh to take hold of a corner of the cloth. Then the Messenger of Allah (peace and blessings be upon him) lifted it with his blessed hand and placed it (in its spot).
The two Shaykhs (Bukhari and Muslim) agreed on recording the long hadith in which Ibn Abbas (may Allah be pleased with them both) narrates the story of Ibrahim, the Friend of Allah (peace be upon him), building the Ka'bah for the very first time; however, this (present) hadith is different from that one.

It is narrated from Sayyidah Aishah (may Allah be pleased with her) that the Prophet (peace and blessings be upon him) said: "Indeed, the stoning of the Jamarat, the tawaf of the House of Allah, and the sa'i between Safa and Marwah have been prescribed only to establish the remembrance of Allah Almighty."
The chain of this hadith is sahih (authentic), but the two Shaykhs (Bukhari and Muslim) did not record it.