What did the Farewell Sermon say about intercalation and the calendar?

In the Farewell Sermon, the Prophet ﷺ said that intercalation (al-nasi') is an increase in disbelief, by which those who disbelieve are led astray: they make it lawful one year and unlawful another year, to match the number of what God has made unlawful. He said that time has returned to its form from the day God created the heavens and the earth, and that the number of months with God is twelve months, of which four are sacred ¹.

The four sacred months in the sermon are three in succession, and Rajab of Mudar, which falls between Jumada and Sha'ban ¹. The editors of the 1936 edition explain that the Prophet said "Rajab of Mudar" because Rabi'a used to make Ramadan unlawful and call it Rajab. He made clear that it was Rajab of Mudar, not Rajab of Rabi'a ¹. The meaning of "time has returned to its form" is that the pilgrimage fell in the true Dhu al-Hijja, after intercalation had shifted the months. The passage is close to At-Tawba 36 and At-Tawba 37.

• Ibn Ishaq mentions the revelation of the verse on intercalation among what was revealed in Bara'a ².
• The full text of the sermon in Ibn Ishaq is on the page of the sermon ³.

How intercalation worked in the calendar of the Jahiliyya, and who ran it from Banu Kinana, will be added from books of tafsir and history.