It is narrated from Ali bin Hussain (may Allah be pleased with him) that he states: "Whenever the Messenger of Allah (peace be upon him) would bow or rise in prayer, he would say the takbeer. This was always his way of praying until he departed to Allah."
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 199
Abu Salamah narrates that Abu Hurairah (may Allah be pleased with him) used to lead the people in prayer, and when he would bow down and when he would rise up, he would say the takbeer. Then when he finished the prayer, he said: "By Allah, among all of you, I am the one whose prayer most closely resembles the prayer of the Messenger of Allah (ﷺ)."
Hadith Referenceمسند الإمام الشافعي / كتاب الصلاة / 200
Hadith Takhrijأخرجہ البخاری، الاذان، باب اتمام التکبیر فی الرکوع: 785 - ومسلم، الصلاۃ، باب اثبات التکبیر فی کل خفض ورفع فی الصلاۃ... الخ: 392۔