Al-Matalib al-'Aliyah 513 — The takbir

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) that he said: "The first person to reduce the takbirs of the prayer was al-Walid bin Uqbah." At this, Sayyiduna Abdullah (may Allah be pleased with him) said: "They have reduced the takbirs; may Allah reduce them (in their reward and rank)." He further said: "Indeed, I saw the Messenger of Allah (peace and blessings be upon him) say the takbir (Allahu akbar) every time he (peace and blessings be upon him) bowed, every time he prostrated, and every time he raised his blessed head from prostration."
The chain of this hadith contains a narrator named Thuwayr bin Abi Fakhitah, who is da'if (weak); however, saying the takbir at the transition to each pillar of the prayer (the takbirs of transition) is established by other authentic and reliable hadith.