"The Messenger of Allah ﷺ used to say the takbir every time he got up, went down, stood and sat. Abu Bakr, 'Umar, and 'Uthman (did likewise)." (Using translation from Nasāʾī 1149)  

«كَانَ رَسُولُ اللهِ ﷺ يُكَبِّرُ فِي كُلِّ رَفْعٍ وَوَضْعٍ وَقِيَامٍ وَقُعُودٍ وَأَبُو بَكْرٍ وَعُمَرُ وَعُثْمَانُ»  

Whenever Messenger of Allah ﷺ stood for the prayer, he said Takbir on starting the prayer and then on bowing. On rising from bowing he said, "Samiʿa llahu liman hamidah," and then while standing straight he used to say, "Rabbana laka-l hamd" (Al- Laith said, "(The Prophet ﷺ said), 'Wa laka l-hamd'." He used to say Takbir on prostrating and on raising his head from prostration; again he would Say Takbir on prostrating and raising his head. He would then do the same in the whole of the prayer till it was completed. On rising from the second rakʿa (after sitting for at-Tahiyyat), he used to say Takbir. (Using translation from Bukhārī 789)  

أَنَّهُ سَمِعَ أَبَا هُرَيْرَةَ يَقُولُ كَانَ رَسُولُ اللهِ ﷺ إِذَا قَامَ إِلَى الصَّلَاةِ يُكَبِّرُ حِينَ يَقُومُ ثُمَّ يُكَبِّرُ حِينَ يَرْكَعُ ثُمَّ يَقُولُ «سَمِعَ اللهُ لِمَنْ حَمِدَهُ» حِينَ يَرْفَعُ صُلْبَهُ مِنَ الرَّكْعَةِ ثُمَّ يَقُولُ وَهُوَ قَائِمٌ «رَبَّنَا لَكَ الْحَمْدُ» ثُمَّ يُكَبِّرُ حِينَ يَهْوِي سَاجِدًا ثُمَّ يُكَبِّرُ حِينَ يَرْفَعُ رَأْسَهُ ثُمَّ يُكَبِّرُ حِينَ يَسْجُدُ ثُمَّ يُكَبِّرُ حِينَ يَرْفَعُ رَأْسَهُ ثُمَّ يَفْعَلُ ذَلِكَ فِي الصَّلَاةِ كُلِّهَا حَتَّى يَقْضِيَهَا وَيُكَبِّرُ حِينَ يَقُومُ مِنَ الثِّنْتَيْنِ بَعْدَ الْجُلُوسِ