[Machine] Ibn Umar and Zaid bin Thabit used to say the takbir and perform the ruku' when they come to the imam while he is in the ruku' position.  

كَانَ ابْنُ عُمَرَ وَزَيْدُ بْنُ ثَابِتٍ إِذَا أَتَيَا الْإِمَامَ وَهُوَ رَاكِعٌ كَبَّرَا تَكْبِيرَةً وَيَرْكَعَانِ بِهَا  

(Another chain) with similar meaning. (Using translation from Tirmidhī 3093)   

عَنْ عَبْدِ اللهِ بْنِ مَسْعُودٍ  

[Machine] If he (the imam) catches up with them while they are bowing, prostrating, or sitting, he should make two takbeers. Malik said, "As for the bowing and prostration, that is what we know. But as for the two takbeers for sitting, I do not know this." I said, "Does he make one takbeer to start with and sit with it?" He (Malik) said, "Yes." The sheikh said, "If this narration of Ibn Mas'ud is authentic, it is possible that he meant it for the prostration, so he made the takbeer for the opening supplication. When he finished the opening supplication, the imam raised his voice with one takbeer and sat with it. He (the follower) follows him in his supplications and actions, and the same goes for the prostration. He (the imam) intended the imam's takbeer for prostration after the opening supplication for the prayer and his following of it. And Allah knows best.  

إِنْ أَدْرَكَهُمْ رُكُوعًا أَوْ سُجُودًا أَوْ جُلُوسًا يُكَبِّرُ تَكْبِيرَتَيْنِ فَقَالَ مَالِكٌ أَمَّا فِي الرُّكُوعِ وَالسُّجُودِ فَذَلِكَ الْأَمْرُ الَّذِي نَعْرِفُهُ وَأَمَّا تَكْبِيرَتَيْنِ لِلْجُلُوسِ فَإِنِّي لَا أَعْرِفُ هَذَا قُلْتُ يُكَبِّرُ وَاحِدَةً يَسْتَفْتِحُ بِهَا وَيَجْلِسُ بِهَا؟ قَالَ نَعَمْ قَالَ الشَّيْخُ إِنْ صَحَّ هَذَا عَنِ ابْنِ مَسْعُودِ فَيُحْتَمَلُ أَنْ يَكُونَ أَرَادَ بِهِ فِي السُّجُودِ فَكَبَّرَ لِلِافِتِتَاحِ فَلَمَّا فَرَغَ مِنَ الِافْتِتَاحِ رَفَعَ الْإِمَامُ بِتَكْبِيرَةٍ وَقَعَدَ فَيُوَافِقُهُ فِي أَذْكَارِهِ وَأَفْعَالِهِ وَكَذَلِكَ فِي السُّجُودِ أَرَادَ أَنْ يَكُونَ تَكْبِيرُ الْإِمَامِ لِلسُّجُودِ بَعْدَ افْتِتَاحِهِ لِلصَّلَاةِ وَاقْتِدَائِهِ بِهِ وَاللهُ أَعْلَمُ  

[Machine] If he catches them in a bowing position, he will say two Takbirs, one Takbir for the opening of the prayer, and one Takbir for the bowing, and he has caught the Rak'ah.  

إِذَا أَدْرَكَهُمْ رُكُوعًا كَبَّرَ تَكْبِيرَتَيْنِ تَكْبِيرَةً لِافْتِتَاحِ الصَّلَاةِ وَتَكْبِيرَةً لِلرُّكُوعِ وَقَدْ أَدْرَكَ الرَّكْعَةَ