It is narrated from Ibn Shihab that Sayyiduna Abdullah bin Umar and Zayd bin Thabit (may Allah be pleased with them both) came while the imam was bowing; they said a single takbir and went into bowing.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2588
It is reported from al-Zuhri (may Allah have mercy on him) that when Zayd bin Thabit (may Allah be pleased with him) entered the mosque and the people were bowing, he faced the qiblah, said the takbir and went into bowing, then, while still in the state of bowing, he walked softly until he joined the row.
Urwah bin al-Zubayr (may Allah have mercy on him) also used to do the same.
Imam al-Bayhaqi (may Allah have mercy on him) said: We have already mentioned before this the narration of Abdullah bin Mas'ud (may Allah be pleased with him).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2589
(a) It is narrated from Sayyiduna Ibn Mas'ud (may Allah be pleased with him) that if a man finds the people praying in congregation in bowing, prostration or sitting, he should say two takbirs. Imam Malik (may Allah have mercy on him) said: As for bowing and prostration, we know this ruling, but two takbirs in the state of sitting are not within my knowledge. The narrator asked: Should he begin the prayer with a single takbir and sit down? He said: Yes.
(b) Imam al-Bayhaqi (may Allah have mercy on him) said: If this narration is authentic from Sayyiduna Ibn Mas'ud (may Allah be pleased with him), it is possible that he meant this in the case of prostration, that is: he said the takbir to begin the prayer, and the imam, saying one takbir, rose from prostration and sat; the ruling for him then is that he conforms to the imam in his words of remembrance and his actions.
And likewise it would be in prostration, that is: the imam said the takbir for prostration, and he began the prayer with a single takbir and followed the imam.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2590
It is narrated from Umar bin Abd al-Aziz (may Allah have mercy on him) that when a person finds the people bowing, he should say two takbirs, one to begin the prayer and the other for bowing; when he has done so, he has caught the rak'ah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2591