There are three types of bodies of the Buddha in Mahayana - Dharmakaya, Nirmanakaya and Sambhogakaya.
I believe that the concepts of Dharmakaya (eternal truth form) and Nirmanakaya (physical form) originated from the following sutta quote.
The Buddha downplayed the importance of his physical form and advised Ven. Vakkali to focus on the teachings, stating that when one sees the Buddha, one sees the Dharma (teachings), and when one sees the Dharma, one sees the Buddha.
In other words, the Dharma is what the Buddha stands for, and the Dharma is what the Buddha represents. The Dharma (teachings) is his eternal "form".
Vakkali: “For a long time, venerable sir, I have wanted to come to see
the Blessed One, but I haven’t been fit enough to do so.”
Buddha: “Enough, Vakkali! Why do you want to see this foul body? One
who sees the Dhamma (teachings) sees me; one who sees me sees the
Dhamma (teachings). For in seeing the Dhamma (teachings), Vakkali, one
sees me; and in seeing me, one sees the Dhamma (teachings).
Vakkali Sutta (SN 22.87)
I believe that the concept where the Nirmanakayas of all the past Buddhas emanate from one Dharmakaya originates from the following sutta quote.
It simply means that all the past and future Buddhas rediscover, understand and teach the same Dharma (teachings), because it is the natural law.
Hence their physical appearance as teachers, emanate from the Dharma (teachings) as their one eternal "form". In other words, all the Buddhas stand for the same Dharma (teachings) and all the Buddhas represent the same Dharma (teachings).
& he who is the Buddha now,
removing the sorrow of many —
all have dwelt,
will dwell, he dwells,
revering the true Dhamma.
This, for Buddhas, is a natural law.
Therefore one who desires his own good,
aspiring for greatness,
should respect the true Dhamma,
recollecting the Buddhas' Teaching.
Garava Sutta (SN 6.2)
And what about the Sambhogakaya (enjoyment/ reward form, or perhaps inspirational form)?
I speculate that it's related to the following quote.
When one recollects the Buddha, who he was, what he achieved, what he contributed and what he stood for, that person becomes inspired and his fears dispelled. So, this inspirational mental image of the Buddha is the Buddha's inspirational "form". He can manifest in this "form" to inspire and dispel fear.
But bhikkhus, I say this: If you have gone to a forest or to the foot
of a tree or to an empty hut, and fear or trepidation or terror should
arise in you, on that occasion you should recollect me thus: ‘The
Blessed One is an arahant, perfectly enlightened, accomplished in true
knowledge and conduct, fortunate, knower of the world, unsurpassed
leader of persons to be tamed, teacher of devas and humans, the
Enlightened One, the Blessed One.’ For when you recollect me,
bhikkhus, whatever fear or trepidation or terror you may have will be
Dhajagga Sutta (SN 11.3)
So, you can say that this is the inspirational form of the Buddhas which bless people's minds.