Lord Buddha, ninth avatar of Viṣṇu appeared circa BC 1887 in order to preach a form of disguised atheism so as to temporarily discredit the Vedas - because they were being misused at the time by brahminical priests in order to perform unsanctioned fire sacrifices (yajña, or agni-hotra) for personal gain. Lord Buddha's main teaching was the principle of non-violence, Ahimsa, taught to invoke compassion so as to spare the poor creatures being innocently killed in such fire sacrifices.
Then, this having been achieved, Adi Shankara aka Shankaracharya (a partial incarnation of Lord Śiva) appeared in Kaladi, Kerala in AD 788, defeating Adi Buddha's teachings with philosophical argument, thereby restoring the validity of the Veda and driving Buddhism out of India. That is why it is extant today only in foreign countries and has mainly died out in its country of origin.
This history is unknown to the general public and of course refuted by practising Buddhists who declare that the mortal Gautama Buddha (BC 560) arose out of nothing and therefore is not an incarnation of Vishnu.
However, all major incarnations of Lord Vishnu throughout all the Four Ages are predestined – each and every one is foretold in Vedic scripture, revealing the identity assumed by each subsequent appearance and the names of the village and family (the mother and father) that He appears in. The next, Lord Kalki, is due in 427,000 years (give or take a decade or two) to usher in the new Golden Age and the demise of the present Kali Yuga.
But of course if you're a dutiful Buddhist you shan't believe the Vedic account because you're taught not to follow the Vedas!
Generally, there seems to be some confusion that remains about the two Buddhas in different times in history. Adi Buddha, the avatar of Vishnu mentioned in the Vedas, was born circa BC 1887 to Anjana (his mother) in Kikata, later named Bodh Gaya denoting this. The later mortal, Shakya Simha Buddha or Adi Buddha, better known as Siddhartha Gautama, was born over a millennium later to Mayadevi in c. BC 560 at Lumbini, Nepal, and travelled to Bodh Gaya where he famously meditated under the banyan tree. The original Lord Buddha is the authorised avatar of Viṣṇu - and the second is the mortal atheist impostor popularly known in modern culture of whom the current practise of Buddhism is associated with, attributed to, and most people are familiar with.
There is a difference. Worshipping the original Buddha will give the guaranteed result of personal association with the Lord on the Vaikuntha planets in the Spiritual Sky – and worshipping the other will lead you to temporarily losing one's eternal individuality and merging in the brahmajyoti (the blinding spiritual effulgence emanating from the Lord's transcendental body), or the spiritual "No Man's Land", concurring with its ṡūnyavādi philosophy of nothingness.
There is a similar confusion around Kapila, of which there are at least two - the original incarnation of Lord Vishnu who expounded Samkhya philosophy; and the later mortal atheist monk. I could provide a string of references but I seriously doubt if anyone will read them all, so I'll just give this one link:
https://controversialhistory.blogspot.com.au/2014/03/is-gautama-buddha-avatar-of-vishnu.html
If you're curious do your own research, I'm sure it will be fruitful!
हरे कृष्ण
हरे कृष्ण
[footnote]
After Adi Buddha's śūnyavādi philosophy of voidism was defeated by Adi Shankara's māyāvādī philosophy, a third incarnation appeared - this time the combined form of Kṛṣṇa and Radha, as Lord Caitanya - who in turn defeated Adi Shanka's impersonalism with acintya bheda-abheda philosophy of the Supreme Lord being simultaneously one with and different from His creation. This dualist bhakti yoga - ecstatic love in devotional service to the Supreme Personality of Godhead, Lord Śrī Kṛṣṇa as preached by Lord Caitanya is also known as Dvaita-vada. Śrī Caitanya Mahaprabhu appeared in Mayapur, West Bengal in AD 1486 and established the sankirtan movement, the congregational chanting of the Lord's Holy Names, singing the famous Hare Kṛṣṇa Mahā-mantra that Iskcon devotees are renowned for in cities all around the world.
After Adi Buddha's śūnyavādi philosophy of voidism was defeated by Adi Shankara's māyāvādī philosophy, a third incarnation appeared - this time the combined form of Kṛṣṇa and Radha, as Lord Caitanya - who in turn defeated Adi Shanka's impersonalism with acintya bheda-abheda philosophy of the Supreme Lord being simultaneously one with and different from His creation. This dualist bhakti yoga - ecstatic love in devotional service to the Supreme Personality of Godhead, Lord Śrī Kṛṣṇa as preached by Lord Caitanya is also known as Dvaita-vada. Śrī Caitanya Mahaprabhu appeared in Mayapur, West Bengal in AD 1486 and established the sankirtan movement, the congregational chanting of the Lord's Holy Names, singing the famous Hare Kṛṣṇa Mahā-mantra that Iskcon devotees are renowned for in cities all around the world.
This inaugurated a Golden Age lasting 10,000 years where it is prophesised that God's name will be heard in every town and village for the benefit of every fortunate soul who is blessed with hearing the liberating transcendental sound vibration of Hare Kṛṣṇa Hare Kṛṣṇa Kṛṣṇa Kṛṣṇa Hare Hare, Hare Rāma Hare Rāma Rāma Rāma Hare Hare.
