SB 1.3.26
avatara hy asankhyeya
hareh sattva-nidher dvijah
yathavidasinah kulyah
sarasah syuh sahasrasah
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
O brahmanas, the incarnations of the Lord are innumerable, like rivulets flowing from inexhaustible sources of water.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The list of incarnations of the Personality of Godhead given herein is not complete. It is only a partial view of all the incarnations. There are many others, such as Sri Hayagriva, Hari, Hamsa, Prsnigarbha, Vibhu, Satyasena, Vaikuntha, Sarvabhauma, Visvaksena, Dharmasetu, Sudhama, Yogesvara, Brhadbhanu and others of the bygone ages. Sri Prahlada Maharaja said in his prayer, “My Lord, You manifest as many incarnations as there are species of life, namely the aquatics, the vegetables, the reptiles, the birds, the beasts, the men, the demigods, etc., just for the maintenance of the faithful and the annihilation of the unfaithful. You advent Yourself in this way in accordance with the necessity of the different yugas. In the Kali-yuga You have incarnated garbed as a devotee.” This incarnation of the Lord in the Kali-yuga is Lord Caitanya Mahaprabhu. There are many other places, both in the Bhagavatam and in other scriptures, in which the incarnation of the Lord as Sri Caitanya Mahaprabhu is explicitly mentioned. In the Brahma-samhita also it is said indirectly that although there are many incarnations of the Lord, such as Rama, Nrsimha, Varaha, Matsya, Kurma and many others, the Lord Himself sometimes incarnates in person. Lord Krsna and Lord Sri Caitanya Mahaprabhu are not, therefore, incarnations, but the original source of all other incarnations. This will be clearly explained in the next sloka. So the Lord is the inexhaustible source for innumerable incarnations which are not always mentioned. But such incarnations are distinguished by specific extraordinary feats which are impossible to be performed by any living being. That is the general test to identify an incarnation of the Lord, directly and indirectly empowered. Some incarnations mentioned above are almost plenary portions. For instance, the Kumaras are empowered with transcendental knowledge. Sri Narada is empowered with devotional service. Maharaja Prthu is an empowered incarnation with executive function. The Matsya incarnation is directly a plenary portion. So the innumerable incarnations of the Lord are manifested all over the universes constantly, without cessation, as water flows constantly from waterfalls.