SB 1.3 - King Pṛthu and Matsya
(9) Prayed for by the sages, the Lord accepted the body of a king (Pṛthu), who cultivated the land to yield produces, and for that reason the earth was beautiful and attractive. He appeared from the right arm of King Veṇa in a golden complexion. Because he milked herbs and other things from the earth, he is considered the most desirable of the avatāras. Before Pṛthu, there was a great havoc of maladministration due to the vicious life of His father. The brāhmaṇas dethroned the king and prayed for the Lord to appear. The brāhmaṇas, however, do not occupy the royal throne because they have much more important duties for the welfare of the public.
(10) When there was a complete inundation after the period of Cākṣuṣa Manu, the Lord accepted the form of a fish (Matsya) and protected the person who would be Vaivasta Manu, keeping him up on a boat. Also the future seven sages remained in the boat. Matsya tied the boat to the pinnacle of the Himālayas and disappeared. When the waters receded, the Manu and the sages performed their respective services. Śrīdhara Svāmī says there is not always a devastation after the change of every Manu, but this illusory inundation took place to show some wonders to King Satyavrata. But Jīva Gosvāmī and Viśvanātha Cakravartī Ṭhākura have given proofs from various scriptures to show that there is always a devastation after the end of each and every Manu. Matsya appeared twice in this day of Brahmā. The first time during the rule of Svāyambhuva Manu, after killing the demon Hayagrīva who had stolen the Vedas, He recovered them. At the end of Cākṣuṣa manvantara, He showed mercy to Satyavrata by putting him on a boat with other things. It should be understood that Matsya will appear at the end of every Manvantara, and thus there will be 14 appearances of Him.