As the ocean of milk is churned a dark young man in yellow silk rises carrying the pot of amrita: Dhanvantari, a portion of Vishnu, the physician of the gods. The asuras snatch the pot. The Harivamsha and the Vishnu Purana tell his second birth as the son of the childless king of Kashi, who divides Ayurveda into eight; the Sushruta Samhita opens with Sushruta learning from Divodasa Dhanvantari of Kashi.
The ocean gives up the cow, the horse, the elephant, the gem, the tree, the dancers, then Lakshmi, who chooses Vishnu, then Varuni, whom the asuras take.
The churning goes on and a young, dark, lotus-eyed man in yellow silk rises with a pot full of amrita.
He is Dhanvantari, a portion of a portion of Vishnu, master of medicine, with a right to a share of sacrifice.
The asuras seize the pot by force; the gods appeal to Vishnu.
Vishnu promises to set the asuras quarrelling; they argue over who drinks first; Mohini follows.
After Surabhi, the horse, Airavata, the Kaustubha, the Parijata and the apsaras, Lakshmi rises and chooses Vishnu; Varuni rises and the asuras take her. The sons of Kashyapa churn again and a strongly built, very young man rises, blackish, with reddish eyes, long arms, a conch-marked neck and broad chest, garlanded, in yellow garments with pearl earrings and bangles, carrying a jug full of nectar. He is Dhanvantari, a plenary portion of a portion of Vishnu, expert in medicine and entitled to a share of sacrifice. The asuras seize the jug by force; the gods take shelter at Vishnu's feet; he promises to set the asuras at odds by his own power; they quarrel over the first drink, the weaker urging a share for the gods to delay the stronger, and Vishnu comes as Mohini.
Harivamsha 29, Vishnu Purana 4.8, Bhagavata 9.17 and the Sushruta Samhita
North India · Kashi (Varanasi)Vaishnava🪔 Dhanteras
In the Harivamsha the physician rises out of the amrita vessel itself, stands before Vishnu and is named Abja, water-born; he asks to be Vishnu's son and to have a share of sacrifice and a place in the world; Vishnu refuses the share (already divided, and he was born after the gods) but promises fame, powers in the womb, worship by the twice-born, the division of Ayurveda into eight parts and a second birth in the second Dvapara. Then Dirghatapas, the childless king of Kashi of Sunahotra's line, does austerities, the god appears and is born as his son Dhanvantari, learns Ayurveda from Bharadvaja, divides it into eight and teaches his disciples; his son is Ketumat, then Bhimaratha, then Divodasa, king of Varanasi. The Vishnu Purana gives the same line with the father as Dirghatamas and Narayana's boon; the Bhagavata (9.17.4) makes Dhanvantari the son of Dirghatama, an incarnation of Vasudeva whose remembered name frees from disease. The Sushruta Samhita opens with Aupadhenava, Vaitarana, Aurabhra, Paushkalavata, Karavirya, Gopurarakshita and Sushruta approaching Kashiraja Divodasa Dhanvantari in his ashram; he tells them Brahma composed Ayurveda, taught it to Prajapati, the Ashvins and Indra, and from Indra he received it and has come to earth again to teach it, in eight branches; they ask for surgery first.
What is different here:
Rises from the vessel, not carrying it; asks for and is refused a share of sacrifice; the second birth in Kashi, Bharadvaja, the eight branches, the line to Divodasa and the teaching of Sushruta are not in the Bhagavata's churning chapter.
Sources: Srimad-Bhagavatam 8.8 (Bhaktivedanta Vedabase); Harivamsha, Harivamsha Parva, chapter 29: the Kashi kings and the birth of Dhanvantari (English, harivamsam.arasan.info; Sanskrit with verse numbers, dvaipayana.net); The Vishnu Purana, tr. H. H. Wilson (1840), Book IV chapter VIII: sons of Ayus, the kings of Kasi, former birth of Dhanwantari (sacred-texts, read on a mirror); Bhagavata Purana 9.17, The Dynasties of the Sons of Pururava (English translation, Vedabase); Sushruta Samhita, Sutrasthana 1 (Vedotpatti adhyaya), Sanskrit of the 1938 Acharya edition, Wujastyk's Sushruta Samhita project on saktumiva.org; Puranic Encyclopaedia (Vettam Mani), entry Dhanvantari, on Wisdom Library