|Canto 1: Creation||Chapter 3: Krishna Is the Source of All Incarnations|
Bhaktivedanta VedaBase: Srimad Bhagavatam 1.3.25
namna kalkir jagat-patih
atha -- thereafter; asau -- the same Lord; yuga-sandhyayam -- at the conjunction of the yugas; dasyu -- plunderers; prayeshu -- almost all; rajasu -- the governing personalities; janita -- will take His birth; vishnu -- named Vishnu; yasasah -- surnamed Yasa; namna -- in the name of; kalkih -- the incarnation of the Lord; jagat-patih -- the Lord of the creation.
Thereafter, at the conjunction of two yugas, the Lord of the creation will take His birth as the Kalki incarnation and become the son of Vishnu Yasa. At this time the rulers of the earth will have degenerated into plunderers.
Here is another foretelling of the advent of Lord Kalki, the incarnation of Godhead. He is to appear at the conjunction of the two yugas, namely at the end of Kali-yuga and the beginning of Satya-yuga. The cycle of the four yugas, namely Satya, Treta, Dvapara and Kali, rotates like the calendar months. The present Kali-yuga lasts 432,000 years, out of which we have passed only 5,000 years after the Battle of Kurukshetra and the end of the regime of King Parikshit. So there are 427,000 years balance yet to be finished. Therefore at the end of this period, the incarnation of Kalki will take place, as foretold in the Srimad-Bhagavatam. The name of His father, Vishnu Yasa, a learned brahmana, and the village Sambhala are also mentioned. As above mentioned, all these foretellings will prove to be factual in chronological order. That is the authority of Srimad-Bhagavatam.
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His Divine Grace A. C. Bhaktivedanta Swami Prabhupada, Founder Acarya of the International Society for Krishna Consciousness