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The Rigveda mentions in several places that Vishnu measured out the Earth:

Rigveda 1.154.1–3

1 "I will declare the mighty deeds of Viṣṇu, of him who measured out the earthly regions, Who propped the highest place of congregation, thrice setting down his footstep, widely striding."

2 "For this his mighty deed is Viṣṇu lauded, like some wild beast, dread, prowling, mountain-roaming; He within whose three wide-extended paces all living creatures have their habitation."

3 "Let the hymn lift itself as strength to Viṣṇu, the Bull far-striding, dwelling on the mountains, Him who alone with triple step hath measured this common dwelling-place, long, far extended."

In fact, the measuring out of the Earth by Vishnu with three steps is a motif that occurs in many, many places in the Yajurveda, and the Samaveda, and also in many other places in the Rigveda itself.

Well, these Rigvedic verses indicate that it was Varuna, not Vishnu, who measured out the Earth:

Rigveda 5.85.5

"I will declare this mighty deed of magic, of glorious Varuṇa the Lord Immortal, Who standing in the firmament hath meted the earth out with the Sun as with a measure."

and

Rigveda 8.42.1

"Lord of all wealth, the Asura propped the heavens, and measured out the broad earth's wide expanses. He, King supreme, approached all living creatures. All these are Varuṇa's holy operations."

So who measured out the Earth? Was it Vishnu with his three steps, or was it Varuna? (I was reading one of Keshav Srinivasan's questions: "Who is addressed as "the step of Vishnu" in the Yajur Veda?" He said that the three steps of Vishnu refer to an avatar of Vishnu--Vamana the dwarf--who "made the Earth safe for humanity" by defeating the demon Mahabali by taking three steps. Does this have something to do with the answer to my question?) Or did Vishnu assign the task of measuring out the Earth to Varuna? This seems unlikely, since the Vedas say that Vishnu himself took three steps to measure out the Earth. Or was Varuna the one who measured out the Earth, and all references to Vishnu references to Vamana?

Also, as a side question: why does Rigveda 8.42.1 refer to Varuna as an asura?

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    Vishnu measuring out the Earth with three steps is definitely a reference to Vamana. I'm not sure Varuna measuring the Earth is referring to, but I doubt it's related to the story of Vamana. Also, I asked a question here about the Ashwini Kumaras measuring the Earth: hinduism.stackexchange.com/q/3281/36 – Keshav Srinivasan Feb 17 '15 at 8:42
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    The reason that Varuna is sometimes called an Asura is that he, like Chandra and Mitra, sided with the Asuras in the famous Tarakamaya war, which I discuss in this question: hinduism.stackexchange.com/q/3106/36 After that war, Varuna rejoined the side of the gods when it came time for Indra to fight the demon Vritrasura; verse 5 of this hymn of the Rig Veda is what the gods said to convince Varuna to rejoin them: sacred-texts.com/hin/rigveda/rv10124.htm They promised him that if he returned, they would make him lord of the waters. (Before he was only god of the Rita or law.) – Keshav Srinivasan Feb 17 '15 at 13:10
  • OK, thanks. So apparently multiple devas are mentioned in the Vedas as measuring the Earth out, and Vishnu's "measuring of the earth" is just a reference to Vamana the dwarf? – AdityaS Feb 17 '15 at 14:13
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    It's because Matsya did not technically save Vaivasvata Manu. He saved Vaivasvata Manu's previous birth king Satyavrata, who lived during the Chakshusha Manvantara. Satyavrata was later reborn as Surya's son Vaivasvata Manu, and it's during the Vaivasvata Manvantara (i.e. the present manvantara) that Vishnu's Vamana incarnation took place. See verse 11 of this chapter of the Srimad Bhagavatam: vedabase.com/en/sb/8/24 – Keshav Srinivasan Feb 17 '15 at 18:03
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    The verses about Vishnu talk about three steps so clearly its a reference to his Vamana incarnation whereas the ones for Varun don't mention these. It has to be a different story than the one for Lord Vishnu. – Dr. Vineet Aggarwal Jan 19 '18 at 11:06

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