Śrīmad-Bhāgavatam 10.14.20
Blended reading (Sanskrit + English inline)
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ajanasya
—
of one who is not born
Genitive of a- + jana. The Lord is structurally unborn; His 'births' are līlā, not karma. Bhagavān's appearance is divya-janma (BG 4.9), distinct from the jīva's bondage-birth.
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asatām durmada-nigrahāya
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for the suppression of the pride of the wicked
Compound: asat (the wicked) + durmada (intoxicated pride) + nigraha (suppression). One pole of avatāra's purpose. Echoes BG 4.8's vināśāya ca duṣkṛtām.
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sat-anugrahāya
—
for the grace of the saintly
Compound: sat (the saintly) + anugraha (grace). The other pole — paritrāṇāya sādhūnām (BG 4.8). Note the asymmetry: the demons are crushed, the devotees are graced. Bhagavān's two hands.
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tiryakṣu
—
among animals
Locative plural of tiryañc — that which moves crookedly, animals. Even Bhagavān becomes Varāha, Hayagrīva, Matsya. No species is too low for His descent. Brahmā's egalitarianism is a function of Kṛṣṇa's lovingness, not philosophical universalism.
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yādaḥsu
—
among the aquatics
Locative plural of yādas — sea-creature. Matsya-avatāra named by its habitat. The deepest reach of Bhagavān's descent: into the water where even sight fails.
Among the demigods Lord Kṛṣṇa appears in such forms as Vāmanadeva, among the sages as Paraśurāma, among human beings as Lord Kṛṣṇa Himself and as Lord Rāmacandra, and among animals as the boar incarnation. Lord Kṛṣṇa appears among the aquatics as Matsya, the gigantic fish. Indeed, the plenary expansions of the Supreme Personality of Godhead are innumerable, as the Lord relentlessly comes down within the universes to smash the false pride of the atheists and show mercy to the saintly devotees. In another sense, the Lord never appears, since He exists eternally. His appearance is like that of the sun, which is always present in the sky but which periodically appears to our vision.
You thus appear in various places in various avatara forms, showing your true form to prevent your devotees from being defeated by these jnanis. To defeat the non devotees (asatam) who think they are learned, and to show mercy to the devotees(satam), so they can remember your spiritual, blissful forms, qualities and pastimes, you appear in different avatara forms. For it is said "O Lord, cause of all causes, if Your transcendental body were not beyond the modes of material nature, one could not understand the difference between matter and transcendence. Only by Your presence can one understand the transcendental nature of Your Lordship, who are the controller of material nature. Your transcendental nature is very difficult to understand unless one is influenced by the presence of Your transcendental form." 10.2.35
The Lord is called ajanasya because he does not take birth like material beings, but appears on his own by his svarūpa-śakti, only for protecting his devotees. He is not attached to material activities. That is described in this verse. O Lord! O controller endowed with inconceivable energy, who appears as unlimited avatāras! In his commentary on the previous verse Śrīdhara Svāmī says the verse answers the objection “O Brahmā! Why do you call the pure conscious forms I showed material māyā?” Brahmā answers by saying “Your manifestations as guṇa and līlā avatāras are related to an independent māyā with special functions.” This means that the Lord reveals his forms of śuddha-sattva different from matter by his independent māyā. In those forms the Lord is not overcome by material māyā. By complete unity with pure consciousness because of pure śuddha-sattva, his form is everything. The jīva becomes controlled by māyā, which is dependent on the Lord and obtains a material form of rajas and tamas and becomes overcome by that. Not understanding his spiritual nature because of the contamination of rajas and tamas, he accepts his material body as everything. That is the difference. Because the word māyā will be used for the svarūpa-śakti, it will be shown that his idea and mine are the same.
To benefit the ignorant, by your unconditional mercy you appear in many forms. Ajanasya refers to he who causes no birth for the devotees. With false pride the ignorant think that they know the scripture and have perfected yoga. You defeat the proud by refuting their ideas. By hearing with devotion about your pastimes, their misconceptions are eradicated. Not only do you appear to defeat the proud but to please the devotees. For the devotees you defeat the ideas of the ignorant, establish proper dharma, and reveal your sweet pastimes. Why do you show mercy to the materialists? O supreme independent (prabho)! Or how can their evil desires be destroyed? O capable one! (prabho)! There is nothing that you cannot do. O manifestor of the avatāras (vidhātaḥ). You are suitable for these purposes mentioned as an avatāra. Or because they are bewildered by māyā, they see your avatāras as jīvas since they hear about your birth for instance. Actually like me, they are your manifestations. Just as I, Viṣṇu and Śiva, for creation, maintenance and destruction manifest, these avatāras appear for their particular purposes without birth etc. like jīvas. The suras refers to upholders of dharma like Nara-nārāyaṇa. Or how do you appear among the devotees? Verse 18 mentioned that Kṛṣṇa alone was real. That is illustrated in verse 19. For purpose of creation you appear as Brahmā. For defeating materialists and pleasing devotees you appear among them as Nara-nārāyaṇae etc. Thus even in the material world the devotees know you as real, either as one or many.
A surgeon enters every ward of his hospital — operating room, paediatric, geriatric, even animal — in different scrubs but the same hands. Kṛṣṇa descends among demigods, sages, humans, animals, and aquatics; the scrubs change, the hands do not. Avatāras are species-specific scrubs of one Bhagavān.
The Bhāgavatam catalogues Kṛṣṇa's descents through species: Matsya as a fish, Kūrma as a tortoise, Varāha as a boar, Nṛsiṁha as half-lion, Vāmana as a brāhmaṇa boy (SB 1.3, 2.7). Each appearance was timed to a particular distress and a particular devotee.
Verse 20 is Brahmā summarizing this catalogue from above: ajanasya janma — the Unborn takes birth precisely because devotees need Him in their particular form. Mercy is species-aware.
My note
Source: vedabase.io