Śrīmad-Bhāgavatam 5.15.6
భూమ్న ఋషికుల్యాయాముద్గీథస్తత: ప్రస్తావో దేవకుల్యాయాం ప్రస్తావాన్నియుత్సాయాం హృదయజ ఆసీద్విభుర్విభో రత్యాం చ పృథుషేణస్తస్మాన్నక్త ఆకూత్యాం జజ్ఞే నక్తాద్ద్రుతిపుత్రో గయో రాజర్షిప్రవర ఉదారశ్రవా అజాయత సాక్షాద్భగవతో విష్ణోర్జగద్రిరక్షిషయా గృహీతసత్త్వస్య కలాఽఽత్మవత్త్వాదిలక్షణేన మహాపురుషతాం ప్రాప్త: ॥ ౬ ॥
bhūmna ṛṣikulyāyām udgīthas tataḥ prastāvo devakulyāyāṁ prastāvān niyutsāyāṁ hṛdayaja āsīd vibhur vibho ratyāṁ ca pṛthuṣeṇas tasmān nakta ākūtyāṁ jajṣe naktād druti-putro gayo rājarṣi-pravara udāra-śravā ajāyata sākṣād bhagavato viṣṇor jagad-rirakṣiṣayā gṛhīta-sattvasya kalātmavattvādi-lakṣaṇena mahā-puruṣatāṁ prāptaḥ.
[bhoomna rishikulyaayaam udgeethas tatah prastaavo devakulyaayaam prastaavaan niyutsaayaam hridayaja aaseed vibhur vibho ratyaam cha prithushenas tasmaan nakta aakootyaam jajshe naktaad druti-putro gayo raajarshi-pravara udaara-shravaa ajaayata saakshaad bhagavato vishnor jagad-rirakshishayaa griheeta-sattvasya kalaatmavattvaadi-lakshanena mahaa-purushataam praaptah.]
Word-for-word
bhūmnaḥ
—
from King Bhūmā
ṛṣi-kulyāyām
—
in the womb of his wife, named Ṛṣikulyā
udgīthaḥ
—
the son named Udgītha
tataḥ
—
again from King Udgītha
prastāvaḥ
—
the son named Prastāva
deva-kulyāyām
—
his wife, named Devakulyā
prastāvāt
—
from King Prastāva
niyutsāyām
—
in his wife, named Niyutsā
hṛdaya-jaḥ
—
the son
āsīt
—
was begotten
vibhuḥ
—
named Vibhu
vibhoḥ
—
from King Vibhu
ratyām
—
in his wife, named Ratī
ca
—
also
pṛthu-ṣeṇaḥ
—
named Pṛthuṣeṇa
tasmāt
—
from him (King Pṛthuṣeṇa)
naktaḥ
—
a son named Nakta
ākūtyām
—
in his wife, named Ākūti
jajṣe
—
was begotten
naktāt
—
from King Nakta
druti-putraḥ
—
a son in the womb of Druti
gayaḥ
—
named King Gaya
rāja-ṛṣi-pravaraḥ
—
most exalted among the saintly royal order
udāra-śravāḥ
—
famous as a very pious king
ajāyata
—
was born
sākṣāt bhagavataḥ
—
of the Supreme Personality of Godhead directly
viṣṇoḥ
—
of Lord Viṣṇu
jagat-rirak-ṣiṣayā
—
for the purpose of giving protection to the whole world
gṛhīta
—
who is conceived
sattvasya
—
in the śuddha-sattva qualities
kalā-ātma-vattva-ādi
—
of being a direct incarnation of the Lord
lakṣaṇena
—
by symptoms
mahā-puruṣatām
—
the chief quality of being the leader of the human society (exactly like the chief leader of all living beings, Lord Viṣṇu)
prāptaḥ
—
achieved.
Blended reading (Sanskrit + English inline)
bhūmna ṛṣikulyāyām udgīthas tataḥ prastāvo devakulyāyāṁ prastāvān niyutsāyāṁ hṛdayaja āsīd vibhur vibho ratyāṁ ca pṛthuṣeṇas tasmān nakta ākūtyāṁ jajṣe naktād druti-putro gayo rājarṣi-pravara udāra-śravā ajāyata sākṣād bhagavato viṣṇor jagad-rirakṣiṣayā gṛhīta-sattvasya kalātmavattvādi-lakṣaṇena mahā-puruṣatāṁ prāptaḥ.
bhūmnaḥ
from King Bhūmā
ṛṣi-kulyāyām
in the womb of his wife, named Ṛṣikulyā
udgīthaḥ
the son named Udgītha
tataḥ
again from King Udgītha
prastāvaḥ
the son named Prastāva
deva-kulyāyām
his wife, named Devakulyā
prastāvāt
from King Prastāva
niyutsāyām
in his wife, named Niyutsā
hṛdaya-jaḥ
the son
āsīt
was begotten
vibhuḥ
named Vibhu
vibhoḥ
from King Vibhu
ratyām
in his wife, named Ratī
ca
also
pṛthu-ṣeṇaḥ
named Pṛthuṣeṇa
tasmāt
from him (King Pṛthuṣeṇa)
naktaḥ
a son named Nakta
ākūtyām
in his wife, named Ākūti
jajṣe
was begotten
naktāt
from King Nakta
druti-putraḥ
a son in the womb of Druti
gayaḥ
named King Gaya
rāja-ṛṣi-pravaraḥ
most exalted among the saintly royal order
udāra-śravāḥ
famous as a very pious king
ajāyata
was born
sākṣāt bhagavataḥ
of the Supreme Personality of Godhead directly
viṣṇoḥ
of Lord Viṣṇu
jagat-rirak-ṣiṣayā
for the purpose of giving protection to the whole world
gṛhīta
who is conceived
sattvasya
in the śuddha-sattva qualities
kalā-ātma-vattva-ādi
of being a direct incarnation of the Lord
lakṣaṇena
by symptoms
mahā-puruṣatām
the chief quality of being the leader of the human society (exactly like the chief leader of all living beings, Lord Viṣṇu)
prāptaḥ
achieved.
In the womb of his wife, Ṛṣikulyā, King Bhūmā begot a son named Udgītha. From Udgītha’s wife, Devakulyā, a son named Prastāva was born, and Prastāva begot a son named Vibhu through his wife, Niyutsā. In the womb of his wife, Ratī, Vibhu begot a son named Pṛthuṣeṇa. Pṛthuṣeṇa begot a son named Nakta in the womb of his wife, named Ākūti. Nakta’s wife was Druti, and from her womb the great King Gaya was born. Gaya was very famous and pious; he was the best of saintly kings. Lord Viṣṇu and His expansions, who are meant to protect the universe, are always situated in the transcendental mode of goodness, known as viśuddha-sattva. Being the direct expansion of Lord Viṣṇu, King Gaya was also situated in the viśuddha-sattva. Because of this, Mahārāja Gaya was fully equipped with transcendental knowledge. Therefore he was called Mahāpuruṣa.
Purport
From this verse it appears that the incarnations of God are various. Some are part and parcel of the direct expansions, and some are direct expansions of Lord Viṣṇu. A direct incarnation of the Supreme Personality of Godhead is called aṁśa or svāṁśa, whereas an incarnation from aṁśa is called kalā. Among the kalās there are the vibhinnāṁśa-jīvas, or living entities. These are counted among the jīva-tattvas. Those who come directly from Lord Viṣṇu are called viṣṇu-tattva and are sometimes designated as Mahāpuruṣa. Another name for Kṛṣṇa is Mahāpuruṣa, and a devotee is sometimes called mahā-pauruṣika.
— A.C. Bhaktivedanta Swami Prabhupāda
Gauḍīya Ācāryas
Viśvanātha Cakravartī Ṭhākura
Gauḍīya
Translation
In the womb of his wife Ṛṣikulyā, King Bhūmā begot a son named Udgītha. From Udgītha's wife, Devakulyā, a son named Prastāva was born, and Prastāva begot a son named Vibhu through his wife, Niyutsā. In the womb of his wife, Ratī, Vibhu begot a son named Pṛthuṣeṇa. Pṛthuṣeṇa begot a son named Nakta in the womb of his wife, named Ākūti. Nakta's wife was Druti, and from her womb the great King Gaya was born. Gaya, the best saintly king of great fame, was a portion of Viṣṇu, situated in viśuddha-sattva, who appeared for protecting the universe. He was a great personality with symptoms such as knowledge of the Lord.
Hṛdaya-jaḥ means a son. Kalā here means a portion of a portion.
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Source: vedabase.io