The above translation states that the Lord descends in three yugas: Satya, Treta, and Dvapara. Or rather, the translation doesn't say that, but the commentary does. This makes no logical sense to me, because the Satya Yuga seems to be the age when everything is perfect, thereby non-necessitating an Incarnation of the Lord to fight demons and atheists.
For example, the "earlier" Incarnation of the Lord is Matsya, but if we correlate the Satya Yuga with the "Garden of Eden" (i.e. when everything is perfect), even the Matsya Incarnation would occur when Manu (i.e. Adam) had already left Eden (when the Satya Age had ended). Therefore the Manu that Matsya helps would be equivalent to Noah, but this wouldn't be in the Satya Yuga, it would be in the... Treta Yuga?
Furthermore we can't even really locate a pure Vaishnava Incarnation like Rama and Krishna as far back as the Satya Age anyways. (We only have animal Incarnations like Matsya, Kurma, and Varaha. Perhaps Narasimha would count as a "Perfect Incarnation," but even so, why would the Lord incarnate in the Satya Yuga?) It would seem to make more sense that the Lord would incarnate in the following three ages: Treta, Dvapara, and Kali, since there would be actual work to be done in those ages, both "intellectual," and "material."
But if everything is perfect... why an Incarnation of the Lord?
This makes way more sense to me:
- Rama in Treta
- Krishna in Dvapara
- Kalki in Kali
We can't really equivocate the Buddha with a "personal" Incarnation of the Lord because he doesn't even teach a theistic doctrine, rather he seems to represent the gradual decline of theism after its peak, which reaches its perfect expression in the Mahabharata (with Krishna). If we consider the Lord as Time, Time definitely reaches its full stature in the Krishna Incarnation, specifically because Krishna is involved in all aspects of life, material and spiritual, the Buddha seems to represent old age and death, this is probably why Krishna is regarded as the purnavatara. Even Krishna Himself states: "I am Time, grown to full stature." After the peak, there can only be the decline.
But it also seems like Kalki is explicitly theistic and IN the Kali Age, so it would make some sense for Kalki to be a personal Incarnation of the Lord. This website has some good information, particularly this page. This also makes sense.
Sometimes Vishnu descends personally, sometimes he sends his bonafide representative in the form of his son or servant, and sometimes he comes himself in a disguised form.
For example, personal descents would include: Rama, Krishna, and Kalki.
Representative in the form of a servant, maybe Muhammad (s.a.w.). Representative in the form of his son, maybe Jesus. As a disguised Incarnation, maybe ‘Ali. (There are some sects of Islam that believe ‘Ali was God, veiled by Muhammad (s.a.w.).)
For example, it's easy to provide correlations between Islam and Hinduism, Islam is the youngest religion and Hinduism is the oldest.
In all three "personal" Incarnations of the Lord, he always comes in "catur-bhuja" form, meaning he always comes with three co-incarnations or relatives who aid him in his fight against atheism. When he was Rama, he came with Laksmana, Bharata, and Satrughna. When he was Krishna, he came with Balarāma, Pradyumna, and Aniruddha. When he was Kalki, he came with Kavi, Sumanta, and Prajna.
This four-armed form doesn't occur for Incarnations like the Buddha, for example. Maybe the Buddha isn't even the "Lord of the World," but at that point we'd be bringing Theosophy into this.
Even in the Islamic "Incarnation" of ‘Ali, we find the Lord disguised by Muhammad (s.a.w.), literally veiled (i.e. hijab).
The most explicit Incarnation is Krishna, but even Krishna states that He is "veiled by His Divine Maya, unknown to the world."
For example, in Gaudiya Vaishnavism, we have, Krishna -> Balarāma, and then Balarāma -> Vāsudeva, Sankarsana, Pradyumna, and Aniruddha.
In Islam we have God (Allāh (s.w.t.)) -> Muhammad, and then Muhammad -> ‘Ali, Fatir (i.e. Fatima), Hasan, and Husayn.
If we want to add Samba, we add Muhsin.
Either way the correlation is clear. ‘Ali seems more like a "disguised" or veiled Incarnation (i.e. by Maya, the ism, or the hijab) then a "personal" Incarnation. But even Krishna in the Gita speaks of being veiled by His Divine Maya.
Veiled by My creative power (yogamaya) I am not revealed to all. This bewildered world knows Me not, the unborn, the unchanging. [Gita Society]
The idea that God (the ma'na) is a "veiled" "Incarnation" who appears concealed by a second divinity called the ism or hijab, is an Islamic one, possessed by a sect called the Nuṣayrī‐ʿAlawīs.