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## Twelfth Body-State] [105 Narakas]
The bound Vaikriya bodies of the 105 Narakas are equal in number to the Nairyikas, as each Naraka has one bound Vaikriya body. Since the number of Naraka beings is innumerable, the number of their bound Vaikriya bodies is also innumerable. Describing this innumerability through time and space, the scriptural scholars say:
**In terms of time:** If one body is taken away at each moment in both the Utsarpini and Avasarpini kalpas, then all the bodies of the innumerable Utsarpini and Avasarpini beings are taken away. In other words, the number of bound Vaikriya bodies of Narakas is equal to the number of moments in the innumerable Utsarpini and Avasarpini kalpas.
**In terms of space:** They are as numerous as the innumerable श्रेणियाँ (Shreṇīs). And an innumerable part of a प्रतर (Pratar) is called a श्रेणी (Shreṇī). The number of bound Vaikriya bodies of Narakas is equal to the number of celestial regions in these innumerable श्रेणियाँ (Shreṇīs).
Now the question arises: If there are innumerable श्रेणियाँ (Shreṇīs) in the entire प्रतर (Pratar), in half of the प्रतर (Pratar), in one-third of the प्रतर (Pratar), and so on, then how many श्रेणियाँ (Shreṇīs) should be considered here? To resolve this curiosity, the Bhulpaṭha says: "An innumerable part of the प्रतर (Pratar)." This means that the number of श्रेणियाँ (Shreṇīs) to be considered here is equal to the number of श्रेणियाँ (Shreṇīs) in an innumerable part of the प्रतर (Pratar).
Then, to specify their particular size, it is said that the list of the विष्कम्भ (Vishkambha) of those श्रेणियाँ (Shreṇīs), i.e., the list of their extent, is as follows:
A श्रेणी (Shreṇī) of one प्रदेश (Pradesha) is equal to the quantity obtained by multiplying the first square root of an angula by its second square root. The meaning is that there are innumerable square roots of the number of प्रदेश (Pradeshas) in a region of one angula measure. For example, the square root of the first square root is the second square root, the square root of the second square root is the third square root, and so on, there are innumerable square roots in succession. Therefore, in the present context, one should imagine a list of as many प्रदेश (Pradeshas) as are obtained by multiplying the first square root by the second square root. Then, extend it lengthwise in the south-north direction. The number of श्रेणियाँ (Shreṇīs) that this established list touches should be considered here.
For example, although there are innumerable प्रदेश (Pradeshas) in a region of one angula measure, let us assume it to be 256 for the sake of calculation. The first square root of this number 256 is sixteen (245=10+6=16). The second square root is 4, and the third square root is 2. Of these, multiplying the second square root, which is four, by the first square root, which is sixteen, gives us 64. So, we should consider only this many श्रेणियाँ (Shreṇīs).
The scriptural scholars say the same thing in another way: "Or, one should consider श्रेणियाँ (Shreṇīs) equal to the cube of the second square root of an angula." This means that one should consider श्रेणियाँ (Shreṇīs) equal to the cube of the second square root, i.e., four, of the number of प्रदेश (Pradeshas) in a region of one angula measure. The cube of a quantity is obtained by multiplying its square by the same quantity. For example, the cube of two is eight. It is as follows: The square of the quantity two is four, multiplying this (four) by two gives us the number eight. Therefore, the cube of the quantity two is eight. Similarly, here also, the square of the quantity four (4) is sixteen, multiplying this (sixteen) by the quantity four gives us the cube of four, which is sixty-four (64). Thus, there is no real difference between these two methods. Here, the वृत्तिकार (Vṛttikāra) gives a third...