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## Gommatasara Karmakanda - 782
**5.2 Proof**
The half-cut of the fifth square root of the Palyaka is 31, the half-cut of the sixth square root of the Palyaka is 6. Adding these three quantities, we get the 64th part of the seven times the half-cuts of the Palyaka (6 6 6 cut). This is 8 times less than the sum of the aforementioned three quantities. Similarly, by adding the half-cuts of the seventh, eighth, and ninth square roots of the Palyaka, which are half of the previous ones, we get the proof. For example:
The half-cut related to the seventh square root of the Palyaka is 128, the half-cut related to the eighth square root of the Palyaka is 0, the half-cut related to the ninth square root of the Palyaka is 6. Adding these three quantities, we get the 512th part of the seven times the half-cuts of the Palyaka, which is the aforementioned proof. This proof is 8 times less than the sum of the three square roots from the fourth onwards. In this way, by adding the half-cuts of three consecutive square places, the result becomes 8 times less each time.
Similarly, the half-cuts of the eighth, seventh, and sixth squares of the Palyaka's square rod are 256, 128, and 64 times the half-cuts of the Palyaka's square rod respectively. Adding these three quantities (256+128+64), we get 448 times the half-cuts. And the half-cuts of the fifth, fourth, and third squares of the Palyaka's square rod are 32, 16, and 8 times the half-cuts of the Palyaka's square rod respectively. Adding these three quantities (32+16+8), we get 56 times the half-cuts. This quantity is 56 times the half-cuts of the Palyaka's square rod, but it is 8 times less than the previous quantity. And the half-cuts of the second, first square, and the square rod of the Palyaka's square rod are 4, 2, and 1 times the half-cuts of the Palyaka's square rod respectively. Adding these three quantities (4+2+1), we get 7 times the half-cuts of the Palyaka's square rod, but this is also 8 times less than the previous quantity. In this way, the quantity becomes 8 times less each time.
Here, the square root of the Palyaka is the first root, the square root of the first root is the second root, the square root of the second root is the third root. Similarly, we can know the fourth and subsequent roots. And by squaring the Palyaka's square rod, we get the first square, by squaring the first square, we get the second square, by squaring the second square, we get the third square. Similarly, we can know the fourth and subsequent squares.
In this way, by adding the half-cuts of the first, second, and third roots of the Palyaka, we get a quantity. Starting from this quantity, we add the half-cuts of three consecutive places, and continue this process until we reach the sum of the half-cuts of the second, first square, and the Palyaka's square rod. All the sums obtained in this process are to be arranged separately in seven places, one after the other, in the form of a structure. In this way, the half-cuts of three consecutive square roots of the Palyaka become 8 times less each time.| SR No. | 090180 |
| Book Title | Gommatasara Karma kanda |
| Original Sutra Author | N/A |
| Author | Nemichandra Siddhant Chakravarti, Jawaharlal Shastri |
| Publisher | Shivsagar Digambar Jain Granthamala Rajasthan |
| Publication Year | |
| Total Pages | 871 |
| Language | Hindi |
| Classification | Book_Devnagari, Discourse, Philosophy, & Religion |
| File Size | 20 MB |