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## Verse 420-421
**Verse 420:** When the desired quantity is divided by the half-sections of the given quantity, the quotient obtained is the multiplier for the given quantity.
**Verse 421:** When the half-sections of the world are divided by the half-sections of the given quantity, and the quotient is divided by the sum of the numbers of the desired position, the quotient obtained is the multiplier for the world. This multiplier is also used for the final position of the Parāvādī.
**Explanation:**
* **Verse 420:** If the given quantity is 4, its half-sections are 2. If the desired quantity is 256, its half-sections are 8. Dividing 8 by 2, we get 4. Multiplying the given quantity (4) by itself 4 times (4 x 4 x 4 x 4), we get the desired quantity (256). This verse explains the first Karana Sutra.
* **Verse 421:** If the given quantity is 4, its half-sections are 2. The world (256) has 8 half-sections. The sum of the numbers of the final position of the Parāvādī (64) is 2080. Dividing the half-sections of the world (8) by the half-sections of the given quantity (2), we get 4. Dividing the sum of the numbers of the final position (2080) by 4, we get 520. Multiplying the world (256) by itself 520 times, we get the multiplier for the final position of the Parāvādī.
**Note:** The given quantity here is actually an infinitesimal part of the infinite Pravāli. Dividing its half-sections by the half-sections of the world, we get...
**References:**
* Dhavla Purana, Vol. 1, Page 5
* Dhavla Purana, Vol. 1, Page 50-51