The Universal System of Astronomy

Siddhānta Sārvabhauma, Folio 11 Now, for the purpose of generating the specific values using the Constant Pulverizer sthira-kuṭṭaka: a mathematical algorithm used to solve linear indeterminate equations to find integer solutions, the dividend, divisor, and remainder are set down.

The Dividend bhājya: the number to be multiplied by the unknown is 1,563,336. The remainder is 0? and 1?.

Following the rule of "mutual division of the two" and so on, when the remainder is zero, the Common Factor apavartaka: the greatest common divisor used to simplify the equation is found to be 24. The Divisor hāra: the number that divides the product is 1,555,200,000.

By dividing both by this common factor (24), the Reduced Dividend dṛḍha-bhājya becomes 661,258 Mathematical note: 1,563,336 divided by 24 is actually 65,139; the manuscript or transcription may contain a calculation error here and the Reduced Divisor dṛḍha-hāra becomes 64,800,000.

The Reduced Additive dṛḍha-kṣepa is the residue of the intercalary months adhimāsa-śeṣa divided by the same factor. Now, to simplify the Constant Pulverizer, the value of 1 is used as the additive. By mutually dividing the dividend and divisor, the chain of quotients valli: a column of integers derived from the Euclidean algorithm is produced:

10, 6, 1, 5, 13

The divisor is 64,800,000. /4/2/2/2/ Below this, the additive is placed. Through the process of multiplying the term above by the one below and adding the last, and then discarding the last term repeatedly, the pair of results rāśi-yugma is produced:

189,900 and 672,581,360.

These are then reduced by the dividend and divisor respectively. To achieve the desired result, these are multiplied by the simplified remainder. This is how the total Omitted Days avamāni: the difference between lunar and solar days for the world-age are calculated, as explained previously.

Note The residues blot/correction? are removed. Divided by the lunar months of a world-age, the residues... 2. The Reduced Dividend and Reduced Divisor are 30... from the Moon, this is obtained. Following the previously stated method, the Reduced Divisor is naturally produced... solar... at the end of the solar month... below the solar degrees. 31.

The value 1,030,000 original: "kharāmattahaṃ," a code for the number 1,030,000 using the Katapayadi system is the divisor for the omitted days. Through this, the minutes and other units are found. These are multiplied by the Sun's position... the Moon is moved by the strength of the lunar days. 32. Therefore, by the result known as "Omitted" mentioned before, combined with the midnight position, the remainder is obtained. This is the understanding of the ocean-like knowledge of the calculation of time. 33.

For the Constant Pulverizer, the Dividend 25,082,252 and the Divisor 2,603,000,008 are reduced by four.
The Reduced Dividend is 6,270,563.
The Reduced Divisor is 650,750,002.

Following the previously stated method, the chain of quotients is:
0, 13, 2, 1, 1, 7, 1, 5, 1, 1, 6, 1, 2, 5, 5, 1, 2, 7, 5, 1, 1, 0.

The pair of results is 8,953,325 and 722,367...

Scribe Mark: Rama 2