The Wonder of Calculation (Karana Kutuhala)

The Sun in degrees original: "lavadiko raviḥ" $= A - \frac{13 A}{903}$. From this, in one solar year of 365 days, 15 minutes, 30 seconds, 22 thirds, and 30 fourths, the Sun's position is calculated as $360° 0' 0'' 2''' 15''''$. However, the true Sun is exactly $360°$. The difference between these two is $0° 0' 0'' 2''' 15''''$, which equals $\frac{9 \text{ units}}{4 \times 60 \times 60} = \frac{1}{1600}$.

Furthermore, by multiplying the elapsed years of the current era the Kalpa by "sky, atmosphere, sky, and sun" original: "khabhrakharkair"; code for 12,000 and so on, the cycles of revolutions are $1,972,947,179 + 1,175 + \text{remainder} = 1,972,948,284 + \text{remainder}$. By simplification, we get $4,284 + \text{remainder}$. Here, the result produced from the explicit parts is already refined within the additive constant kshepa: a fixed value added to a calculation to account for the planet's position at the start of the epoch. The result related to the remainder is $\frac{3 \times \text{remainder}}{200}$. This itself is the result in minutes and further units produced in one year $= \frac{3}{200}$. By applying the correction for the difference brought forward previously, the correction for one year becomes $= \frac{3}{200} + \frac{1}{1600} = \frac{25}{1600} = \frac{1}{64}$. By proportion, for the desired number of years, it becomes $\frac{\text{Years}}{64}$. Thus, everything is mathematically proven.

Now, regarding the remainder of $4,284 + \text{remainder} = 6,000$, as long as it follows the method stated by the Teacher referring to Bhaskara II, the author, the Sun's motion is continuous. Otherwise, the wise should understand it as discontinuous. That difference is $1,716$; this difference in year-counting will occur from the start of the work, so everything is faultless. In this way, the method of bringing the positions of all planets near to their true values should be performed with one's own sharp intellect. Enough of further elaboration.

Calculation of the Mean Moon—

The count of days Ahargana multiplied by fourteen original: "shakra"; the 14 Indras and diminished by the seventeenth original: "svatyashti"; code for 17 part, results in the Moon in degrees. Then, subtract the result in degrees and further units obtained by dividing the day-count by eight thousand six hundred original: "khabhra-sara-ashta"; 8600. ॥ 8 ॥

Sumatiharsa The Commentator—

"Of the days" original: "ahnam" etc. For an example of this: Let the day-count Ahargana be 159,316. Multiplied by "the Indras" (fourteen), it becomes 2,230,424. The day-count multiplied by fourteen is then diminished by the "seventeenth" part. Dividing 2,230,424 by 17, we obtain degrees and units as $131,200; 12, 4, 42$. Subtracting this from 2,230,424 gives $2,099,222; 35, 18$. Now for the correction: the day-count 159,316 is divided by "sky, atmosphere, arrows, and eight" 8,600. The resulting degrees and units are $18; 31, 30$. Subtracting this from the previous value of 2,099,222...

...leaves $2,099,204; 3, 48$. As before, calculating revolutions and remaining signs, we get $5,831$ revolutions, $11$ signs, $14$ degrees, $3$ minutes, and $48$ seconds. When added to its epochal constant kshepa of $10$ signs, $29$ degrees, $5$ minutes, and $50$ seconds, the Mean Moon is found. The revolutions are $5,832$; the position starting from signs is $0$ signs, $13$ degrees, $9$ minutes, and $38$ seconds. ॥ 8 ॥

Calculation of the Apogee Ucca: the point where the planet is farthest from Earth—

The day-count is placed in two positions; the sum of the results obtained by dividing by nine original: "go" and by four thousand twelve original: "ina-abhra-veda"; 12, 0, 4, read as 4012 becomes the Moon’s apogee in degrees and further units. ॥

Sumatiharsa—

The day-count 159,316 is placed in two positions. In one, it is divided by "the cows" (nine), yielding $17,701; 46, 40$ in degrees and units. In the other position, the day-count 159,316 is divided by "the Sun, atmosphere, and Vedas" (four thousand twelve), yielding $39; 42, 35$. Adding these results gives $17,741; 29, 15$. Calculating revolutions as before, we get $49$ revolutions, $3$ signs, $11$ degrees, $29$ minutes, and $15$ seconds. Adding the epochal constant of $4$ signs, $15$ degrees, $12$ minutes, and $59$ seconds, the resulting Moon’s apogee is $4$ signs, $17$ degrees, $26$ minutes, $42$ seconds, and $14$ thirds. ॥

Calculation of the Node Pata: the ascending node of the Moon, Rahu—

From the day-count placed in two positions, divided by nineteen original: "anka-chandra"; 9 and 1 and by twenty-seven hundred original: "kha-kha-bha"; 0, 0, 27, the sum of the degrees becomes the Moon's node. ॥ 9 ॥

Sumatiharsa—

From the day-count 159,316 placed in two spots: in one, divided by "numerals and the Moon" (nineteen), the degrees and units are $8,385; 3, 9$. In the other, divided by "sky, sky, and asterisms" 27 asterisms (twenty-seven hundred), the result is $59; 0, 21$. The sum of these two results is $8,444; 3, 30$. Calculating revolutions as before: $23$ revolutions, $5$ signs, $14$ degrees, $3$ minutes, and $30$ seconds. Adding the epochal constant of $9$ signs, $17$ degrees, $25$ minutes, and $9$ seconds, the mean node becomes $2$ signs, $4$ degrees, $3$ minutes, $12$ seconds, $8$ thirds, and $39$ fourths. ॥ 9 ॥

Calculation of Mars and the Mercury's Fast Apogee—

The day-count multiplied by eleven original: "rudra"; the 11 forms of Shiva is placed in two positions. Divided by twenty-one original: "shashi-maya" and by fifty-two thousand four hundred forty-four original: "veda-abdhi-siddha-ishu"; 4, 4, 4, 52, the sum of the results is Mars.
The day-count multiplied by four original: "veda" and added to its own part divided by four hundred thirty-three original: "dahana-abdhi"; 3, 4 becomes degrees; then subtract the day-count divided by one hundred twenty-one thousand original: "gana-akshiti-yama-indra"... ॥ 10 ॥

Sumatiharsa—

The day-count 159,316 is multiplied by "the Rudras" (eleven), resulting in 1,752,476. In one place, divided by "the Moon and Maya" (twenty-one), the degrees are $83,451; 14, 17$. In the other, divided by "the Vedas, oceans, Siddhas, and arrows" (fifty-two thousand four hundred forty-four), the degrees are $33; 24, 58$. The sum of these two results is $83,484; 39, 15$. Previously...