The Wonder of Calculation (Karana Kutuhala)

In this way, this motion is of two kinds: one measured in minutes and seconds, which varies according to the small or large size of the planet's orbit. However, the daily motion expressed in linear distance yojana: a traditional Indian unit of distance, roughly 8-9 miles is always to be known as equal for all planets, being 11,858 yojanas and 45 minutes. In a Great Age original: "kalpa," a vast cosmic cycle, all planets are understood to wander an equal distance of 18,720,692,000,000,000 yojanas. Excluding the lunar apogee, the motions of the other "slow apogees" mandocca: the point in a planet's orbit furthest from the Earth are recorded here from other treatises. The motion of the Sun's apogee is one second of arc every seventy years. For Mars, it is one second in twelve years. For Mercury, it is one second in twelve years. For Jupiter, one in four years. For Venus, one in five years. For Saturn, one in eleven years. To repeat, their motions in minutes and seconds over ten thousand years would be as follows: generally, the motion of Mars's node pāta: the point where a planet's orbit crosses the ecliptic is one second in thirteen years. The motion of Mercury's node is one second in a little over twenty-six years. For Jupiter's node, it is one second in slightly less than twenty-four, twenty-five, or twenty-six years. For Venus's node, one second in slightly less than four years. For Saturn's node, one second in slightly less than twenty-six years. || 13 ||

Sudhākara’s Commentary:

The meaning is clear. The underlying explanation original: "vāsanā," the rational or geometric proof is very easy to follow. || 13 ||

Description of the Prime Meridian (Cities on the Line):

The City of the Demons [Lanka], Devakanya, Kanchi, the White Mountain, Paryali, Vatsagulma,
the city named Ujjayini, Gargarata, Kurukshetra, and Meru—these constitute the central meridian of the Earth. || 14 ||

Sumatiharsha’s Commentary:

One end of a string is tied at the city of Lanka and the other end is held at the peak of Mount Meru The mythical axis mundi at the North Pole. This is the central meridian. The meaning is that the cities situated directly under this string are the cities of the central meridian. || 14 ||

Procedure for Longitudinal Correction:

The distance between the meridian and one's own place in yojanas is multiplied by the planet's motion and divided by eighty original: "abhra-gajaiḥ," literally 'sky' (0) and 'elephants' (8), meaning 80.
The resulting seconds should be applied to the planet: subtract them if the place is to the east [of the meridian], and add them if it is to the west. || 15 ||

Sumatiharsha’s Commentary:

The distance in yojanas between the prime meridian and one's own location on the east-west line is used. Multiply the planet's daily motion by these yojanas and divide by eighty. The resulting seconds of arc are subtracted from the planet's position if the location is east of the meridian, and added if west. For example, by tradition, Shivapuri is located 30 yojanas west of the meridian city Gargarata (or Ujjain). Therefore, using 30 yojanas and the Sun's mean daily motion of 59 minutes and 8 seconds...

...multiplied, it gives 1774. Divided by eighty original: "agragajaiḥ," likely a scribal variant for 'abhragajaiḥ' (80), the result is 22 seconds of arc. This is the Sun's longitudinal correction deshāntara: the difference in local time/position due to longitude, which is added because the location is to the west. Having calculated this for the Moon and other planets using their mean motions, it is recorded on the leaf.
Regarding the meridian:
"The seconds of arc derived from the latitude and the Sun's position are applied for the east or west at sunset..." The commentator notes this quote is "inconsistent" or misplaced here.
The reading is inconsistent. For example, if the Sun in the central region is 1 sign, 1 degree, 3 minutes, and 14 seconds, and the correction is 22 seconds, then the longitude-corrected Sun is 1 | 1 | 3 | 36. All others should be understood in this way. || 15 ||

Sudhākara’s Commentary:

Now for the proportion. If for the yojanas of the Earth's circumference we get the motion in seconds, then what do we get for the yojanas of local distance? Here, the teacher has taken the Earth's circumference to be 4800 yojanas. From this, the resulting calculation for the longitude-related result is:
$\frac{\text{Motion (in minutes)} \times 60 \times \text{Distance (yojanas)}}{4800} = \frac{\text{Motion} \times \text{Distance}}{80}$
Thus, the rule stated is proven. || 15 ||

Secular Correction of the Planets:

The years are divided by seventy-eight and sixty-three; the results are subtracted in seconds from the Moon and Jupiter respectively.
For the Nodes, the [Lunar] Apogee, Mercury, and Venus, divide the years by thirteen, thirty, twenty-two, and nine, and add the result. || 16 ||

Sumatiharsha’s Commentary:

"Years" refers to the years elapsed since the start of the epoch karaṇa-gatābda. Divide these years by seventy-eight; the result is the seconds to be subtracted from or added to the Moon. Similarly, dividing by sixty-three gives the seconds for Jupiter. Then, dividing by thirteen, thirty, twenty-two, and nine gives the seconds to be added respectively to the Node, the Lunar Apogee, and the "Fast Apices" of Mercury and Venus. If the elapsed years are 436: divided by 78, we get 5 seconds to be subtracted/added for the Moon. Again, 436 divided by 63 gives 6 seconds of subtraction for Jupiter. 436 divided by 13 gives 33 seconds to be added for the Node. 436 divided by 30 gives 14 seconds to be added for the Lunar Apogee. 436 divided by 22 gives 19 seconds to be added for Mercury’s Fast Apex. 436 divided by 9 gives 48 seconds to be added for Venus’s Fast Apex. There is no such correction for the Sun, Mars, or Saturn; this is the tradition. People call this the "Yearly Seed Correction" abda-bīja. There are six types of operations: 1. Longitude correction, 2. Yearly seed correction, 3. Rama’s correction, 4. Degree-result correction, 5. Equation of time, and 6. Ascensional difference. Among these, longitude has been explained, and the author has already included the yearly seed correction in the initial epoch constants. Now, regarding the total amount of correction from the start of the book...