Treatise on the Sun

Now, that which was mentioned previously is explained in detail (28). Having subtracted the planet's position from its slow-anomaly mandocca the apogee, or the point where the planet is furthest from Earth or from its fast-anomaly śīghra the perigee/conjunction point, the remainder is called the anomaly kendra. From that, one derives the base-sine bhujajyā and the cosine koṭi (29).

In an odd quadrant the 1st and 3rd 90-degree sections of the orbital circle, the part already traversed is the base-sine, and the part remaining to be traversed is the cosine. However, in an even quadrant the 2nd and 4th 90-degree sections, the part to be traversed is the base-sine, and the part already traversed is the cosine (30).

Divide the minutes of arc 1/60th of a degree by 225 original: "tattva-yamaiḥ" — 25 and 2, indicating 225, the standard interval for sine tables. The result is the number of sine-segments jyāpiṇḍa already passed. Multiply the remainder by the difference between the current and the next sine-segment, and divide the result by 225 original: "tattva-locanaiḥ" — 25 and 2 (31).

The result obtained should be added to the value of the sine-segment already passed. This is the method for the Order Sine kramajyā; it is also remembered as the rule for Versed Sines utkramajyā (32). To find the arc from a given sine, multiply the remainder by 225 and divide by the difference. Add this to the total number of minutes represented by the passed segments (33).

For the Sun, the degrees of the slow-epicycle manda-paridhi are 14 original: "manavaḥ" — the 14 Manus. For the Moon, they are 32 original: "radāḥ" — the 32 teeth. These values apply at the end of even quadrants; in the odd quadrants, they are decreased by 20 minutes for both (34).

At the end of the even quadrants, the values for the other planets are: 75 original: "adri-indriya" — 7 and 5, 30 original: "khāgni" — 0 and 3, 33 original: "surāḥ" — the 33 gods. For the Sun, it is 45 original: "nava-iśavāḥ" — 9 and 5, perhaps a variation or specific calculation. In the odd quadrants, the values are 12, 28, 32, 11, and 88 original: "gajāḥ" (35).

Regarding Mars and the other planets, one should subtract from the end of the even quadrants the values: 235 original: "agni-dasrakāḥ", 133 original: "guṇāgni-candrāḥ", 70 original: "kha-nagā", 66 original: "du-rasā", 262 original: "liptā", and 29 original: "go-nayaḥ". At the end of the odd quadrants, the values are: 232, 22, 72, 26, and 40. These are proclaimed for the "fast" calculation śīghra-karma (37).

The difference between the odd and even quadrant values should be multiplied by the base-sine and divided by the radius. When the even value is smaller, add it; when the odd value is smaller, subtract it. This yields the "true" epicycle (38). With that corrected value, multiply the base-sine and cosine, then divide by the 360 degrees of the circle...