Small Manual of Astronomical Computation with the Commentary of Paramesvara

Now, the Second Chapter.

Now begins the Chapter on the Three Questions.

The equinoctial shadow multiplied by twenty, then diminished by its own fifth part, and then divided by three;
these are the multipliers for the signs of the arc of the Sun starting from the North Equinox to find the ascensional difference. || 1 ||

The Chapter on the Three Questions is now explained: "Multiplied by twenty," etc. When the Sun with precession original: "Sāyana-arka"; the tropical sun used for seasonal calculations reaches the end of Pisces, the shadow of a twelve-digit gnomon term: "Gnomon" (Shanku); a vertical rod used to measure time and latitude by its shadow at midday is called the equinoctial shadow. The digits of the equinoctial shadow of one's own location multiplied by "nails" (twenty) becomes the multiplier for the first sign of the arc. Again, those digits of the equinoctial shadow multiplied by twenty and diminished by their own "axis-portion" original: "svākṣāṃśa"; interpreted here as one-fifth becomes the multiplier for the second sign of the arc. Again, those digits of the equinoctial shadow multiplied by twenty and divided by three becomes the multiplier for the third sign of the arc. These are the multipliers for the signs of the arc of the Sun starting from the North Equinox. This is what is meant: having placed the Sun with precession at the desired time and calculating the signs of the arc, one should multiply the first sign by the first multiplier, the second by the second, and the third by the third separately, and then sum them. The result will be the "ascensional difference" in vināḍīs term: "Vināḍī"; a unit of time equal to 24 seconds. In this way, the ascensional difference for others should also be taken. || 1 ||

Two-hundred seventy-eight, two-hundred ninety-nine, and three-hundred twenty-three, in direct and inverse order;
diminished by half of their respective ascensional difference factors, and in the middle six signs, the opposite, are the risings. || 2 ||

"Two-hundred seventy-eight," etc. The measures of the rising times at the equator original: "Lanka"; the traditional Hindu astronomical reference point on the equator for the sign of Aries is 278 vināḍīs. For Taurus, it is 299. For Gemini, it is 323. These are applied in direct and inverse order, then direct and inverse again. Thus is the knowledge of the rising measures at the equator. However, at one's own location, they are "diminished by half of their respective ascensional difference factors, and in the middle six signs, the opposite." This is what is meant: 278 diminished by half of the first ascensional difference factor are the rising measures for Pisces and Aries. 299 diminished by half of the second factor are the rising measures for Aquarius and Taurus. 323 diminished by half of the third factor are the rising measures for Capricorn and Gemini. Again, 323 increased by half of the third factor are the rising measures for Sagittarius and Cancer. 299 increased by half of the second factor are the rising measures for Scorpio and Leo. 278 increased by half of the first factor are the rising measures for Libra and Virgo. Thus, the rising measures for one's own location are to be brought forth. || 2 ||

The Sun increased by the rising times of the signs and the time of the query through proportion
is the Ascendant; likewise, if the Sun is increased to equal the Ascendant, the result is the time. || 3 ||

1. Variant: ...starting from the equinox for the Sun...

2. Variant: ...they are. Like the Sun, for others...