Treatise on the Sun

5 9

And thus it moves. From the intersection of the ropes emerging from the mouth and tail of the fish original: "matsya"; a traditional Indian geometric construction where two intersecting arcs create a fish-like shape used to draw a perfect North-South or East-West line, one should draw a circle that encompasses the three points of the shadow. The circle does not deviate from its path,

The shadow created by the line remains fixed like a clear bamboo staff. 38 = 6

standing upright. 38. Now, the calculation of the time by the inverse method: the desired shadow chāyā is multiplied by the radius trijyā; the standard radius used in calculations, often 3438 minutes of arc and divided by the hypotenuse of the shadow chāyā-karṇa. 39.

The result is the sine of the zenith distance dṛgyā. The square of that is subtracted from the square of the radius; the square root of the remainder is the gnomon śaṅku; here referring to the sine of the Sun’s altitude. That gnomon is multiplied by the radius and divided by the sine of the colatitude lambajyā. 40.

This is then multiplied by the radius and divided by the radius of the day-circle dyujyā; the radius of the circle the sun travels on a specific day. The result is the sine of the altitude unnatadjyā, which is subtracted from the arc of the day antyā. The remaining value is converted into its arc kārmuka. 41.

Using the sine kramajyā, the time in respirations asavaḥ; a unit of time equal to 4 seconds before or after noon is determined. Now, the calculation of the Sun from the shadow at midday at one’s own location:

Radius • what Twice-thrice-radius Gemini-Cancer Radius • what Own-day-circle • this

The day-arc antyā of the desired time is multiplied by the sine of the colatitude and divided by the hypotenuse of the digits? of the shadow. 42. The resulting sine of declination krāntijyā is multiplied by the radius and divided by the maximum declination paramāpakrama; the tilt of the Earth, approximately 24 degrees in ancient Indian astronomy.

The arc of that result is known as the Sun’s position, beginning with Aries. One should state the position of the Sun from that. 43. At the desired time—at midday, or before or after—the distance between the arms of the shadow, combined with the intersection of the "fish" arcs, creates the movement of the shadow's path. 44. The hypotenuse of the shadow is multiplied by the sine of the altitude and divided by the radius of the day-circle. 45. In one's own month, the values are: 795, 1814. Subtracting these from the arcs of the radius, one finds the specific values. Now, the rising times at the equator laṅkodayāsavaḥ; the time it takes for zodiac signs to rise at the Earth's equator starting from Aries: 46.

Aries: 1670 The manuscript transcription "610" likely refers to the "1670" standard value; Taurus: 1795; Gemini: 1935. These values, when reduced by the local ascensional difference cara; the correction for the observer's latitude, become the rising times at one's own location. 47. These are used in reverse order for the following signs. These six signs, and similarly those from Libra onwards, are calculated in reverse order. 48. Now, the method for calculating the ascendant lagna; the point of the zodiac rising on the eastern horizon at the desired time:

The rising time already passed gatāstavaḥ and the time yet to come bhogyāstavaḥ are to be calculated based on the Sun's position and the desired time, using the rising times of the signs.