The Universal System of Astronomy

Verse 54–55

A circle with a radius trijyā: the standard sine of 90 degrees used as a base unit should be carefully drawn upon a level patch of ground. In the center of this circle, a staff yaṣṭi equal in length to the radius should be fixed, pointing toward the zenith original: koṇ-mukha, literally "facing the corner," here implying the overhead point or vertical alignment. This staff must be established with great precision. 54

A plumb line dropped from the tip of this staff represents the gnomon śaṅku. From the center of its base, the sine of the altitude dṛg-jyā is laid out. From the position of the staff, the tip of the shadow is then produced. 55

Verse 56–57

Where the shadow touches the edge of the circle, an east-west line is drawn, appearing like an arrow original: śara-vat, likely referring to the segment of a circle or the "sine" line. The interval between the northern and southern portions provides the known measure of the staff. Through the center of the radius nābhi-trijyā, one calculates the dimensions. 56

By dividing the solar value, the resulting figure is joined to the end of the shadow. This, when multiplied by the measures of the gnomon, determines the solar amplitude arka-jāgrā: the distance of the Sun at sunrise from the east-west line in either the north or south direction. 57

Verse 58–61

Regarding the rising and setting points, using the method previously described as the "five planets" pañca-gra-prākāra: a technical method for determining planetary positions or coordinates, the sine of the altitude is adjusted, and the northern direction is fixed. 58

The east-west line is maintained there. One should mark the path on the circle like a hunter tracking an arrow. Then, from the center, another line representing the day-radius dyujyā: the radius of the diurnal circle on which the Sun moves is established, following the same threefold essence. 59–60

Between the center and the tips of the shadow-staff, the measure of the cord is taken. That measure represents the full sine sampūrṇa-guṇo: the chord of the arc. In whatever region this is used, that same arc appears on the second circle. 61

Verse 61 (continued)–62

By the number of divisions, the time elapsed since sunrise ahargata is found when the Sun is in the eastern hemisphere; if the Sun is in the western hemisphere, the remaining time until sunset is found. This is calculated using the line of the rising and setting sun on the eastern circle. 61

Using the end of the cord and a twelve-digit gnomon original: dvādaśa-nara, the standard 12-finger-breadth gnomon, the beautiful state of the shadow is determined. The clear mathematical proofs vāsanā: the underlying logic or derivation of a formula for these calculations have thus been stated by me. 62

Verse 63–64

This instrument was described by Gaṇeśa Gaṇeśa Daivajña, author of several 16th-century astronomical treatises for the purpose of understanding time. It should be constructed with its various parts according to one’s own requirements, ensuring it is neither too thick nor unstable, and derived from the circles and arcs. 63

Beyond these measures, the instrument should be made in correct proportion, following the numerical specifications of its various angles. It must always be fashioned with a stable support to ensure its length and orientation remain true for the intended calculations. 64

From the base and all around, the total length and dimensions...