The Universal System of Astronomy, Part Two

Ti-Ti-Vi These are likely abbreviations for technical time units or specific observation points, possibly tithi (lunar day) and vighaṭī (a unit of time equivalent to 24 seconds). In the innermost part [of the instrument], the shadow of the gnomon original: kīla; a central pin or rod used to cast a shadow should be located in this section. Because of its multiple purposes, the position of the shadow there—in that location on the ground nearby—represents the intervening parts between the observers. This [line of] sight is the zenith distance original: natāṃśa; the angular distance of a celestial body from the point directly overhead, which is one [unit]. The center of the solar disk original: sūrya-vimba-kendra is positioned there.

In those three regional divisions, the visible portion is [measured] in yojanas original: yojana; a traditional Indian unit of distance, roughly 8 to 9 miles, used here to map celestial distances onto the instrument. Furthermore, the distance between the various positions of the shadow is indeed called the zenith distance.

With the knowledge of the right-angle line original: sama-sūtra; a fundamental alignment line used in Indian astronomy to ensure the instrument is level, one should summarize [the data]. Having perfected the shadow, it is situated in its place. The shadow, measured in yojanas, is established in those positions. || 9 ||

The zenith distance multiplied by the [position of] the Sun's tip is explained in the four verses regarding the primary importance. From the position of the zenith distance, that same value is adjusted in the direction of the region. The Sun's center [is observed] through the instrument original: yantra. From the gnomon-pin at the top to the single line, and the tip of the shadow of the gnomon... || 9 ||

The measure of the face/opening, and so on... Night etc. The marginal note indicates that these rules may also apply to nighttime observations, perhaps involving the moon or stars. The equinoctial shadow original: palaprabhā; the length of the shadow cast by a vertical gnomon at noon on the day of the equinox at a specific latitude is multiplied by the gnomon. The result is separated by the difference. Following the path of the day, when there is equality, [the calculation] is completed.

8. In the same way, the zenith distance is the multiplier for the shadow. The result is produced by that measure. Here, the desired [value] is multiplied and destroyed original: nihantṛ; in a mathematical context, this means to multiply or calculate out a value...