The Universal System of Astronomy, Part Two

Regarding the horizon kṣitija; the horizontal baseline of the instrument, when observing the total sine samastajyā; the chord or full sine on the Earth-surface original: bhūmau; referring to the base of the quadrant, the Earth-line bhūrekhā extending to the edge of the horizon is considered one unit of measure for that region.

The R-sine kramajyā; the standard trigonometric sine used in Indian astronomy is similarly determined. From the term "sky-direction-degrees," the total sine is observed on the base. Starting from that point and extending to the center kendra, the Earth-line constitutes one unit of measurement for the R-sine. The half-earth-line original: arddhaca-bhūrekhā... its measure as a sine is self-evident. Otherwise, in its natural position, the horizon-sines kṣitijyā are indeed the R-sines. Each of these is marked in digits aṅgula; a standard unit of measurement, roughly a finger-breadth, and these must be known by the practitioner.

The sine-lines jyārekhā are not all established by simple measurement. In this way, the Sky-line ākāśarekhā; the vertical axis representing the zenith... provides the successful calculation of the R-sine.

Because of the eighteen sines, twelve digits the standard length of a gnomon (shadow-casting pole) in Indian astronomy is 12 digits remain from the center... This is the altitude-complement koṭi; the vertical side of the right-angled triangle. From the eighteen sines, seven parts are taken; these constitute the sine-arm bhuja; the horizontal side of the triangle. The equinoctial shadow palabhā; the shadow cast by a vertical gnomon at noon on the day of the equinox of the object at the center extends to that point.

The sine is the "arm" (bhuja). This Earth-line extending to the center is situated within the circumference paridhi of the astronomical circle. This is established through careful effort and observation...

From the middle of the center... the parts are made manifest... The final lines of the transcription are fragmentary and appear to describe the physical engraving or manifestation of the degree marks on the instrument's surface.