The Universal System of Astronomy, Part Two

Since it is limited to a single direction, the sum of the sine of the longitude bhujajyā; the horizontal component of the planetary position is at its maximum. Therefore, by the cosine-gnomon koṭi-śaṅku and the thread aligned with the sun, the multipliers for the northern direction are set down. These are established; then, in the region of seventy degrees, at the location of the arc, the reduction of the center occurs. The proper multiplier of the sine, whose multipliers are the lights... are the cosines koṭi... as stated in the previous opinion.

Its nature is not [merely] small. By three... the result in fingers aṅgula; a traditional unit of measurement roughly equal to the width of a finger is obtained. It is extended by the length of the fingers... with the width of a finger... or by another method it is well-known and should be done. Just as the ears... the face and the sides are bound with cloth and a wick.

Here is the derivation:
original: atropattiḥ; this marks the beginning of the formal geometric proof common in Sanskrit scientific texts.

When the noon-sun madhyārka is in the southern hemisphere dakṣiṇa-gola, the gnomon śaṅku; a vertical pillar used to cast a shadow for measurement is at its lowest. The cosine koṭi is the result-sine, and the hypotenuse karṇa is the distance from the eye. In this position, the calculation of the minutes of arc kalā is done. From the radius trijyā; the total radius of the circle, usually taken as 3438 minutes in Indian trigonometry, the minutes are calculated. Above the cosine, the sine is equal. That which is the maximum gnomon parama-śaṅku is the hypotenuse. The radius is the hypotenuse... the cosine is given here. In the calculation board, which represents the center, the measure is given in fingers aṅgula and other units.