The Universal System of Astronomy, Part Two

In accordance with the rules of the manuscript, there are twelve cells original: dvādaśa koṣṭhā designated for the sines jyā. In a similar way, if the maximum cosine parama-koṭijyā is established as the base... then by the Rule of Three anupāta; a mathematical proportion, the cosine koṭijyā is calculated. When multiplied by twenty-five original: pañcaviṃśa and divided by the divisor, the result is more than seventeen original: saptadaśa.

The maximum earth-sine parama-kujyā; the sine of the arc of the sun's daily circle between the horizon and the six-o'clock circle is positioned within the circle. This is derived from the sine of the declination krānti-jyā, which is placed as before. From the three points... at the half-point of the intersection, the sine and cosine original: jyā-ko are formed where the radius trijyā acts as the hypotenuse karṇa. From this, another primary earth-sine kujyā is found.

Thus, appearing from the center kendra... when the time is known, one calculates the maximum ascensional difference sine parama-carajyā; the sine of the difference between the sun's right ascension and oblique ascension based on the radius.

The resulting earth-sine and the sine of the circle's position are established. These parts are then divided. Following the measurement of the point connected to the maximum ascensional difference sine, a line rekhā is drawn. By means of two observations original: dṛṣṭikābhyāṃ... the protected ascensional difference sine carajyā is found. Just as the radius serves as the hypotenuse, this value extends until the boundary of the line. The maximum ascensional difference sine acts as the hypotenuse... and by the two observations, the ascensional difference sine is identified once more, extending to the limit of the line.