The Universal System of Astronomy

Siddhānta Sārvabhauma original: "Si. Sā. Mau."; the "Universal Doctrine" written by Munīśvara in 1646

Verse 31-40

At the thirtieth division of the circumference, the wise observer should fix the position of the Sun Taraṇi: the Sun; specifically referring to the solar longitude. 31 Here, having placed the plate paṭṭikā: a calibrated strip or plate used on astronomical instruments at the stated solar degree, the mark that appears on the instrument board phalaka: the main body or "face" of the instrument indicates the stars. Below the north-pointing cord, the distance between the circumference and the vertical line determines the "inclination of the hour" namra-nāḍyāḥ: the time-angle or the depression of the hour-line. 32

Having determined the sine of the co-latitude lambajyā: the trigonometric sine of the angle complementary to the observer's latitude, the sine of the time in ghaṭikās: units of 24 minutes should be calculated. This sine, when inverted, is placed on the ground-plane. If the shadow falls exactly on the mark of the gnomon-pin yaṣṭi: a small rod or stylus used to cast a shadow at the thirty-degree point, then that is the shadow's measure. 33

The proof upapatti: the mathematical derivation or rationale for this should be done on a well-drawn circle. From that, the Sun-god described the four-sided instrument called the Board. 34

Following the previously mentioned method, the width of the radius trijyā: the "radius-sine" or the sine of 90 degrees is twelve digits original: arkāṅgula; 'Arka' (Sun) represents the number 12. In a place calculated by the final sine parāntyā: the sine of the maximum declination, the length is measured as if at the North Pole sumeru: the mythological mountain at the North Pole, used as a reference for 90-degree latitude. 35

This circle should be set up as explained by the ancient masters; it must be fashioned with care. In the middle of its length, a suspension chain śṛṅkhalā: a chain or ring used to hang the instrument so it remains vertical should be held as the support. 36

This instrument is made of two sections from the base. Following the previously mentioned method, the maximum sine of altitude drgjyakā: the sine of the zenith distance should be applied here. 37

A line measuring one-third of the radius of the instrument is drawn. Where the shadow of the rays of the Sun Aryama: another name for the Sun falls, at the end of that calculation, a hole chidra is to be made. 38

The circle is marked by the radius from the center according to the digits of the gnomon. In this circle, the degrees are marked for the purpose of knowing the Sun's altitude. The number 65 is noted original: svarasāśca; 'sva' (1) and 'rasa' (6), though the context suggests a specific graduation of 65 or 66 units. 39

To understand the time in ghaṭī, a plate equal to the measure of the final sine is fixed at its base. A pin with a hole is provided there, through which the altitude is clearly revealed. 40

According to the teaching on the "Great Gnomon" and the base, the product of the square... The text breaks off into mathematical formulas involving the sine of the day and the radius

The mark is the product of the equinoctial shadow and the hypotenuse. At that place, the vertical sine is composed of two times twenty-four degrees. The hypotenuse of the gnomon is always twelve digits. What is the hypotenuse? The product is always the measure of the radius. The maximum sine of the time-arc is at thirty-three degrees or more. When the planet is placed on the plate, the result of the board... therefore the measure given for this board is established. That is to say, the offset of the direction is equal to the gnomon's hypotenuse. There, the gnomon is twelve digits. By the measure of the three qualities, the plate is fixed on the board. The gnomon is 30, and the shadow moves to the north. This is the method. Thus it is well-said.