The Universal System of Astronomy

SSB 8 original: "si-sā-bho," abbreviation for Siddhānta Śiromaṇi Bhāṣya, page 8 This staff instrument, which has been described, is the singular essence of all observation. 85

By looking at a planet or object through one eye from both the tip and the base of the staff, and by drawing a line from the base of that staff, the distance on the ground is the base bhuja: the horizontal side of a right-angled triangle. 86

The perpendicular distance from the eye to the ground is the vertical koṭi: the upright side of a right-angled triangle. The staff itself is the hypotenuse śruti: the diagonal connecting the base and the vertical produced by the observation. From this direct perception, all measurements are known by wise men through the application of mathematical proportions. 87

The base and the vertical, when multiplied by the radius and divided by the staff length, yield the sines of the zenith distance nata-aṃśa: the angular distance from the point directly overhead and the altitude unnata-bhāga: the angular height above the horizon respectively. This is the method for determining those values. 88

9 By observing the Pole Star original: "dhruva" ...and? the Sun, the result of the base calculation provides the equinoctial shadow equinoctial shadow original: "palabhā," the shadow cast by a vertical gnomon at noon on the day of the equinox. One should establish this using the stated method when the opportunity arises. 89

Regarding the measurement of a bamboo pole original: "vaṃśa," often used in Sanskrit geometry as a placeholder for any vertical height to be measured and similar objects: the product of the base and the height, divided by the vertical, gives the distance from the root of the pole to the observer on the ground. 90

The ground distance multiplied by the vertical obtained from sighting the top of the pole, and divided by the sighting distance eye-level, gives the result: the height of the pole. 91

By merely sighting the tip, one can find the interval between the ground and the base of the pole. The ground measurement is found by using the sine ...sine? corresponding to the pole’s tip. 92

Whether sitting or standing, the locations of the base and the vertical must be known; here, the vertical is known from the sighting of the top of the pole. 93

The distance from the eye is determined by the vertical divided by its own base; from this, the ground and the pole’s height are known separately as before. The proof for this lies in the known 94 distance from the root of the straight pole.

By the previously described method of using a "hidden" assumption original: "gupta-prakalpa," likely a method of algebraic substitution or the "rule of supposition", the nature of the degrees is found through two separate sightings. 95

The vertical is multiplied by its own... here, the height of the pole is found by adding the height of the observer’s eye to the result of the sighting. If the pole's measurements are equal, there is no difference in the pole's dimensions. 96

By subtracting the unknown original: "avyakta," an algebraic term for a variable from the other side, the distance on the ground is established. This objective for the purpose of sighting was previously taught by Bhaskara in his own treatise. 97

For example: Sighting the top of a pole situated above a desired staff, the base is seen to be four cubits; the staff is then moved or "placed" such that it is some number of fingers... 98