Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s7.1

v2.c12.s7.1

The Adhikāra on three problems is so called in our astronomical works because it deals with the questions of direction, region and time. The method of determining directions is given in it in different ways. It is explained how to find the ascendant for a given moment or conversely the unknown moment from the given ascendant. The calculation by other methods is also possible, e.g. four shadows, etc. The question of ‘deśāntara’ (longitude) from Ujjain is usually dealt with in the chapter on mean motions and therefore omitted in this chapter. It, however, contains methods for finding the distance of a place from the equator, that is, latitude. The question of shadow is dealt with at considerable length. For calculation, a gnomon 12 ‘aṅgulas’ long, is taken as the unit while determining the length of the shadow. What will be the length of the shadow cast by a gnomon at a given moment and in what direction it would fall, and what would be the length and direction of the shadow cast by the Sun (or a planet) posited on any side of the gnomon, and such other questions are included under “determination of shadow”. The authors preceding *Bhāskarācārya* have given only the method of calculating the shadow cast by the gnomon in an East-West, North-South, and the (four) intermediate directions. *Bhāskarācārya* alone has described the method of finding the shadow cast by the gnomon when the sun stands in any direction with regard to it. And on this point he proudly remarks :