पृष्ठम्:महाभास्करीयम्.djvu/१४६

LATITUDE AND COLATITUDE, ZENITH DISTANCE AND ALTITUDE 61 "When to the radius of the circle of shadow corresponds the shadow of the gnomon, what will correspond to the radius of the celestial sphere? The result is the Rsine of the Sun's zenith distance". Rules for finding the latitude and colatitude and the zenith distance and altitude of the Sun : 5. Multiply the radius by (the length of) the shadow and (at another place) by (the length of) the gnomon. Divide (the two results) separately by the square root (obtained above). When this calculation is performed for an equinoctial midday, the (two) results denote the Rsine of the latitude and the Rsine of the colatitude (respectively); elsewhere, they denote the great shadow (i.e., the Rsine of the Sun's zenith distance) and the great gnomon (i.e., the Rsine of the Sun's altitude) (respectively).¹ That is Rsin and = -Rsin C = Rsin z = Rsin a = equinoctial midday shadow x radius hypotenuse of equinoctial midday shadow gnomon X radius hypotenuse of equinoctial midday shadow shadow x radius hypotenuse of shadow gnomon x radius hypotenuse of shadow 2 where and C denote the latitude and colatitude of the place, and z and a denote the zenith distance and altitude of the Sun.² These results are easily proved by assuming that the rays coming from the Sun are parallel. This rule is found also in SuSi, iii. 13-14; BrSpSi, iii, 10; LBh, iii. 2-3; ŚiDVṛ, I, iii. 4-5; Siśe, iv. 7; and SïŚi, I, iii. 18. 2 The equinoctial midday shadow is the shadow cast by the gnomon at midday at an equinox.