सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

231 The East-West line is roughly the join of the extremities of the morning shadow as well as that in the after-noon of a gnomon placed at the centre of a circle drawn on a plane with any arbitrary radius, when those shadows equal the radius of the circle. But this line is to be deflected keeping its western point ie. the extremity of the morning shadow fixed through a distance K (sin δ₁ ~ sin δ₂) / cos ϕ at the eastern end perpendi- cular to it, where the above distance is measured in units, which measure K. Comm. The east and west points are where the celestial equator cuts the horizon. The east point is thus the point where the Sun-rises when he is exactly at the vernal equinox. The question is how to draw the east-west line on a plane. For this we are asked to draw a circle with any radius on that plane. The plane is described here as अम्भःसुसमीकृतक्षिति that kind of sur- face as is determined by the surface of water there. Such a kind of surface forms approximately a horizontal plane not of course exactly because such a surface is really spherical, the earth being a sphere. But because the radius of the earth is sufficiently large, we can take such a surface to be a horizontal plane for all practical purposes. Having drawn a circle place the gnomon vertical at the centre. In the morning note the extremity of the shadow when it equals the radius. In the afternoon also mark the point when the shadow equals the radius. Join those two points. It represents roughly the east-west line, roughly because the Sun's declination changes in between the two moments however small the change might be. Ignoring the change in the declination, this line will be east-west because of the following reason. The length of the shadow is 12 tan z where 12 units are the measure of the gnomon. But since the shadow on both the occasions is equal to the radius of the circle z, the zenith-distance