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

291 Comm. Under verse 58, we had to form Hvers h; a doubt might arise as to what this Hvers h would be if h > 90. Hence Bhāskara defines it and the definition is clear from fig. 57. The Unmandala S'anku has the formula R sin δ sin φ so that either when δ is negative or when φ is negative, it will be negative which means it will be in the opposite direction ie. vertically downwards. Since negative latitudes are not considered by the Hindu astronomers, the other case alone is considered. Even from a figure it is evident that when the Sun is in the south of the Equator, the Unmandala S'anku is vertically downwards. In proportions like I given under verse 62, we can use the magnitude of this Unmandala S'anku also and it does not vitiate the results, when we take its numerical value. Verse 65. The Sun crosses the prime-vertical when his northern declination falls short of the latitude. Then alone there is sense in giving the magnitude of his shadow at that moment. When the Sun does not cross the prime- vertical at all, the Sama S'anku which could be computed out of its formulation, though it does not exist, under the Sun, yet, it could be used in proportions (like I under verse 62) and no blunder is committed. Comm. This is a beautiful example cited by Bhāskara where he intuitively uses the so-called principle of geometrical continuity. We have formulated Sama S'anku as (R sin δ) / (sin φ) ie. H cos z = (R sin δ) / (sin φ) . We have a real value of z when δ > φ, for, then only H cos z < R. When φ > δ, then H cos z > R which is impossible, for, no Hindu sine or Hindu cosine could be greater than R just as no modern sine or cosine could be greater than unity.