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

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gupta's definition of Karṇa, it will be in this particular case. √(R² + R²) = R√2 so that the Koṭi will be √(2 R² — R²) = √R² = R, where the Bhuja also is R (projection of the line joining the Sun and the Moon on the north-south line. Though in the verse (11) above one particular position of the Sun and one of the Moon, are contemplated, the same argument holds good, says Bhāskara in the course of the commentary, whatever positions are occupied by the Sun and the Moon on the ecliptic. In this case there is only Bhuja existing and no Koṭi, so that the cusps will be vertical. But in all these cases, there is Koṭi aecording to Brahmagupta's definition, so that the ousps will not be vertical according to him, which is clearly against truth. Here we have to note that in the example cited by Bhāskara the Bhuja equal to R is along the north-south direction, and even though the Koṭi according to Bhās- karajs definition is conceived to be vertical, the Karṇa according to Brahmagupta's conception being ES where E and S are the east and south points, his Koṭi will be horizontal coinciding with OE, O being the centre of the horizontal ecliptic. Further according to Brahmagupta, the join of the ousps will be perpendioular to the Karṇa whioh does not therefore go against truth. Similarly in all the cases wherever be the Sun and the Moon on the horizon, Brahmagupta's Karṇa being a line joining the centres of the disos of the Sun and the Moon, it will be a horizontal line and so the ousps could be vertical. It is not clear whether or not Bhāskara recognized this namely that the Karṇa and Koṭi of Brahmagupta in the cases cited above are all horizontal lines so that the cusps could be vertical even according to Brahmagupta. That is why he pays homage to Brahmagupta in the last line of (12). Probably Bhāskara expected that Brahmagupta's Koṭi also should have been vertical as his. The fact that he recognized that Brahmagupta's Koṭi will not be vertical