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

11 Manvantaras and a Kaḷpa. Since in many ancient astro- nomical works, the revolutions of the planets and the planetary points like nodes, apogees or aphelia are given as integers during the course of a yuga, the concept of a yuga must have arisen as follows. The durations of the sidereal revolutions of the planets and the apogee of the Moon and its node having been ascertained by observation, a period was calculated in which are contained integral multiples of those durations. In other words a yuga of 4320000 mean solar years is construed as the period in which the planets the node and apogee of the Moon make an integral number of revolutions with respect to the stars. We have excluded here the aphelia and the nodes of the planets, as we shall see later that their sidereal revolu- tions were not based on observation but by an assumption that those points also must be having an integral number of revolutions during the course of a Kaḷpa, having started at the beginning of the Hindu Zodiac ie the beginning point of Aswini at the beginning of the Kaḷpa. On this assumption cited, and using indeterminate analysis the number of their sidereal revolutions were got as reported by Bhāskarāchārya in his Commentary in the chapter Bhaga- nādhyāya. He has given us a clue that the numbers of sidereal revolutions of the planets including the node and apogee of the Moon were originally determined by observa- tions though he appeals to Āgama that those numbers were given by Āgana, as accepted and transmitted by Brahma- guptāchārya. Even in the Upapatthis or proofs that Bhās- karāchārya gives regarding the numbers of sidereal revolu- tions known as Bhagaṇas, we perceive that he consciously commits the logical flaw known as इतरेतराश्रयदोष as we are going to show in that context. The proofs he adduces are indeed based upon Aryabhatāchārya's verse 48, Golapāda namely क्षितिरवियोगाद्दिनकृत्, रवीन्दुयोगात्प्रसाधितश्चेन्दुः शशिताराग्रहयोगात् तथैव ताराग्रहाः सर्वे