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

352 K¹ = R (1 + (K - R) / R + (K - R)² / R²) = R + K - R + (K - R)² / R = K + (K - R)² / R ∴ K¹ - K = δ K = (K - R)² / R as found above. Note. Bhāskara, having formulated this, appeals to ' Dhulikarma' ie. arithmetical computation, for convin- cing those who may not be able to follow his logio. Here one may note also the wrong directive given by the Samśodhaka in the text. The proof furnished by us above gives a mathematical veracity to Bhāskara's formulation. Verse 5. To rectify the Yōjanakarṇa or the spatial radius Vector. The above Kalākarṇa multiplied by the Karṇa given in Yōjanas and divided by the Radius gives the rectified Yōjanakarṇa. Comm. In the formula given above δ K = (K - R)² / R which is in units of spatial minutes (on the scale of R=3438). (K' × y) / R where K' is the rectified Kalā-karṇa, and y the Yōjanakarṇa given in verse 3, gives the rectified Yōjana- ·karṇa. Second half of verse 5. The spherical radii of the Sun and the Moon. The spherical diameters of the Sun and the Moon are respectively 6522 and 480 Yōjanas. Comm. The word- ‘ Bimba ’ is used to connote the spherical diameter. The diameter of Moon as given will be equal to 480×5=2400 miles in modern terms which is not far from truth. Once we accept that the method indicated by us in the Kakshādhyāya of chapter I was that