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