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

THE SECTION BHŪ-PARIDHI-MĀNĀDIKA-
CIRCUMFERENCE OF THE EARTH
Verse 1. The circumference of the earth's globe is
4967 yojanas ; its diameter 1581. A yojana is equal to
(d × 360) / (C × δϕ) where δϕ is the difference in the latitudes of two
places on the same terrestrial meridian in degrees, C the
circumference of the earth's globe given above and d the
distance between the two places.
Comm. The second half of the verse gives the method
of computing the circumference of the earth's globe, which
is mathematically correct ; for, by the rule of three "If by
a difference of 90° in latitude we have ¼ C, what shall we
have for 1° difference in latitude ? " The answer is C / 360°
Again "If by distance of d between two places on the same
meridian, we have a difference of δϕ° in latitude, what
shall we have for 1° difference in latitude ? ' The answer
is d / δϕ. Both the answers must be the same ; so equating
them, we have C / 360 = d / δϕ = number of yojanas = x
say. Hence one yojana = x / x = (d / δϕ) ÷ (C / 360) = (d × 360) / (C × δϕ)
N.B. Here it must be noted that a yojana's length is
derived from the number of yojanas contained in the
circumference as reported in the Āgama.
In the course of the commentary under this verse,
Bhāskara explains why he had recourse to this kind of
definition, which is based upon āgama and as such does
not contain a proof. He says that in as much as the defi-