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-