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

326 Verse 102. In a place where s = 5″, the sum of H sin δ, S. S., Taddhṛti, Kujyā and Agrā is 6500 ; find them individually oh, mathematician, if thou art adept in understanding the sphere and dealing with the latitudinal triangles. Verse 103. Answer to the problem above. Assuming H sin δ to be equal to 12 s and computing the various quantities cited ; take their sum. Then by rule of three “ If for this sum got, the individual magni- tudes are such and such what will they be for the given sum ” each can be had. Comm. The cited magnitudes are respectively H sin δ, (R H sin δ) / (H sin ϕ), (R² H sin δ) / (H sin ϕ H sin ϕ), (H sin δ H sin ϕ) / (H sin φ) and (R H sin δ) / (H cos ϕ) which are all proportional to H sin δ, ϕ being given through ‘ s ’. With this idea of proportionality at the back of his mind, Bhāskara sets this ingenious ques- tion, and gives an easy way of solving it by assuming H sin δ to be 5 × 12 = 60, so that the others can be got rationally. With this H sin δ, S. S. (3438 × 60) / (3438 × 5/13) = 156, Taddhṛti = (3438² × 60) / (3438 × 5/13 × 3438 × 12/13) = 169 ; Kujyā = (60 × 5) / (13 × 12/13) = 25 Agrā = (3438 × 60) / (3438 × 12/13) = 65 The sum of these is 475. So, by the rule of three men- tioned above, H sin δ = 1200, S. S. = 3120, Taddhṛti = 3380, Kujyā = 500 and Agrā = 1300. Or alternatively given s = 5, k = 13 so that H sin ϕ = (3438 × 5) / 13, H cos ϕ = (3438 × 12) / 13. Hence the values of