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

360 (alternate angle) = Semivertical angle of the shadow cone (say θ). Now EĈB − ÊVB = CÊD = angular measure of CD ie. the angular radius of the shadow cone (expressed in radian measure). Converting ½e/Km into angular measure, the propor- tion used by Bhāskara is "If by the daily spatial motion of 11859¾ Yojanas of the Moon, we have its daily motion in arc, what shall we have for e = 1581 Yojanas?" The result is 1581/11859¾ m₁. Converting the coefficient into a continued fraction we have 1/(7+) 1/(1+) 1/(1+) 1/175 ......... The penultimate convergent is ²/₁₅. Hence e/Km = ²/₁₅ m₁. Converting ½ ((s − e)/Ks) into arc, the proportion used is "If by the daily spatial motion of 11859¾ Yojanas, we have the daily motion of s₁, what shall we have for s − e = 6522 − 1581 = 4941 Yojanas?" The result is 4941/11859¾ s₁. Converting the coefficient into a continued fraction, we have 1/(2+) 1/(2+) 1/(2+) 1/146 . The penultimate convergent is ⁵/₁₂. Hence, the result is ⁵/₁₂ s₁. Note (1) It might be asked whether the Hindu astronomers used the theory of continued fractions. The answer is, they did though they did not write the con- tinued form in the form we do now. They arranged the successive quotients in a vertical line and called the column as a 'Valli' or 'creeper'. One may refer to the chapter in Bhāskara's Bijaganita on 'Kuttaka' in this context. Note (2) The formula derived above to obtain the Rahu-Bimba or diameter of the shadow-cone at the lunar orbit, is one which could be conveniently used in practice,