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

355 where ɑ = FB = CD required ∵ ɑ = ½ { e - Km/Ks (s - e) } I as formulated 2ɑ being what is called Rāhu-Bimba or diameter of the Earth's shadow cone at the lunar orbit which is called Ku-bhā Vistṛti in the verse (Ku = Earth ; Bha = Shadow ; Vistṛti = diameter). Note (1) We shall prove that this formula accords with the modern formula given for the radius of the shadow cone. Divide I throughout by 2 Km, so that ɑ/Km = e/2Km - (s - e)/2Ks II But from fig. 67. ɑ/Km = sin Ê = Ê = angular radius of the shadows cone expressed in radius. From fig. 68, e/2Km = Horizontal parallax of the Moon ; s/2Ks = sin Ê = Ê = angular radius of the Sun expressed in radians from fig. 69 ; and e/2Ks = (from fig. 70) Horizontal parallax of the Sun. Thus Equation II means ρ = P - σ + P¹ III where ρ = angular radius of the shadow cone, P = Horizontal parallax of the Moon ; P¹ = that of the Sun and σ = angular radius of the Sun. Note (2) If we don't divide I by 2 Km, we have the radius of the shadow-cone in Yojanas, substituting the values of e and s, Km and Ks. Note (3) It is worth hearing Bhāskara in his commentary under this verse. Observe the Sun's disc while rising on the day when his true motion is equal to his mean, with a compass composed of two rods hinged at one end and carrying a protractor at the other. We get the mean diameter of the Sun equal to 32' - 31" - 33"'. Similarly, observe the Moon's disc on a full-moon-day