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