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

309
Sun to the Earth and a knowledge of the Sun's distance,
we can compute similar decrease as we proceed from the
Earth to the lunar orbit knowing the distance of the
Moon. Such a decrease measured in Yojanas is termed by
Bhāskara as 'अपचययोजनानि' ie. Yojanas of decrease in
diameter. It was this concept that led to the formulation
of 2a in Yojanas in the form 2a = e — ((s — e) Km) / Ks of verse
6 and is indeed based upon the similarity of triangles as
proved by us in that context. Dividing the above equation
by 2 Km, we have
a/Km = e / (2 Km) — 1/2 ((s — e) / Ks) I
Dividing a, e and (s—e) thus by the distances Km and Ks is
termed 'Kalā-Karaṇa' ie. converting spatial distance
into angular measure. Thus dividing a by Km is con-
verting the radius of the shadow cone into angular measure
at the lunar orbit ; dividing 1/2e by Km is estimating the
angular measure of the earth's radius as seen from the
Moon's distance or what is the same the horizontal parallax
of the Moon, whereas dividing 1/2s by Ks is getting the
angular radius of the Sun's disc as seen from the Earth
and dividing 1/2e by Ks is getting the angular radius of the .
Earth's disc as seen from the Sun or what is the same the
horizontal parallax of the Sun.
Equation I which gives a/Km the angular radius of
the shadow cone, may also be interpreted as follows. e / (2Km)
= Horizontal parallax of the Moon as mentioned above
which is equal to the angle (fig. 66) EĈB, for, 1/2e = EB ;
Km = EC so that e/2Km = EB/EC = sin EĈB = EĈB
expressed in radian measure. Also
1/2 (s—e) / Ks = (SA—GA) / SE = SG / SE = sin SÊG = SÊG = EṼB