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