पृष्ठम्:महाभास्करीयम्.djvu/२०२

TRUE DISTANCE OF THE SUN OR MOON 117 T,...will converge to T. This is the basis of the method used. The details are as follows: MT, is taken as the first approximation r, to the radius of the Sun's true epicycle and likewise ES₁, which is equal to¹ R+kotiphala)2+(bahuphala), is taken as the first approximation H, to the Sun's true distance.² Now from the similar triangles S₁D₂E and SDE, SDXH₁_XH₁ S₂D₁ R But MT, S,D₁. Therefore, LXH₁ MT₂= R Again from the similar triangles T,B,M and MAE, we have T₂B₂= Similarly, B.M Therefore, MAXT,M R R = MAX₁, H₂ R bahuphalax H₁ R kotiphalax H₁ R ET,= R+MB₂)+T₂B₂³, where MB, and T₂B, are given by (3) and (2) respectively. (1) (2) (3). MT, is taken as the second approximation r₂ to the radius of the Sun's true epicycle and likewise ES, (=ET, ) is taken as the second approximation H, to the Sun's true distance. Since H, > R, therefore from (1) 1₂1₁; and consequently, H₂> H₂. ¹ For, ES₁=ET,; and from the right-angled triangle T₁B₁E, we have ET, EB,+B₁T₂³=(EM+MB₂)²+B₂T₁³, where EM-R, MB, is the kotiphala and B₂T, is the bahuphala. In the right-angled triangle EB₂T, BT, is called the base, EB, is called the upright, and ET, is called the hypotenuse.