116 TRUE LONGITUDE OF A PLANET Fig. 12 is a reproduction of the previous figure. As in the previous figure, M is the mean Sun and T the true Sun.. ET is the true distance of the Sun. The above rule relates to the determination of ET. The method used is the method of successive approximations. In the triangle ESD, where SD is parallel to EU, we have ES = R, and SD = T',M, the radius of the Sun's mean epicycle. If the value of TM, the radius of the Sun's true epicycle, were known, the Sun's true distance ET could be easily derived from a comparison of the similar triangles ESD and ETM. But the value of TM is unknown and is itself dependent on that of ET. Hence the necessity of the method of successive approximations (usakṛtkarma). B²B M1/D₂ D U C Fig. 12 With centre E and radius ET, draw an arc of a circle cutting ET at S₁; through S₁ draw a line S₁D, parallel to EU and a line S,T, parallel to EM meeting MT, produced at T₂; and from T₂ draw a line T₂B₂ perpendicular to EM produced. Again with centre E and radius ET, draw an arc of a circle cutting ET at S₂; through S, draw a line S₂D₂ parallel to EU and
- line S₂T, parallel to EM meeting MT, produced at T3; and from T, draw
a line T,B, perpendicular to EM produced. Continue this process succes- sively. The sequence of points S₁, S₁, S,... and also that of points T₁, T₂,
