पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

208 PAÑCASIDDHĀNTIKĀ IX.9 = degrees of epicycle × sine anomaly ÷ 360°, as in the text. We shall now see how the use of the epicycle gives the Eq.C. [Diagram showing epicycle model with centre E (Earth), deferent circle, epicycle centred at C, body S, apogee A, A', direction to first point of Meṣa, and point O] Fig. IX. 1-b. Here too, E, the centre of the earth is the centre of the orbit circle of radius 120'. On the orbit circle, the centre C of the epicycle on which the body S is situated, moves according to the mean motion of the body. The radius of the epicycle is the degrees of epicycle given in the text × 120' ÷ 360°, which is the maximum Eq.C, as already seen. At the two points of intersection of the epicycle with the line of apogee, EA, arc A the apogee, and P the perigee. The body moves on the circumference of the epicycle, with its mean motion in the direction opposite to the motion of C. Angle ACS is the anomaly. Now, draw EA' parallel to CS. Then angle AEA' also is the anomaly. Since CEO is the mean body, A'EO is equal to the longitude of apogee. Since SEO is the true longitude and CEO is the mean longitude, angle CES is the Eq.C. Therefore, mean longitude minus Eq.C. = true long, (the anomaly being less than 6 rāśis in the figure. If the anomaly is more than 6 rāśis, S is greater than P, and the Eq. C. becomes additive). The Eq. C. is got in the same way as in the excentric method. We have now to show that in either of the methods, the Eq. C. is the same, i.e. angle XSE in fig 1a = angle CES in fig 1b. In the two triangles XSE and CES in the respective figures, it has been