TRUB LONGITUDE OF MARS, ETC., BY EPICYCLIC THEORY If T be the first point of Aries, then L MET (or are MUT) is the mean longitude of the planet, and LSET (or arc SUT) is the true-mean longitude of the planet. The arc MS by which the true-mean longitude of the planet differs from the mean longitude of the planet is obtained as follows: Let MA be the perpendicular from M on EU, M,B, and SD the per- pendiculars from M, and S on EM. Then comparing the triangles M₂B₂M and MAE, we have M₁B₁, i.e., SD = MA X MM₂ EM 139 Rsin (bahu due to mandakendra) × (radius of corrected manda epicycle) R (corrected manda epicycle) × Rsin 80 where denotes the bahu due to mandakendra.¹ Reducing the right-hand side of (1) to the corresponding are, we get the arc MS. This arc MS has been referred to by Bhaskara 1 as the arc corres- ponding to the mandakendraphala, because it corresponds to M₂B, which denotes the mandakendraphala. Generally it is known as mandaphala. It is. subtracted from or added to the mean longitude of the planet, according as the mandakendra is less than or greater than 180°, as in the case of the Sun and Moon. Thus true-mean longitude-mean longitude-mandaphala, according as the mendakendra is less than or greater than 180°. Now consider Fig. 15. Here also E is the Earth and the bigger circle centred at E is the deferent (kaksävṛtta); U is the planet's mandocca ("apogee") and V the planet's fighrocca. S is the position of the true-mean planet on the deferent. The small circle centred at S is the planet's sighra epicycle: it is derived as taught in stanzas 38-39(i). ST is drawn parallel to EV. Then T denotes the position of the true planet. ET is called the sighrakarna. ¹ The bahu due to mandakendra is derived in the same way as in the case of the Sun. The corrected manda epicycle used in this last result is that divided by 4).
- It may be pointed out that in the case of the Sun and Moon the
mandaphala is the equation of the centre, called bahuphala by Bhāskara 1.
