110 TRUE LONGITUDE OF A PLANET Form (1) occurs in P. C. Sengupta's edition of the Khandakhadyaka¹ of Brahmagupta and also in the Siddhanta-siromani of Bhaskara II. Form (2) is found to occur in Parameśvara's commentary on the Laghu-Bhas- kariya³. This formula agrees with Newton's interpolation formula for equidistant knots. 2. Madhava's formula. If t be a positive integer and 0<225', then Rsin (225' t+0')=sum of t Rsine-differences + This formula is ascribed to Madhava by Nilakantha in his commen- tary on the Aryabhatiya. It occurs also in the Tantra-sangraha.5 In Chapter VII of the present work, Bhāskara I gives a very interes- ting method for finding the Rsine of a given arc without the use of a table.6 A rule for finding the Sun's equation of the centre: 4(ii). The Rsines and Rversed-sines (of the parts of the Sun's mean anomaly lying in the odd and even quadrants res- pectively) should be (severally) multiplied by the (Sun's) own epicycle and divided by 80: the resulting quantities should be subtracted and added (in the manner prescribed below).' 0x[Rcos (225'(t+1)} + Rcos (225't)] 2R Application of the Sun's equation of the centre: 5. The resulting quantities due to the first, second, third and fourth anomalistic quadrants should always be respectively subtracted from, added to, added to, and subtracted from the Sun's mean longitude corrected for the (local) longitude.Ⓡ 1 ix. 8. 2 3 4 5 8 I, ii, 16. ii. 2(ii)-3(i). ii. 12. ii. 10-13(i). See infra chapter VII, stanzas 17-19.
7 This correction is found also in BrSpSi,i i. 15(ii) and Sise, iii, 27. This correction is found also in BrSpSi, ii. 16(i). Also see Sise, iii. 28(i).
