ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

116 INDIAN LUNI-SOLAR ASTRONOMY As to the positive or negative character of the "sine" and the 'cosine' he gives the rule:— The mean planet diminished by its ucca, the apogee, aphelion or the Śīghra, is called Kendra or mean anomaly; its "sine" from above six signs (180°) arises from half circles and are respectively positive or negative, and its "cosine" in different quadrants are respectively positive, negative, negative, and posi- tive.¹ The convention followed is that the "sine" is negative from 0° to 180° and positive from 180° to 360° of the arc and that the cosine is positive between 0° and 90°, negative between 90° and 270° and positive between 270° and 360°. We may now symbolically express Mañjula's second ineq- uality thus :- —(13° 11′ 35″—11°) × 8ᵖ 8′ cos (θ—α) × 8ᵖ 8′ sin (D—θ) where D stands for the Moon as corrected by the 1st equation; we leave out the correction to the Moon's daily motion as given in the stanzas quoted above. The moon's new equation comes out to be =—143′58″ cos (θ—α) sin (D—θ). This, it will be seen, is exactly the modern form of the evection as combined with a part of the equation of apsis shown before. The difference in the main is that Mañjula's constant is 144′, a quantity less by 8′. In form the equation is most perfect, it is far superior to Ptolemy's, it is above all praise. It is from this inequality, we trust, that Mañjula should have an abiding place in the history of astronomy. The next writer who gives the second equation is Śrīpati (1028 A.D.). Śrīpati's Second Inequality of the Moon The following stanzas from Śrīpati's Siddhānta Śekhara, it is said, were communicated to Sengupta by Pandit Babua Misra. Though they are probably not very correct still the general meaning is clear. They carry the following sense : "From the Moon's apogee subtract 90°, diminish the Sun by the remainder left; take the "sine" of the

1. ग्रहः स्वोच्चोनितः केन्द्रं षडूर्द्धादर्द्धजो भुजः । धनर्णैः पदशः कोटिर्धनर्णै धनात्मिका ॥