सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

197 equal and similarly those of Meṣa and Kanyā. It will be noted that the equatorial risings alone are equal in the above cases but not at any other place, for in a place with some latitude when a point like B (fig. 26) comes to the horizon, the foot of its declination circle namely b will not be on the horizon and there arises the chara in bet- ween, which has to be taken into account, and be subtract- ed from or added to the equatorial rising time as the case may be. Now regarding the chara-khanda of Karkaṭa it is again 56; why it should be so is not proved by Bhāskara but merely stated, nor any commentator took the pains to prove. It can be proved as follows. Let in fig. 26, δ₁, δ₂, δ₃ be the declinations at the ends of Vṛṣabha, Mithuna and Karkaṭaka respectively. We know δ₁ = δ₃. The chara-segments for Mithuna and Karkaṭaka i.e. when Mithuna and Karkaṭaka are rising are to be proved to be equal, here 56 asus. Their expressions are tan ϕ tan δ₂ − tan ϕ tan δ₁ and tan ϕ tan δ₃ − tan ϕ tan δ₂ i.e. tan ϕ (tan δ₂ − tan δ₁) and tan ϕ (tan δ₃ − tan δ₂). Since δ₁ = δ₃ we perceive that they are equal but of opposite signs. So Bhāskara says rightly “अपचीयमानत्वात् धनम्” i.e. because of negative sign, the chara-segment of Karka- taka while being subtracted will be rendered positive’. Hence the rising times of Karkaṭaka, Simha and Kanya will be respectively 1937+56, 1793+134, 1670+168 asus or 1993, 1927, 1838 asus or 332, 321, 306 Vinadis or 5-32, 5-21 and 5-6 nadis. Thus, in as much as the rising times of Meṣa to Kanyā are 1670−168, 1793−134, 1937−56, 1937+56, 1793+134, 1670+168 their total is 30 nadis as should be expected because the equator bisects the ecliptic between ♈ and ♎ and the equatorial interval between ♈ and ♎ is 30 nadis. It will be noted that while the equatorial rising times of Meṣa to Kanyā are symmetrical as 1670, 1793, 1937, 1937, 1793, 1670, their rising times at any other place are not like that but