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

202 the preceding from the succeeding, we have successively the rising times. Thus the rising time of Mesha is √3 sin² ω tan² ϕ + cos² ω (cos² ω + 3 − √3 sin ω tan ϕ II ──────────────────────────────────────────────────────── 3 + cos² ω That of Meṣa and Vṛṣabha put together, the rising time is . √sin² ω tan² ϕ + 3 cos² ω (cos² ω + ⅓) − sin ω tan ϕ III ─────────────────────────────────────────────────── √3 (cos² ω + ⅓) The combined rising time of the 3 Rasis Meṣa, Vṛṣa- bha and Mithuna is from I using tables cos⁻¹ (tan ω tan ϕ) = 5046 asus which exactly accords with what we have found previously namely 1505+1659+1882 = 5046. Also putting in I λ = 180°, we have sin x = 0 or x = 180° = 10800 asus ; subtracting 5046, we have the combined times of rising of Karkataka, Simha ahd Kavya to be 5754 asus as we have had. Putting again λ = 270, we have cos°⁻¹ (tan ω tan ϕ) = 2π − 5046 whioh signifies that the sum of the rising times of the last three rasis is the same as that of the first three which again means that the sum of the rising times of Tula to Dhanus is equal to the sum of the rising times of Karkaṭaka, Simha and Kanya establish- ing Bhaskara's statement “विलोमसंस्थाः”. Verse 60. Computations of Lagna, Udayāntara and the like from the rising times of big arcs of the ecliptic like Rasis will be approximate, whereas one desirous of greater approximation has to find the same from the rising times of smaller arcs likes Horas and Dṛkkāṇas, so as to be more correct. Comm. Rasis divided into halves are called horas and if divided into one-third parts are called Dṛkkāṇas. The meaning of the verse is that if after having found the rising time of a particular Rāśi say Meṣa, we say that one-third of that rising time is that of one-third of that Rāśi, we will be making only an appro-