पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

264 PAÑCASIDDHĀNTIKĀ XIV.6 The chord DMD' of the circle enws, with its middle point at M, is equal to 2dl. Let 2c₁ be the angle subtended by DD' at 0 (or, wdhat is the same thing, the arc DWD' subtended by DD'). Then ½ DD' = DM = OD sin c₁ = Rcos δ₁ . sin c₁. ½ DD' = dl = Rsin δ₁ . tan Ø, from (1). ∴ Rcos δ₁ sin c₁ = Rsin ε₁ . tan Ø. ∴ sin c₁ = tan δ₁ . tan Ø (2). This c₁ is the ascensional difference of the end point of the sign Aries, or the ascensional differ- ence for the sign Aries. See supra, IV. 26. See also IV. 34. Since c₁ is equal to the number of degrees lying in half the arc DwD', therefore the degrees in half the arc DwD' give the ascensional difference of the sign Aries. These degrees multiplied by 10 give the corresponding vinâḍîs. Similarly, in the case of Taurus and Gemini. But in these cases if c₂ and c₃ be the ascensional differences for the end-points of Taurus and Gemini respectively, then ascensional difference for Taurus = c₂ - c₁ and ascensional difference for Gemini = c₃ - c₂. [नाडीतः छाया छायातः नाडी च] नाड्यः (षड्घ्न्यो) भागास्तज्ज्या व्यासार्धशोधिता छाया । माध्यन्दिनीसमेता नाड्यर्थे सा तया हीना ॥५॥ छायाहरिजाभ्यन्तरजीवाचापांशषष्ठभागो यः । ता नाड्यः (प्राग् याताः) पश्चाच्छेषास्तथा (प्राप्ताः) ॥६॥ Rsine of the Sun's zenith distance for the given time, (and vice versa). 5. The nâḍîs (elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon) multiplied by 6 are degrees; the (versed) Rsine of that sub- tracted from the radius (R) and then increased by the Rsine of the Sun's zenith distance for midday gives the Rsine of the Sun's zenith distance (for that time). In order to find the nâḍîs (from the given Rsine of the Sun's zenith dis- tance) the (given) Rsine of the Sun's zenith distance should be diminished by the Rsine of the Sun's zenith distance for midday. 6. Whatever is the sixth part of the degrees of the arc corresponding to the (versed) Rsine equal to the difference between the given Rsine of the Sun's zenith distance (as diminished by the Rsine of the Sun's zenith distance for midday) and the radius (chāyāharijābhyantara), gives the nāḍīs elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon. Let n be the nāḍīs elapsed since sunrise in the forenoon or to elapse before sunset in the after- noon, and zₒ the Sun's zenith distance at midday. Then, according to the rule stated in verse 5 above, the Rsine of the Sun's zenith distance for that time (which we shall denote by Rsin z) is given by Rsinz = R - Rvers (6n) + Rsin zₒ, (3) where R stands for the radius.