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

285 Hṛti — phala = Iṣṭa-Hṛti ie. fq — cq = fc = an (fig. 53) Comm. (Ref. fig. 52). Nata = arc QN ∴ H. vers (Nata) = QC. (Called Śara) = H. vers (h) Antyā — Śara = FQ — CQ = FC = AN = Iṣṭāntya II Śara × (H cos δ / R) = phala = cq (fig. 53) = (Hvers h × H cos δ) / R Hṛti — phala = fq — cq = fc = an = Iṣṭa-hṛti IV Verse 59. (Phala × Koti of a latitudinal triangle) / Karṇa = Ūrdhwa V = βr (of fig. 54) Comm. (Ref. fig. 54) βr is the corresponding line in the plane of the meridian corresponding to phala in the plane of the diurnal circle. As the angle between these two planes is the latitude itself, by the principle of ortho- gonal projection namely. Magnitude of a projected segment = cosine of the dihedral angle × the magnitude of the segment projected, since Ūrdhwa is the orthogonally projected segment of phala, so, Ūrdhwa = phala × cos φ = (phala × H cos φ) / R VI (31) = (phala × Koti of a latitudinal triangle) / (Karna of the latitude triangle) as stated Thus Ūrdhwa = βr (of fig. 54). Verse 60. Ūrdhwa is also given by Ūrdhwa = [U.S. (Unmandala Śanku) × Śara] / Charajyā Dinārdha-Śanku (D.S.)—Ūrdhwa = Iṣṭa-Śanku (I.S.) = H cos z.