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

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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.