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

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First half of verse 56. The Unmandala S'anku
multiplied by the Sūtra and divided by Charajyā is also
Iṣṭayaṣṭi.
Comm. The Unmandala S'anku and Iṣṭayaṣṭi are
the lines in vertical planes corresponding to Charajyā and
Sūtra in the Equatorial plane. Hence the proportion. It
will be noted that the Unmandala S'anku and Iṣṭayaṣṭi
are not in the same vertical plane but parallel vertical
planes. None the less the proportionality holds good.
Latter half of verse 56 and first half of verse 57.
The Sūtra increased or decreased by the Charajyā
according as the Sun is in the northern or southern hemi-
sphere is what is known as Iṣṭāntyā ; similarly the Kalā
increased or decreased by Kujyā is what is known as Iṣṭa-
Hṛti.
Comm. In fig. 52, Iṣṭāntyā = AN = AB + BN =
ME + BN = Charajyā + Sūtra. Similarly in fig. 53,
Iṣṭa Hṛti = an = ab + bn = sg + bn = Kujyā + Kalā.
∴ Iṣṭāntyā = H cos h + R tan δ tan φ =
R (sin φ sin δ + cos φ cos δ cos h) / (cos φ cos δ) in modern terms (28)
Latter half of verse 57. Similarly Iṣṭayaṣṭi
increased or decreased by the Unmandala S'anku is Iṣṭa
S'anku or H cos z.
Comm. Let in fig. 54 which represents the plane of
the prime-vertical AA', EW, BB', FF', qq' represent the
lines of intersection of this plane with planes parallel to
the horizon and passing through A, B, F, q of fig. 21. Then
Oa = Unmanda-S'anku, Oβ = Sama S'anku, Or =
Dinārdha S'anku. If xx' be the line of intersection of this
plane of the prime-vertical with a plane passing through
an arbitrary position of the Sun in the diurnal circle and
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