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

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Note. T₂ will be less than or greater than T₁ accord-
ing as β₂ ≷ β₁.
Verse 14. Rectification of the Sammilana-Marda-
Khanda and Unmilana-Marda-Khanda.
Proceeding on the same lines as above and obtaining
β₃ and β₄ the rectified latitudes of the Moon for the
moments of the commencement and end of totality of the
eclipse, the Sammilana-Marda-Khanda and Unmilana-
Marda-Khanda, T₃ and T₄ are to be rectified.
Note. We have the formula sin β = sin λ sin i so
that by differentiating. we have cos βδβ = cos λδλ × sin i
sin i cos λ Δλ
∴ δβ = ——————————————
cos β
This formula gives in one stroke the rectified latitudes
of the Moon at the respective moments from which the
respective rectified times could be got.
Verse 15 and the first half of verse 16. The definition
of Bhuja and the method of finding it at an intermediate
point of time.
The word ‘Iṣṭa’ is used to connote ‘At any given
time’. The word ‘Spārśika-Iṣṭa’ means ‘At a given
time after the moment of first contact’; similarly the
word ‘Maukṣika Iṣṭa’ means ‘At a given time before
the moment of last contact’. (T–t) (m₁—s₁) where
(m₁—s₁) is in degrees (m₁ and s₁ of course being expressed
in minutes); T stands for the Sthiti-Khanda (Spārśika
or Maukṣika) and t stands for the Iṣṭa (Spārśika or
Maukṣika) gives the Bhuja. Similarly with respect to
obtaining the Marda-Bhuja. (The former is called Sthiti-
Bhuja).
Comm. In fig. 77, let C and M be the centres of the
Rāhu (cross-section of the shadow-cone at the lunar orbit)