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

370 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)