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

232 will be the same on both the occasions. Then the spherical triangles PZS₁ and PZS₂ where P is the celestial pole, Z the Zenith and S₁ and S₂ are the positions of the Sun on the two occasion, are congruent their three sides being respe- ctively equal, provided we take PS₁ = PS₂ ie. 90 — δ₁ = 90 — δ₂ ie. δ₁ = δ₂ on both the occasions. When the two triangles are thus congruent, PẐS₁ = PẐS₂ ie. S₁ and S₂ are equidistant from the plane of the Prime-Vertical. Hence the extremities of the shadows will be equidistant from the East-West line ; or this may be seen in another way ; S₁ S₂ will be perpendicular to the meridian plane and as such parallel to the plane of the Prime-Vertical. The correction mentioned in the verse is known as the Agrāntara correction which was originally given by Chaturvedā chārya and then accepted by Sripati. Why it is called Agrāntara is because it is a change in what are called Karnavrittāgras of the two occasions where we shall see in due course that the formula for Karnavrittāgra is (K sin δ) / (cos φ) where K is hypotense of the gnomonic triangle formed by the gnomon and its shadow S at any place and time. This correction is a very minute correction and as a matter of fact could be ignored. But the fact that the correction was cognized and correctly formulated testifies to the knowledge of the sphere which the above acharyas had. Assuming the formula of the Karnāgra here (it will be proved by us later in this chapter) if δ₁ and δ₂ be the declinations on the two occasions respectively the Karnāgras will be (K sin δ₁) / (cos φ) and (K sin δ₂) / (cos φ) , K being equal on the two occasions because the shadows are equal. Hence the correction being the difference of the Agrās, it is [K (sin δ₁ ~ sin δ₂)] / (cos φ) as stated by Bhās- kara,