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

180 (vii) Lambāṁsa-chāpa is the arc of the colatitude QS where S is the South point so that Lam- bajyā is the H sine of QS or H cosine of ZQ. This Lambajyā will be seen to be the diameter of a small circle parallel to the Equator and passing through Z. Verses 49-51. A different method of obtaining chara. This chara can be had by the so-called chara-segments of the locality using a process similar to that of finding the H sines of the smaller table of nine H sines using λ/3 where λ is the Sāyana longitude of the Sun (i.e. The Hindu longitude plus the arc of ayanāṁśas is called the Sāyana longitude or the modern longitude measured from v along the ecliptic to the Sun). Find the charas of 30°, 60° and 90° of the ecliptic measured from v. Subtract the first from the second, the second from the third. Thus we have C30°, C60°-C30°, C90°-C60°, (where Cθ° signifies the chara of θ°) which are called chara-Khandas or chara-seg- ments. The equinoctial shadow multiplied by 10, 8, 3⅓ gives the approximate values of the chara-segments in Vinādīs (a sidereal day is divided into 60 nādīs and each nādī consists of 60 Vinādīs). The chara-segments thus measured in Vinādīs are rather approximate. If further exactitude is required, better take the arc in units each of which rises in ⅙th of a Vinādī (This ⅙th part of a Vinādī is known as a prāṇa i.e. the duration of the interval between two inhales of a healthy person reckoned as 4″ of time). Comm. The charas of 30°, 60° and 90° of modern longitude are the values of the arc EA, (Ref. Fig. 21) when S has longitudes 30°, 60° and 90°. We have the folmula Charajyā = R tan δ tan ϕ