Page:Aryabhatiya of Aryabhata, English translation.djvu/102

 72 ARYABHATIYA

horizon of Lanka (the unmandala). When trans- formed to the plane of a great circle it becorrfes the ascensional difference.^

27. The first and fourth quadrants of the ecliptic rise in a quarter of a day (15 ghatikds) minus the ascensional difference; The second and third quadrants rise in a quarter of a day plus the ascensional difference, with regular increase and decrease.

The last phrase means that the values for signs 1, 2, 3 are equal, respectively, to those of signs 6, 5, 4 and that the values of 7, 8, 9 are equal, respectively, to those of 12, 11, 10. They increase in the first quadrant, decrease in the second, increase in the third, and decrease in the fourth. There are, there- fore, only three numerical values involved, those cal- culated for the first three signs. See the table given in Siiryasiddhdnta, III, 42-45 n.^

28. The sine of the Sun at any given point from the horizon on its day-circle multiplied by the sine of co-latitude and divided by the radius is the sahku when any given part of the day has elapsed or remains.

The sanku is the sine of the altitude of the Sun at any time on the vertical circle from the zenith pas- sing through the Sun. Cf. Brahmagupta, XXI, 63, drgmandale natdrhsajya drgjya sankur unnatarhsajyd,

Samanyagolabandha, 4; Brahmagupta, II, 57-60; Paricasiddhantika, IV, 26 and note; Bhaskara, Qaiyitadhydya, Spa§tadhikara, 48; Kaye, op. dt., p. 73.
 * Cf. Suryasiddhanla, 11, 61-63; Lalla, Spa^tadhikdra, 17, and

^ Cf. Lalla, Madhyagativasand, 15; Bhaskara, Gardiddhydya, Spa^tddhikdra, 65 {Vdsan&bha^ya) who names Aryabhata in connec- tion with this rule.