Page:Aryabhatiya of Aryabhata, English translation.djvu/104

 74 ARYABHATIYA

31. The measure of the Sun's amplitude north of the Equator [i.e., when the Sun is in the Northern hemisphere], if less than the sine of latitude, multipUed by the sine of co-latitude and divided by the sine of latitude gives the sine of the altitude of the Sun on the prime vertical.^

Bhau Dajl^ first pointed out that Brahmagupta (XI, 22) contains a criticism of stanzas 30-31.

uttaragole 'grayam vi§uvajjyato yad uktam unayam | samamandalagas tad asat krantijyayam yato bhavati ||

Paramesvara remarks: visuvajjyond cet. visuvaj- jyonayd krdntya sddhitd ced ity arthah. visuvaj- jyonakrdntisiddhd sodaggatdrkdgrd.

32. The sine of the degrees by which the Sim at midday has risen above the horizon will be the sine of altitude of the Sim at midday. The stae of the degrees by which the Swa is below the zenith at midday will be the midday shadow.

33. Multiply the meridian-sine by the orient-sine and divide by the radius. The square root of the difference between the squares of this result and of the meridian-sine will be the sine of the ecliptic zenith-distance.

The madhyajyd or "meridian-sine" is the sine of the zenith-distance of the meridian ecliptic point.

The udayajyd or "orient-sine" is the sine of the amplitude of that point of the ecliptic which is on the horizon.

The sine of the ecliptic zenith-distance of that point of the ecliptic which has the greatest altitude (nonagesimal point) is called the drkksepajyd.^

^Cf. Suryasiddhanta, III, 25-26 n.; Brahmagupta, III, 52; Pancasiddhdntika, IV, 32-3, 35 n.

2 JRAS, 1865, p. 402.

^ Cf. Suryasiddhanta, V, 4-6; Pancasiddhdntika, IX, 19-20 and note; Lalla, Suryagrahanadhik&ra, 5-6; Kaye, op. cit., pp. 76-77; BCMS, XIX (1928), 36. ,