Page:Aryabhatiya of Aryabhata, English translation.djvu/9

Rh the method by which the corrections themselves are to be calculated. It is a descriptive summary rather than a full working manual like the later karanagranthas or the Sūryasiddhānta in its present form. It is questionable whether Āryabhata himself composed another treatise, a karanagrantha which might serve directly as a basis for practical calculation, or whether his methods were confined to oral tradition handed down in a school.

Brahmagupta implies knowledge of two works by Āryabhata, one giving three hundred sāvana days in a yuga more than the other, one beginning the yuga at sunrise, the other at midnight. He does not seem to treat these as works of two different Āryabhatas. This is corroborated by Pañcasiddhāntikā, XV, 20: "Āryabhata maintains that the beginning of the day is to be reckoned from midnight at Lankā; and the same teacher [sa eva] again says that the day begins from sunrise at Lankā." Brahmagupta, however, names only the Daśagītika and the Āryāstaśata as the works of Āryabhata, and these constitute our Āryabhatīya. But the word audayikatantra of Brāhmasphutasiddhānta, XI, 21 and the words audayika and ārdharātrika of XI, 13-14 seem to imply that Brahmagupta is distinguishing between two works of one Aryabhata. The published Āryabhatīya (I, 2) begins the yuga at sunrise. The other work may not have been named or criticized by Brahmagupta because of the fact that it followed orthodox tradition.

Alberuni refers to two Āryabhatas. His later