The Aryabhatiya of Aryabhata (An Ancient Indian Work on Mathematics and Astronomy)

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The Aryabhatiya of Aryabhata is of great work in the annals of the history of Indian mathematics and astronomy. This volume is expected to give a complete translation (with notes) of the Aryabhatiya with references to some of the most important parallel passages. It is a brief descriptive work intended to supplement matters and processes which are generally known and agreed upon to give only the most distinctive features of Aryabhata's own system. Many common places and many simple processes are taken for granted.

The book vividly addresses topics such as dasagitika, ganitapada, kalakriya and gola in much details. Withstanding many a criticism from people like Brahmagupta on the theories of Aryabhata, this volume through the introductory chapter contends that the Aryabhatiya, on the whole, is quite genuine. It presents Aryabhata as an innovator, thus his difference from Smrti or tradition in his approach to many astronomical matters is fully justified. It also discusses a serious internal discrepancy in the Aryabhatiya about the stationary and revolutionary nature of earth.

This book helps in introducing Aryabhata and the quintessential of Aryabhatiya to the mathematicians and astronomers of the new generations, for whom the original language Sanskrit and the old processes might be unknown.

Walter Eugene Clark (8 September 1881 - 30 September (1960), was an American philologist. He was the second Wales Professor of Sanskrit at Harvard University and the editor of the Harvard Oriental Series, vols. 38-44. He made ready this volume just one year before his demise.

In 1874 Kern published at Leiden a text called the Aryabhatiya which claims to be the work of Aryabhata, and which gives (Ill.10) the date of the birth of the author as 476 AD. If these claims can be substantiated, and if the whole work is genuine, the text is the earliest preserved Indian mathematical and astronomical text bearing the name of an individual author, the earliest Indian text to deal specifically with mathematics, and the earliest preserved astronomical text from the third or scientific period of Indian astronomy. The only other text which might dispute this last claim is the Suryasiddhanta (translated with elaborate notes by Burgess and Whitney in the sixth volume of the Journal of the American Oriental Society). The old Suryasiddhanta undoubtedly preceded Aryabhata, but the abstracts from it given early in the sixth century by Varahamihira in his Pancasiddhantika show that the preserved text has undergone considerable revision and may be later than Aryabhata. Of the old Paulisa and Romaka Siddhania, and of the transitional Vasistha Siddhanta, nothing has been preserved except the short abstracts given by Varahamihira. The names of several astronomers who preceded Aryabhata, or who were his contemporaries, are known, but nothing has been preserved from their writings except a few brief fragments.

The Aryabhatiya, therefore, is of the greatest importance in the history of Indian mathematics and astronomy. The second section, which deals with mathematics (the Ganitapadai), has been translated by Rodet in the Journal Asiatique (1879), I:393-434, and by Kaye in the Journal of the Asiatic Society of Bengal, 1908, pages 111-41. Of the rest of the work no translation has appeared, and only a few of the stanzas have been discussed. The aim of this work is to give a complete translation of the Aryabhatiya with references to some of the most important parallel passages which may be of assistance for further study. The edition of Kern makes no pretense of giving a really critical text of the Aryabhatiya. It gives merely the text which the sixteenth-century commentator Paramesvara had before him. There are several uncertainties about this text. Especially noteworthy is the considerable gap after 1V.44, which is discussed by Kern (pp. v-vi). The names of other commentators have been noticed by Bibhutibhusan Datta in the Bulletin of the Calcutta Mathematical Society, XVIII (1927): 12. All available manuscripts of the text should be consulted, all the other commentators should be studied, and a careful comparison of the Aryabhatiya with the abstracts from the old siddhantas given by Varahamihira, with the Suryasiddhanta, with the Sisyadhiceddhida of Lalla, and with the Brahmasphutasiddhanta and the Khandakhaduaka of Brahmagupta should be made. All the later quotations from Aryabhata, especially those made by the commentators on Brahmagupta and Bhaskara, should be collected and verified. Some of those noted by Colebrooke do not seem to fit the published Aryabhatiya. If so, were they based on a lost work of Aryabhata, on the work of another Aryabhata, 'or were they based on later texts composed by followers of Aryabhata rather than on a work by Aryabhata himself? Especially valuable would be a careful study of Prthudakasvamin or Caturvedacarya, the eleventh-century commentator on Brahmagupta, who, to judge from Sudha-kara's use of him in his edition of the Brahmasphuiasiddhanta, frequently disagrees with Brahmagupta and upholds Aryabhata against Brahmagupta's criticisms.

The present translation, with its brief notes, makes no pretense at completeness. It is a preliminary study based on inadequate material. Of several passages no translation has been given or only a tentative translation has been suggested. A year's work in India with unpublished manuscript material and the help of competent pundits would be required for the production of an adequate translation. I have thought it better to publish the material as it is rather than to postpone publication for an indefinite period. The present translation will have served its purpose if it succeeds in attracting the attention of Indian scholars to the problem, arousing criticism, and encouraging them to make available more adequate manuscript material.

There has been much discussion as to whether the name of the author should be spelled Aryabhata or Aryabhatta. Bhata means "hireling," "mercenary," "warrior," and bhatta means "learned man," "scholar." Aryabhatta is the spelling which would naturally be expected. However, all the metrical evidence seems to favor the spelling with one i, It is claimed by some that the metrical evidence is inclusive, that bhata has been substituted for bhatta for purely metrical reasons, and does not prove that Aryabhata is the correct spelling. It is pointed out that Kern gives the name of the commentator whom he edited as Paramadisvara. The name occurs in this form in stanza at the beginning of the text and in another at the end, but in the prose colophons at the ends of the first three sections the name is given as Paramesvara, and this doubtless is the correct form. However, until more definite historical or metrical evidence favoring the spelling Aryabhatta is produced I prefer to keep the form Aryabhata, The Aryabhatiya is divided into four sections which contain in all only 123 stanzas. It is not a complete and detailed working manual of mathematics and astronomy. It seems rather to be a brief descriptive work intended to supplement matters and processes which were generally known and agreed upon, to give only the most distinctive features of Aryabhata's own system. Many common places and many simple processes are taken for granted. For instance, there are no rules to indicate the method of calculating the ahargana and of finding the mean places of the planets. But rules are given for calculating the true places from the mean places by applying certain corrections, although even here there is no statement of 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 karana-granthas or the Suryasiddhanta in its present form. It is questionable whether Aryabhata himself composed another treatise, a karana-grantha 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 Aryabhata, one giving three hundred sauana 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 Aryabhatas. This is corroborated by Pancasiddhnntika, XV.20: Aryabhata maintains that the beginning 'of the day is to be reckoned from midnight at Lanka; and the same teacher [saeva] again says that the day begins from sunrise at Lanka." Brahmagupta, however, names only the Dasagitika and the Aryastasata as the works of Aryabhata, and these constitute our Aryabhatiya. But the word audayikatantra of Brahmasphuiasiddhanta, XI.21 and the words audayika and ardharatrika of XI.13-14 seem to imply that Brahmagupta is distinguishing between two works of one Aryabhata. The published Aryabhatiya (1.2) 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.