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. Of the rest of the work no translation has appeared, and only a few of the stanzas have been discussed. There are several uncertainties about this text. Especially noteworthy is the considerable gap after IV, 44, which is discussed by Kern pp.

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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.

Of the rest of the work no translation has appeared, and only a few of the stanzas have been discussed. There are several uncertainties about this text. Especially noteworthy is the considerable gap after IV, 44, which is discussed by Kern pp. 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. 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.

However, all the metrical evidence seems to favor the spelling with one t. It is not a complete and detailed working manual of mathematics and astronomy. Many commonplaces 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. The other work may not have been named or criticized by Brahmagupta because of the fact that it followed orthodox tradition.

If this author really composed two works which represented two slightly different points of view it is easy to explain Alberuni's mistake. The published text begins with 13 stanzas, 10 of which give in a peculiar alphabetical notation and in a very condensed form the most important numerical elements of system of astronomy.

In ordinary language or in numerical words the material would have occupied at least four times as many stanzas. I see nothing suspicious in the discrepancy as Kaye does. Other stanzas are clearly referred to but without direct quotations. The second section in 33 stanzas deals with mathematics.

These three sections contain exactly stanzas. No stanza from the section on mathematics has been quoted or criticized by Brahmagupta, but it is hazardous to deduce from that, as Kaye does, [4] that this section on mathematics is spurious and is a much later addition. This seems to be most unlikely. It is, of course, possible that at a later period some few stanzas may have been changed in wording or even supplanted by other stanzas.

Such criticism would not arise in regard to mathematical matters which had nothing to do with theological tradition. The silence of Brahmagupta here may merely indicate that he found nothing to criticize or thought criticism unnecessary. It seems probable to me that Brahmagupta had before him these two stanzas in their present form.

It must be left to the mathematicians to decide which of the two rules is earlier. Later writers attack him bitterly on this point. Even most of his own followers, notably Lalla, refused to follow him in this matter and reverted to the common Indian tradition. And yet the very next stanza IV, 10 seems to describe a stationary Earth around which the asterisms revolve. Is it capable of some different interpretation?

Has its wording been changed as has been done with I, 4? I see at present no satisfactory solution of the problem. This would indicate a knowledge of a libration of the equinoxes. The quotation should be verified in the unpublished text in order to determine whether Colebrooke was mistaken or whether we are faced by a real discrepancy. The matter needs careful investigation. So much additional material has been added, so many changes have been made, and so many of the views expressed would be unacceptable to him that I have not felt justified in placing his name, too, upon the title-page as joint-author and thereby making him responsible for many things of which he might not approve,.

Unfortunately it has not been possible to make use of it in the present publication. Having paid reverence to Brahman, who is one in causality, as the creator of the universe, but many in his manifestations , the true deity, the Supreme Spirit, Aryabhata sets forth three things: mathematics [ ganita ], the reckoning of time [ kalakriyaa ], and the sphere [ gola ]. Baidyanath suggests that satya devata may denote Sarasvati, the goddess of learning.

For this I can find no support, and therefore follow the commentator Paramesvara in translating "the true deity," God in the highest sense of the word, as referring to Prajapati, Pitamaha, Svayambhu, the lower individuahzed Brahman, who is so called as being the creator of the universe and above all the other gods. Then this lower Brahman is identified with the higher Brahman as being only an individuafized manifestation of the latter.

As Paramesvara remarks, the use of the word kam seems to indicate that Aryabhata based his work on the old Pitamahasiddhanta. Support for this view is found in the concluding stanza of our text IV, 50 , dryabhatiyam namna purvam svayambhuvam sada sad yat. However, as shown by Thibaut [10] and Kharegat, [11] there is a close connection between Aryabhata and the old Suryasiddhanta.

The stanza has been translated by Fleet [12]. As pointed out first by Bhau Daji, [13] a passage of Brahmagupta XII, 43 , janaty ekam api yato naryabhato ganitakalagolanam , seems to refer to the Ganitapada , the Kalakriyapada , and the Golapada of our Aryabhatiya see also Bibhutibhusan Datta.

As Fleet remarks, [15] Aryabhata here claims specifically as his work only three chapters. But Brahmagupta A. There is no good reason for refusing to accept it as part of Aryabhata's treatise. Beginning with ka the varga letters are to be used in the varga places, and the avarga letters are to be used in the avarga places. Ya is equal to the sum of na and ma.

The nine vowels are to be used in two nines of places varga and avarga. Navantyavarge va. The words varga and avarga seem to refer to the Indian method of extracting the square root, which is described in detail by Rodet [26] and by Avadhesh Narayan Singh. The varga or "square" places are the first, third, fifth, etc. The avarga or "non-square" places are the second, fourth, sixth, etc.

The words varga and avarga seem to be used in this sense in II, 4. There is no good reason for refusing to take them in the same sense here. The avarga letters are those from y to h , which are not so arranged in groups. The phrase "beginning with ka " is necessary because the vowels also are divided into vargas or "groups.

Therefore the vowel a used in varga and avarga places with varga and avarga letters refers the varga letters k to m to the first varga place, the unit place, multiplies them by 1. The vowel a used with the avarga letters y to h refers them to the first avarga place, the place of ten's, multiplies them by In like manner the vowel i refers the letters k to m to the second varga place, the place of hundred's, multiplies them by It refers the avarga letters y to h to the second avarga place, the place of thousand's, multiplies them by 1, And so on with the other seven vowels up to the ninth varga and avarga places.

From Aryabhata's usage it is clear that the vowels to be employed are a, i, u, r, I, e, ai, o, and au. No distinction is made between long and short vowels. From Aryabhata's usage it is clear that the letters k to m have the values of The letters y to h would have the values of , but since a short a is regarded as inherent in a consonant when no other vowel sign is attached and when the virama is not used, and since short a refers the avarga letters to the place of ten's, the signs ya , etc.

They merely serve to refer the consonants which do have numerical values to certain places. The commentator Paramesvara takes it as affording a method of expressing still higher numbers by attaching anusvara or visarga to the vowels and using them in nine further varga and avarga places. It is doubtful whether the word avarga can be so supplied in the compound. Fleet would translate "in the varga place after the nine" as giving directions for referring a consonant to the nineteenth place.

In view of the fact that the plural subject must carry over into this clause Fleet's interpretation seems to be impossible. Fleet suggests as an alternate interpretation the emendation of va to hau.

But, as explained above, au refers h to the eighteenth place. It would run to nineteen places only when expressed in digits. There is no reason why such a statement should be made in the rule. Rodet translates without rendering the word nava , " separement ou a un groupe termini par un varga.

So giri or gri and guru or gru. Such, indeed, is Aryabhata's usage, and such a statement is really necessary in order to avoid ambiguity, but the words do not seem to warrant the translation given by Rodet.

However, I know no other passage which, would warrant such a translation of antyavarge. Sarada Kanta Ganguly translates, "'[Those] nine [vowels] [should be used] in higher places in a similar manner. If navantyavarge is to be taken as a compound, the translation "in the group following the nine" is all right. But Ganguly's translation of antyavarge can be maintained only if he produces evidence to prove that antya at the beginning of a compound can mean "the following.

If nava is to be separated from antyavarge it is possible to take it with what precedes and to translate, "The vowels are to be used in two nine's of places, nine in varga places and nine in avarga places," but antyavarge va remains enigmatical. The translation must remain uncertain until further evidence bearing on the meaning of antya can be produced.

Whatever the meaning may be, the passage is of no consequence for the numbers actually dealt with by Aryabhata in this treatise. The largest number used by Aryabhata himself 1, 1 runs to only ten places. Rodet, Barth, and some others would translate "in the two nine's of zero's," instead of "in the two nine's of places. This, of course, will work from the vowel i on, but the vowel a does not add two zero's.

It adds no zero's or one zero depending on whether it is used with varga or avarga letters. The fact that khadvinavake is amplified by varge 'varge is an added difficulty to the translation "zero. It is possible that computation may have been made on a board ruled into columns. Only nine symbols may have been in use and a blank column may have served to represent zero.

There is no evidence to indicate the way in which the actual calculations were made, but it seems certain to me that Aryabhata could write a number in signs which had no absolutely fixed values in themselves but which had value depending on the places occupied by them mounting by powers of Compare II, 2, where in giving the names of classes of numbers he uses the expression sthanat sthanam dasagunam syat , "from place to place each is ten times the preceding.


What is the Aryabhatiya, a Sanskrit treatise, on?

Based on the parameters used in the text, the philosopher of astronomy Roger Billard estimated that the book was written around CE. Aryabhata I — CE was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. More Info: en. Test your knowledge.


Aryabhatiya - Sanskrit

Biography Name While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus,[4] including Brahmagupta's references to him "in more than a hundred places by name". This corresponds to CE, and implies that he was born in Evidences justify his birth there. There is no evidence that he was born outside Patliputra and traveled to Magadha, the centre of instruction, culture and knowledge for his studies where he even set up a coaching institute. Education It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.


India’s Ancient Genius: Unraveling the Story of Aryabhatta’s Astounding Scientific Feats!

Aryabhatta was only 23 when he composed his mathematical treatise— Aryabhatiya. The entire script was written in Sanskrit and hence reads like a poetic verse rather than a practical manual. A ryabhatta, also called Aryabhatta I was born possibly around C. Aryabhatta was one of the earliest Indian mathematicians and astronomers whose pioneering work in these fields is still referenced by many modern scholars. The work in Aryabhatiya is so extensive and detailed that it was years ahead of any work of the time. There were also other Jain mathematicians whose work also contributed to mathematics.

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