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Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical . External links[edit]. The Āryabhaṭīya by Āryabhaṭa (translated into English by Walter Eugene Clark, ) hosted online by the Internet Archive . We now present a Kaṭapayādi code for the English alphabet: An English Kaṭ apayādi . References. 1. S. Kak, Aryabhata and Aryabhatiya. Aryabhatiya of Aryabhata, English In Kern published at Leiden a text called the Āryabhatīya which claims to be the work.

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There is also a table of sines jyagiven in a single verse.

Taken syllable by syllable this gives the numbers 6 and 30 and and 3, and 50, andand 7, aryabhatya 50, It is more precise than quantities derived by some of the greatest ancient Greek mathematicians. Aryabhata’s methods of astronomical calculations have been in continuous use for practical purposes of fixing the Panchangam Hindu calendar.

The Aryabhatiya of Aryabhata – Wikisource, the free online library

The other half, plus the radius of the Earth, is cut off by the Earth. By using this site, you agree to the Terms of Use and Privacy Policy. It has been suggested by some commentators, most notably B. The History of Ancient Indian Englihs. The phrase “beginning with ka ” is necessary because the vowels also are divided into vargas or “groups. Of several passages no translation has been given or only a tentative translation has been suggested.


Paramesvara interprets it as referring to the construction of a triangle of which the three sides are known and of a quadrilateral of which the four sides and one diagonal are known. Upload an image to replace this placeholder. 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.


It seems probable to me that Brahmagupta had before him these two stanzas in their present form.

Next, Aryabhata lays out the numeration system used in the work. The subsequent confusion from this blunder ensued until it was disproved in Suzuki He mentions proportions of triangles with respect to shadows. While some of the verses have a logical flow, some do not, and its unintuitive structure aryabhafiya make it difficult for a casual reader to follow.

Aryabhatiya With English Commentary

Then this lower Brahman is identified with the higher Brahman as being only an individuafized manifestation of the latter. Revolutions of Sun, Moon, Earth, and Planets in a yuga. He divides up history astrologically – it is from this exposition that historians deduced that the Aryabhatiya was written in C. Bibhutibhusan Datta, [37] in criticism of the number of revolutions of the planets reported by Alberuni II,remarks that the numbers given for the revolutions of Venus and Mercury really refer aryabhatiyz the revolutions of their apsides.

System of Expressing Numbers by Letters of Alphabet.

At any rate, the context shows that the rule deals with the actual construction of plane figures. It is highly likely that the study of the Aryabhatiya would be accompanied by the teachings of a well-versed tutor. It is hard to believe that such a descriptive alphabetical notation was not based on a place-value notation.

It is possible that computation may have been made on a board ruled into columns.

It does not read like a practical manual as does the Chinese Nine Chapters nor does it read like a basic set of theoretical proofs like Euclid’s Elements.

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Aryabhata’s method for finding cube roots, though, seems to be original Srinivasiengar This stanza, as being a technical paribhasa stanza which indicates the system of notation employed in the Dasagitikais not counted.


Strange to Westerners is the appearance in the Aryabhatiya of precise formulas alongside approximations with no distinction between the two. It further uses the armillary sphere and details rules relating to problems of trigonometry and the computation of eclipses.

Aryabhata was not the first Indian mathematician to display that he could find square roots – Jain mathematicians had shown great proficiency at this before him – but the Aryabhatiya is the oldest extant work which provides a method for aryabhatiga square roots. This area multiplied by its own square root is the exact volume of a sphere Aryabhata Lalla Madhyamadhikara, 8 gives the same numbers for the arryabhatiya of the planets, and differs only in giving “revolutions of the asterisms” instead of “revolutions of the Earth.

Some of them have a logical flow while some englisj to come out of nowhere. 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 In fact, some later commentaries on the Aryabhatiya by notable mathematicians attempted to reconcile Aryabhata’s findings with their belief in a stationary Aryabhztiya.