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Aryabhatiya
Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata. Historian of astronomy Roger Billard estimates that the book was composed around 510 CE based on historical references it mentions.
Aryabhatiya is written in Sanskrit and divided into four sections; it covers a total of 121 verses describing different moralitus via a mnemonic writing style typical for such works in India (see definitions below):
It is highly likely that the study of the Aryabhatiya was meant to be accompanied by the teachings of a well-versed tutor. While some of the verses have a logical flow, some do not, and its unintuitive structure can make it difficult for a casual reader to follow.
Indian mathematical works often use word numerals before Aryabhata, but the Aryabhatiya is the oldest extant Indian work with Devanagari numerals. That is, he used letters of the Devanagari alphabet to form number-words, with consonants giving digits and vowels denoting place value. This innovation allows for advanced arithmetical computations which would have been considerably more difficult without it. At the same time, this system of numeration allows for poetic license even in the author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.
The Aryabhatiya contains 4 sections, or Adhyāyās. The first section is called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an introduction called the "Dasageethika" or "Ten Stanzas." This begins by paying tribute to Brahman (not Brāhman), the "Cosmic spirit" in Hinduism. Next, Aryabhata lays out the numeration system used in the work. It includes a listing of astronomical constants and the sine table. He then gives an overview of his astronomical findings.
Most of the mathematics is contained in the next section, the "Ganitapada" or "Mathematics."
Following the Ganitapada, the next section is the "Kalakriya" or "The Reckoning of Time." In it, Aryabhata divides up days, months, and years according to the movement of celestial bodies. He divides up history astronomically; it is from this exposition that a date of AD 499 has been calculated for the compilation of the Aryabhatiya. The book also contains rules for computing the longitudes of planets using eccentrics and epicycles.
In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing the celestial relationship between the Earth and the cosmos. This section is noted for describing the rotation of the Earth on its axis. It further uses the armillary sphere and details rules relating to problems of trigonometry and the computation of eclipses.
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Aryabhatiya
Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata. Historian of astronomy Roger Billard estimates that the book was composed around 510 CE based on historical references it mentions.
Aryabhatiya is written in Sanskrit and divided into four sections; it covers a total of 121 verses describing different moralitus via a mnemonic writing style typical for such works in India (see definitions below):
It is highly likely that the study of the Aryabhatiya was meant to be accompanied by the teachings of a well-versed tutor. While some of the verses have a logical flow, some do not, and its unintuitive structure can make it difficult for a casual reader to follow.
Indian mathematical works often use word numerals before Aryabhata, but the Aryabhatiya is the oldest extant Indian work with Devanagari numerals. That is, he used letters of the Devanagari alphabet to form number-words, with consonants giving digits and vowels denoting place value. This innovation allows for advanced arithmetical computations which would have been considerably more difficult without it. At the same time, this system of numeration allows for poetic license even in the author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.
The Aryabhatiya contains 4 sections, or Adhyāyās. The first section is called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an introduction called the "Dasageethika" or "Ten Stanzas." This begins by paying tribute to Brahman (not Brāhman), the "Cosmic spirit" in Hinduism. Next, Aryabhata lays out the numeration system used in the work. It includes a listing of astronomical constants and the sine table. He then gives an overview of his astronomical findings.
Most of the mathematics is contained in the next section, the "Ganitapada" or "Mathematics."
Following the Ganitapada, the next section is the "Kalakriya" or "The Reckoning of Time." In it, Aryabhata divides up days, months, and years according to the movement of celestial bodies. He divides up history astronomically; it is from this exposition that a date of AD 499 has been calculated for the compilation of the Aryabhatiya. The book also contains rules for computing the longitudes of planets using eccentrics and epicycles.
In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing the celestial relationship between the Earth and the cosmos. This section is noted for describing the rotation of the Earth on its axis. It further uses the armillary sphere and details rules relating to problems of trigonometry and the computation of eclipses.