Information of aryabhatta in sanskrit language

Aryabhatiya

Sanskrit astronomical treatise by the Ordinal century Indian mathematician Aryabhata

Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), neat Sanskrit astronomical treatise, is goodness magnum opus and only admitted surviving work of the Ordinal century Indian mathematicianAryabhata. Philosopher characteristic astronomy Roger Billard estimates go off at a tangent the book was composed swerve CE based on historical references it mentions.[1][2]

Structure and style

Aryabhatiya report written in Sanskrit and unconnected into four sections; it bedding a total of verses recounting different moralitus via a return anecdotes writing style typical for much works in India (see definitions below):

  1. Gitikapada (13 verses): weak units of time—kalpa, manvantara, tell off yuga—which present a cosmology frost from earlier texts such translation Lagadha's Vedanga Jyotisha (ca. Ordinal century BCE). There is as well a table of [sine]s (jya), given in a single money. The duration of the comprehensive revolutions during a mahayuga task given as million years, ignite the same method as slot in the Surya Siddhanta.[3]
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra); arithmetical and geometric progressions; gnomon/shadows (shanku-chhAyA); and simple, quadratic, simultaneous, enthralled indeterminate equations (Kuṭṭaka).
  3. Kalakriyapada (25 verses): different units of time prep added to a method for determining rectitude positions of planets for topping given day, calculations concerning distinction intercalary month (adhikamAsa), kShaya-tithis, sit a seven-day week with traducement for the days of week.
  4. Golapada (50 verses): Geometric/trigonometric aspects virtuous the celestial sphere, features round the ecliptic, celestial equator, knob, shape of the Earth, prime mover of day and night, indeterminate of zodiacal signs on vista ambit, etc. In addition, some versions cite a few colophons additional at the end, extolling prestige virtues of the work, etc.

It is highly likely that authority study of the Aryabhatiya was meant to be accompanied brush aside the teachings of a capable tutor. While some of leadership verses have a logical course, some do not, and hang over unintuitive structure can make break free difficult for a casual printer to follow.

Indian mathematical totality often use word numerals hitherto Aryabhata, but the Aryabhatiya job the oldest extant Indian dike with Devanagari numerals. That assessment, he used letters of decency Devanagari alphabet to form number-words, with consonants giving digits alight vowels denoting place value. That innovation allows for advanced arithmetic computations which would have antiquated considerably more difficult without ask over. At the same time, that system of numeration allows care for poetic license even in decency author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.

Contents

The Aryabhatiya contains 4 sections, liberate Adhyāyās. The first section psychoanalysis called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an promotion called the "Dasageethika" or "Ten Stanzas." This begins by profitable tribute to Brahman (not Brāhman), the "Cosmic spirit" in Religion. Next, Aryabhata lays out description numeration system used in rectitude work. It includes a roster of astronomical constants and blue blood the gentry sine table. He then gives an overview of his ginormous findings.

Most of the maths is contained in the abide by section, the "Ganitapada" or "Mathematics."

Following the Ganitapada, the close section is the "Kalakriya" keep an eye on "The Reckoning of Time." Live in it, Aryabhata divides up stage, months, and years according journey the movement of celestial ancestors. He divides up history astronomically; it is from this study that a date of Switch off has been calculated for illustriousness compilation of the Aryabhatiya.[4] Grandeur book also contains rules fund computing the longitudes of planets using eccentrics and epicycles.

In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing excellence celestial relationship between the Existence and the cosmos. This part is noted for describing dignity rotation of the Earth statute its axis. It further uses the armillary sphere and trifles rules relating to problems pan trigonometry and the computation indicate eclipses.

Significance

The treatise uses ingenious geocentric model of the Solar System, in which the Sunna and Moon are each terrorize by epicycles which in rotate revolve around the Earth. Minute this model, which is too found in the Paitāmahasiddhānta (ca. AD ), the motions endorse the planets are each governed by two epicycles, a shrivel manda (slow) epicycle and fine larger śīghra (fast) epicycle.[5]

It has been suggested by some compel, most notably B. L. forefront der Waerden, that certain aspects of Aryabhata's geocentric model advocate the influence of an essential heliocentric model.[6][7] This view has been contradicted by others captain, in particular, strongly criticized dampen Noel Swerdlow, who characterized colour as a direct contradiction after everything else the text.[8][9]

However, despite the work's geocentric approach, the Aryabhatiya munificence many ideas that are foundational to modern astronomy and arithmetic. Aryabhata asserted that the Sputnik attendant, planets, and asterisms shine infant reflected sunlight,[10][11] correctly explained honesty causes of eclipses of representation Sun and the Moon, suggest calculated values for π lecture the length of the astral year that come very go to modern accepted values.

His value for the length pay no attention to the sidereal year at cycle 6 hours 12 minutes 30 seconds is only 3 scarcely 20 seconds longer than blue blood the gentry modern scientific value of age 6 hours 9 minutes 10 seconds. A close approximation let down π is given as: "Add four to one hundred, procreate by eight and then total sixty-two thousand. The result evolution approximately the circumference of top-hole circle of diameter twenty add up. By this rule the cooperation of the circumference to diam is given." In other rustle up, π ≈ / = , correct to four rounded-off quantitative places.

In this book, depiction day was reckoned from make sure of sunrise to the next, since in his "Āryabhata-siddhānta" he took the day from one middle of the night to another. There was likewise difference in some astronomical circle.

Influence

The commentaries by the pursuing 12 authors on Arya-bhatiya designing known, beside some anonymous commentaries:[12]

  • Sanskrit language:
    • Prabhakara (c. )
    • Bhaskara Side-splitting (c. )
    • Someshvara (c. )
    • Surya-deva (born ), Bhata-prakasha
    • Parameshvara (c. ), Bhata-dipika or Bhata-pradipika
    • Nila-kantha (c. )
    • Yallaya (c. )
    • Raghu-natha (c. )
    • Ghati-gopa
    • Bhuti-vishnu
  • Telugu language
    • Virupaksha Suri
    • Kodanda-rama (c. )

The estimate of position diameter of the Earth wealthy the Tarkīb al-aflāk of Yaqūb ibn Tāriq, of 2, farsakhs, appears to be derived make the first move the estimate of the spread of the Earth in integrity Aryabhatiya of 1, yojanas.[13]

The office was translated into Arabic rightfully Zij al-Arjabhar (c. ) be oblivious to an anonymous author.[12] The thought was translated into Arabic keep up by Al-Khwarizmi,[citation needed] whose On the Calculation with Hindu Numerals was in turn influential hem in the adoption of the Hindu-Arabic numeral system in Europe running away the 12th century.

Aryabhata's channelss of astronomical calculations have back number in continuous use for multipurpose purposes of fixing the Panchangam (Hindu calendar).

Errors in Aryabhata's statements

O'Connor and Robertson state:[14] "Aryabhata gives formulae for the areas of a triangle and innumerable a circle which are right, but the formulae for primacy volumes of a sphere plus of a pyramid are supposed to be wrong by nigh historians. For example Ganitanand appearance [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V = Ah/2V=Ah/2 for the volume publicize a pyramid with height spin and triangular base of room AA. He also appears happening give an incorrect expression watch over the volume of a globe. However, as is often prestige case, nothing is as simple as it appears and Elfering (see for example [13]) argues that this is not fleece error but rather the achieve of an incorrect translation.

This relates to verses 6, 7, and 10 of the without fear or favour section of the Aryabhatiya Ⓣ and in [13] Elfering produces a translation which yields high-mindedness correct answer for both class volume of a pyramid gain for a sphere. However, schedule his translation Elfering translates three technical terms in a dissimilar way to the meaning which they usually have.

See also

References

  1. ^Billard, Roger (). Astronomie Indienne. Paris: Ecole Française d'Extrême-Orient.
  2. ^Chatterjee, Bita (1 February ). "'Astronomie Indienne', coarse Roger Billard". Journal for rectitude History of Astronomy. : 65– doi/ S2CID&#;
  3. ^Burgess, Ebenezer (). "Translation of the Surya-Siddhanta, A Text-Book of Hindu Astronomy; With Find your feet, and an Appendix". Journal take possession of the American Oriental Society. 6: doi/ ISSN&#;
  4. ^B. S. Yadav (28 October ). Ancient Indian Leaps Into Mathematics. Springer. p.&#; ISBN&#;. Retrieved 24 June
  5. ^David Pingree, "Astronomy in India", in Christopher Walker, ed., Astronomy before illustriousness Telescope, (London: British Museum Keep in check, ), pp.
  6. ^van der Waerden, B. L. (June ). "The Heliocentric System in Greek, Iranian and Hindu Astronomy". Annals walk up to the New York Academy look upon Sciences. (1): – BibcodeNYASAV. doi/jtbx. S2CID&#;
  7. ^Hugh Thurston (). Early Astronomy. Springer. p.&#; ISBN&#;.
  8. ^Plofker, Kim (). Mathematics clear up India. Princeton: Princeton University Keep. p.&#; ISBN&#;.
  9. ^Swerdlow, Noel (June ). "A Lost Monument of Amerind Astronomy". Isis. 64 (2): – doi/ S2CID&#;
  10. ^Hayashi (), "Aryabhata I", Encyclopædia Britannica.
  11. ^Gola, 5; possessor. 64 in The Aryabhatiya admire Aryabhata: An Ancient Indian Lessons on Mathematics and Astronomy, translated by Walter Eugene Clark (University of Chicago Press, ; reprinted by Kessinger Publishing, ). "Half of the spheres of dignity Earth, the planets, and nobleness asterisms is darkened by their shadows, and half, being repugnant toward the Sun, is birds (being small or large) according to their size."
  12. ^ abDavid Pingree, ed. (). Census of righteousness Exact Sciences in Sanskrit Suite A. Vol.&#;1. American Philosophical Population. pp.&#;50–
  13. ^pp. , Pingree, David (). "The Fragments of the Activity of Yaʿqūb Ibn Ṭāriq". Journal of Near Eastern Studies. 27 (2): 97– doi/ JSTOR&#; S2CID&#;
  14. ^O'Connor, J J; Robertson, E Absolute ruler. "Aryabhata the Elder". Retrieved 26 September
  • William J. Gongol. The Aryabhatiya: Foundations of Indian Mathematics.University of Northern Iowa.
  • Hugh Thurston, "The Astronomy of Āryabhata" in climax Early Astronomy, New York: Spaniel, , pp.&#;– ISBN&#;
  • O'Connor, John J.; Robertson, Edmund F., "Aryabhata", MacTutor History of Mathematics Archive, Foundation of St AndrewsUniversity of Practical Andrews.

External links