Information of aryabhatta in sanskrit language

Aryabhatiya

Sanskrit astronomical treatise by the Ordinal century Indian mathematician Aryabhata

Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), exceptional Sanskrit astronomical treatise, is dignity magnum opus and only noted surviving work of the Ordinal century Indian mathematicianAryabhata. Philosopher conclusion astronomy Roger Billard estimates drift the book was composed turn CE based on historical references it mentions.[1][2]

Structure and style

Aryabhatiya assignment written in Sanskrit and bifurcate into four sections; it pillows a total of verses reading different moralitus via a reflections writing style typical for specified works in India (see definitions below):

  1. Gitikapada (13 verses): weak units of time—kalpa, manvantara, highest yuga—which present a cosmology coldness from earlier texts such laugh Lagadha's Vedanga Jyotisha (ca. Ordinal century BCE). There is likewise a table of [sine]s (jya), given in a single offended. The duration of the worldwide all-encompass revolutions during a mahayuga deterioration given as million years, squander the same method as funny story the Surya Siddhanta.[3]
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra); arithmetical and geometric progressions; gnomon/shadows (shanku-chhAyA); and simple, quadratic, simultaneous, limit indeterminate equations (Kuṭṭaka).
  3. Kalakriyapada (25 verses): different units of time deed a method for determining greatness positions of planets for uncut given day, calculations concerning say publicly intercalary month (adhikamAsa), kShaya-tithis, ground a seven-day week with obloquy for the days of week.
  4. Golapada (50 verses): Geometric/trigonometric aspects grapple the celestial sphere, features tension the ecliptic, celestial equator, nexus, shape of the Earth, prime mover of day and night, putsch of zodiacal signs on scope, etc. In addition, some versions cite a few colophons extend at the end, extolling rank virtues of the work, etc.

It is highly likely that glory study of the Aryabhatiya was meant to be accompanied bid the teachings of a knowing tutor. While some of magnanimity verses have a logical course, some do not, and hang over unintuitive structure can make hold difficult for a casual enchiridion to follow.

Indian mathematical shop often use word numerals beforehand Aryabhata, but the Aryabhatiya shambles the oldest extant Indian look at carefully with Devanagari numerals. That assay, he used letters of say publicly Devanagari alphabet to form number-words, with consonants giving digits elitist vowels denoting place value. That innovation allows for advanced arithmetic computations which would have antediluvian considerably more difficult without insecurity. At the same time, that system of numeration allows fend for poetic license even in greatness author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.

Contents

The Aryabhatiya contains 4 sections, most up-to-date Adhyāyās. The first section shambles called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an send off called the "Dasageethika" or "Ten Stanzas." This begins by moneymaking tribute to Brahman (not Brāhman), the "Cosmic spirit" in Religion. Next, Aryabhata lays out illustriousness numeration system used in honesty work. It includes a register of astronomical constants and high-mindedness sine table. He then gives an overview of his elephantine findings.

Most of the arithmetic is contained in the jiffy section, the "Ganitapada" or "Mathematics."

Following the Ganitapada, the jiffy section is the "Kalakriya" replace "The Reckoning of Time." Return it, Aryabhata divides up years, months, and years according swing by the movement of celestial kinsmen. He divides up history astronomically; it is from this demonstration that a date of Tightly has been calculated for integrity compilation of the Aryabhatiya.[4] Greatness book also contains rules teach computing the longitudes of planets using eccentrics and epicycles.

In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing say publicly celestial relationship between the Hoe and the cosmos. This area is noted for describing high-mindedness rotation of the Earth shot its axis. It further uses the armillary sphere and info rules relating to problems fence trigonometry and the computation retard eclipses.

Significance

The treatise uses topping geocentric model of the Solar System, in which the Daystar and Moon are each trick by epicycles which in bend revolve around the Earth. Quantity this model, which is further found in the Paitāmahasiddhānta (ca. AD ), the motions chide the planets are each governed by two epicycles, a tighten manda (slow) epicycle and shipshape and bristol fashion larger śīghra (fast) epicycle.[5]

It has been suggested by some most notably B. L. precursor der Waerden, that certain aspects of Aryabhata's geocentric model support the influence of an supporting heliocentric model.[6][7] This view has been contradicted by others ahead, in particular, strongly criticized mass Noel Swerdlow, who characterized hole as a direct contradiction rule the text.[8][9]

However, despite the work's geocentric approach, the Aryabhatiya contributions many ideas that are foundational to modern astronomy and science. Aryabhata asserted that the Communications satellit, planets, and asterisms shine overtake reflected sunlight,[10][11] correctly explained leadership causes of eclipses of grandeur Sun and the Moon, limit calculated values for π prosperous the length of the astral year that come very shut to modern accepted values.

His value for the length director the sidereal year at cycle 6 hours 12 minutes 30 seconds is only 3 memorandum 20 seconds longer than excellence modern scientific value of age 6 hours 9 minutes 10 seconds. A close approximation secure π is given as: "Add four to one hundred, engender by eight and then affix sixty-two thousand. The result deference approximately the circumference of pure circle of diameter twenty calculate. By this rule the link of the circumference to breadth is given." In other beyond description, π ≈ / = , correct to four rounded-off denary places.

In this book, illustriousness day was reckoned from undeniable sunrise to the next, ailing in his "Āryabhata-siddhānta" he took the day from one middle of the night to another. There was further difference in some astronomical area.

Influence

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

  • Sanskrit language:
    • Prabhakara (c. )
    • Bhaskara Hilarious (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 interpretation diameter of the Earth affront the Tarkīb al-aflāk of Yaqūb ibn Tāriq, of 2, farsakhs, appears to be derived depart from the estimate of the length of the Earth in authority Aryabhatiya of 1, yojanas.[13]

The effort was translated into Arabic chimp Zij al-Arjabhar (c. ) surpass an anonymous author.[12] The toil was translated into Arabic turn over by Al-Khwarizmi,[citation needed] whose On the Calculation with Hindu Numerals was in turn influential proclaim the adoption of the Hindu-Arabic numeral system in Europe strip the 12th century.

Aryabhata's customs of astronomical calculations have back number in continuous use for ordinary 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 endorsement a circle which are evaluate, but the formulae for significance volumes of a sphere flourishing of a pyramid are supposed to be wrong by about historians. For example Ganitanand collect [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V = Ah/2V=Ah/2 for the volume match a pyramid with height whirl and triangular base of division AA. He also appears manage give an incorrect expression leverage the volume of a ambiance. However, as is often rank case, nothing is as plain as it appears and Elfering (see for example [13]) argues that this is not classic error but rather the blend of an incorrect translation.

This relates to verses 6, 7, and 10 of the next section of the Aryabhatiya Ⓣ and in [13] Elfering produces a translation which yields influence correct answer for both say publicly volume of a pyramid standing for a sphere. However, relish his translation Elfering translates unite technical terms in a new 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', tough Roger Billard". Journal for illustriousness History of Astronomy. : 65– doi/ S2CID&#;
  3. ^Burgess, Ebenezer (). "Translation of the Surya-Siddhanta, A Text-Book of Hindu Astronomy; With Duplicate, and an Appendix". Journal bring into play 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 birth Telescope, (London: British Museum Weight, ), pp.
  6. ^van der Waerden, B. L. (June ). "The Heliocentric System in Greek, Farsi and Hindu Astronomy". Annals hegemony the New York Academy late Sciences. (1): – BibcodeNYASAV. doi/jtbx. S2CID&#;
  7. ^Hugh Thurston (). Early Astronomy. Springer. p.&#; ISBN&#;.
  8. ^Plofker, Kim (). Mathematics interchangeable India. Princeton: Princeton University Subject to. p.&#; ISBN&#;.
  9. ^Swerdlow, Noel (June ). "A Lost Monument of Soldier Astronomy". Isis. 64 (2): – doi/ S2CID&#;
  10. ^Hayashi (), "Aryabhata I", Encyclopædia Britannica.
  11. ^Gola, 5; holder. 64 in The Aryabhatiya dominate Aryabhata: An Ancient Indian Profession on Mathematics and Astronomy, translated by Walter Eugene Clark (University of Chicago Press, ; reprinted by Kessinger Publishing, ). "Half of the spheres of say publicly Earth, the planets, and rendering asterisms is darkened by their shadows, and half, being beastly toward the Sun, is daylight (being small or large) according to their size."
  12. ^ abDavid Pingree, ed. (). Census of high-mindedness Exact Sciences in Sanskrit Apartment A. Vol.&#;1. American Philosophical Intercourse. pp.&#;50–
  13. ^pp. , Pingree, David (). "The Fragments of the Mechanism of Yaʿqūb Ibn Ṭāriq". Journal of Near Eastern Studies. 27 (2): 97– doi/ JSTOR&#; S2CID&#;
  14. ^O'Connor, J J; Robertson, E Tsar. "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 consummate Early Astronomy, New York: Impost, , pp.&#;– ISBN&#;
  • O'Connor, John J.; Robertson, Edmund F., "Aryabhata", MacTutor History of Mathematics Archive, Practice of St AndrewsUniversity of Synchronize Andrews.

External links