| From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, p. 64 |
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Courtesy of 
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Āryabhaṭa II
A. Vagiswari
Alternate
name
Āryabhaṭa
the Younger
Flourished (India),
circa 9501100
Āryabhaṭa
II, the Hindu astronomer, is best known for his work entitled Mahāsiddhānta
or Āryasiddhānta. It has been established indirectly that
he lived and worked around the 10th century. In order not to confuse him with
the well‐known astronomer Āryabhaṭa, who lived in the fifth
century, he is known
as Āryabhaṭa
II or the Younger.
The Mahāsiddhānta or Āryasiddhānta
is an astronomical compendium based on the orthodox tradition of Smṛtis (passages from Vedic literature). The treatise written
in Sanskrit consists of 18 chapters and 625 ślokas (verses). The
first 12 chapters deal with mathematical astronomy. Detailed derivations are
presented on topics such as the mean and true longitudes of the planets, eclipses
of the Sun and the Moon, the projections of eclipses, the lunar crescent,
and the heliacal rising and settings of planets, including some calculations
on conjunctions of planets as well as planets with stars. The remaining six
chapters of the Mahāsiddhānta form a separate section called
the Golādhyāya (On the sphere) where topics on geometry,
geography, and algebra are discussed with reference to celestial astronomy.
In Chapter 17, for example, shortcuts are provided for determining the mean
longitudes of the planets. In Chapter 18, under the section called Kuṭṭakādhyāya, Āryabhaṭa
II discusses the topic of the solution of indeterminate equations of the first
degree. He improves upon earlier methods and suggests a shorter procedure.
In his work, Āryabhaṭa II also touches upon several arithmetical
operations such as the four fundamental operations, operations with zero,
extraction of square and cube roots, the rule of three, and fractions. To
represent numbers, he adopts the famous kaṭapayādi system of letter numerals. This practice
does not conform to the method followed by some of his predecessors, who used
the well‐known bhūta saṃkhyā
system of word numerals. The text does not say anything about the year and
place of Āryabhaṭa II's birth, nor does it give any other
personal information. In recent years several scholars have tried to establish
an approximate period in which he lived based on the cross‐references
to his work made by other contemporary and younger scholars. D. Pingee believed
that Āryabhaṭa
II's treatise was written between 950 and 1100, and G. R. Kaye concludes that
he lived before Bīrūnī
(973circa 1050). However, B. Datta disagrees with the date given by
Kaye and argues that Āryabhaṭa
II must have lived much later. Many recent articles on this subject state
that his main work was written in 950. Brahmagupta
(born: 598) leveled several criticisms on Āryabhaṭa I but not on Āryabhaṭa II. S. Dikshita has therefore put forward the argument that places
Āryabhaṭa II later than Brahmagupta. Another important
point noted is that Āryabhaṭa II tried to remove some discrepancies involving the criticism of
Brahmagupta on Āryabhaṭa I. Thus Dikshita assigns him a date around
śātavāhana śaka 875, which corresponds to 953. This corroborates
the opinions of other historians as well.
Selected References
Bose,
D. M., S. N. Sen, and B. V. Subbarayappa
(1971).
A Concise History of Science in India. New Delhi: Indian National Science
Academy, p. 167.
Datta, B.
(1926). Two Āryabhaṭas
of al‐Bīrūnī. Bulletin
of the Calcutta Mathematical Society 17: 5974.
Dikshit, S.
B. (1896). Bhāratīya Jyotisha. Poona. (English translation by R. V. Vaidya. 2 pts. New Delhi: Government of India Press, Controller
of Publications, 1969, 1981, pp. 9599.)
Dvivedin, Sudhkara (ed. and comm.) (1910). Mahāsiddhānta. Benares Sanskrit Series Vol. 36,
nos. 148150. Benares. (Reprint, New Delhi: Caukamba Sanskrit Prathista, 1995.)
Jha, V.
N. (1994). Indeterminate Analysis in the Context of the
Mahāsiddhānta of Āryabhaṭa II. Indian Journal
of History of Science 29: 565578.
(1997). Āryabhaṭa II's Method for Finding Cube Root of a Number. Ganita Bhāratī
19: 6068.
Kaye, G. R. (1910). The
Two Āryabhaṭas. Bibliotheca
Mathematica 10: 289292.
Pingree, David
(1970). Āryabhaṭa II. In Dictionary
of Scientific Biography, edited by Charles Coulston
Gillispie. Vol. 1, pp. 309310. New York: Charles
Scribner's Sons.
Census of the Exact Sciences in Sanskrit.
Series A. Vol. 1 (1970): 53b54a; Vol. 2 (1971): 15b16a; Vol. 4 (1981): 28a;
Vol. 5 (1994): 17a. Philadelphia: American Philosophical Society.
(1992). On
the Date of the Mahāsiddhānta of the Second Āryabhaṭa.
Ganita Bhāratī
14: 5556.