Background
Āryabhaṭa II was born ca. 920-950 in India. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I.
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Āryabhaṭa II was born ca. 920-950 in India. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I.
Of life of Aryabhata II, who was the author of the Mahdsiddhdnta (or Aryasiddhanta), virtually nothing is known. His date can be established only by his alleged dependence on Sridhara, who wrote after Mahavlra (/?. 850) and before Abhayadeva Suri (fl. 1050); and by his being referred to by Bhaskara II (b. 1114). He must be dated, then, between ca. 950 and 1100. Kaye’s strange theories about the two Aryabhatas, which would have placed Aryabhata II before al-BTrunl (963-after 1048), have been refuted by Datta. Nothing further can be said of Aryabhata II; manuscripts of his work are found in Maharastra, Gujarat, and Bengal.
Aryabhata's most eminent work was "The treatise", which consists of eighteen chapters and was written in the form of verse in Sanskrit. The initial twelve chapters deals with topics related to mathematical astronomy and covers the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitudes of the planets, lunar and solar eclipses, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars.
The next six chapters of the book includes topics such as geometry, geography and algebra, which were applied to calculate the longitudes of the planets. In about twenty verses in the treatise, he gives elaborate rules to solve the indeterminate equation: by = ax + c. These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is an even number, when this number of quotients is an odd number, etc.
Aryabhata II also deduced a method to calculate the cube root of a number, but his method was already given by Aryabhata I, many years earlier. Indian mathematicians were very keen to give the correct sine tables since they played a vital role to calculate the planetary positions as accurately as possible. Aryabhata II played a vital role in it by constructing a sine table, which was accurate up to five decimal places.
Aryabhata II covered the positions of the planets and their conjunctions with each other and the stars, eclipses of the sun and moon, and the phases and rising and setting of the moon and planets.
His work The Mahdsiddhdnta consists of eighteen chapters, as follows:
1. On the mean longitudes of the planets.
2. On the mean longitudes of the planets according to the (otherwise unknown) Pardsarasiddhanta.
3. On the true longitudes of the planets.
4. On the three problems relating to diurnal motion.
5. On lunar eclipses.
6. On solar eclipses.
7. On the projection of eclipses and on the lunar crescent.
8-9. On the heliacal risings and settings of the planets.
10. On the conjunctions of the planets.
11. On the conjunctions of the planets with the stars.
12. On the patas of the sun and moon.
Chapters 13-18 form a separate section entitled
Goladhyaya (“On the Sphere”).
13. Questions on arithmetic, geography, and the mean longitudes of the planets.
14-15. On arithmetic and geometry.
16. On geography.
17. Shortcuts to finding the mean longitudes of the planets.
18. On algebra.
The Mahdsiddhdnta was edited, with his own Sanskrit commentary, by MM. Sudhakara Dvivedin, in Benares Sanskrit Series 148-150 (Benares, 1910).
Aryabhata II also gave a method to calculate the cube root of a number, but his method was not new, being based on that given many years earlier by Aryabhata I.
