By Agathe Keller
Within the fifth century the Indian mathematician Aryabhata (476-499) wrote a small yet well-known paintings on astronomy, the Aryabhatiya. This treatise, written in 118 verses, offers in its moment bankruptcy a precis of Hindu arithmetic as much as that point. 2 hundred years later, an Indian astronomer known as Bhaskara glossed this mathematical bankruptcy of the Aryabhatiya.An english translation of Bhaskara's remark and a mathematical complement are awarded in volumes.Subjects taken care of in Bhaskara's statement diversity from computing the quantity of an equilateral tetrahedron to the curiosity on a loaned capital, from computations on sequence to an difficult procedure to resolve a Diophantine equation.This quantity comprises an advent and the literal translation. The advent goals at offering a basic history for the interpretation and is split in 3 sections: the 1st locates Bhaskara's textual content, the second one seems at its mathematical contents and the 3rd part analyzes the kin of the remark and the treatise.
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Extra info for Expounding the Mathematical Seed: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya
In the case of Kerala, this was the privilege of a caste of princely astronomers. However, we do not know if this story is speciﬁc to Kerala or can be extended to the whole of the Indian subcontinent. ab, volume I, p. 11, volume I, p. 58. 2, volume I, p. 12. ab, volume I, p. 44. sya109 . cause they require an interpretation108 . Bh¯askara often quotes the M¯ Although the structure of his commentary has nothing to do with Pata˜ njali’s, this work seems to have the status of a model. Thus the principal objective of Bh¯ askara’s commentary is to give an interpretation ¯ of Aryabhat a’s verses.
Bh¯ askara, to expound the seed in Aryabhat . a’s verse, used special reading methods. This raises a certain number of questions, which provide as many programs of future research. Firstly, up to what point was Bh¯ askara’s text integrated into the larger tradition of commentarial literature in Sanskrit? Indeed, many of the reading techniques employed seemingly belong to this tradition. And Bh¯ askara appears as an author who can quote from some of this literature. Additionally, these technical readings also highlight the technical aspect of the composition of the verses themselves, the fact that they were probably written to be read in such a way.
S emerge when a computation using the procedure corresponding to the “Pythagoras Theorem” produces a square whose root cannot be extracted93 . The length of the segment, and not its square, is however needed to solve a problem. Thus quadratic irrationals appear in the computation of the area of trilaterals, the volume of an equilateral pyramid and that of a sphere94 . ¯ıs. In other words, we have to put them under the square-root symbol. And to do so, we have to square them. ¯ı integers (as square roots of perfect squares) and irrationals (as square roots of non-perfect squares) are referred to.