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. 200 years later, an Indian astronomer known as Bhaskara glossed this mathematical bankruptcy of the Aryabhatiya.An english translation of Bhaskara's observation and a mathematical complement are provided in volumes.Subjects handled in Bhaskara's statement variety from computing the quantity of an equilateral tetrahedron to the curiosity on a loaned capital, from computations on sequence to an intricate technique to resolve a Diophantine equation.This quantity comprises an creation and the literal translation. The creation goals at supplying a normal historical past for the interpretation and is split in 3 sections: the 1st locates Bhaskara's textual content, the second one appears at its mathematical contents and the 3rd part analyzes the kinfolk of the remark and the treatise.
Read or Download Expounding the Mathematical Seed: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya PDF
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Additional info for Expounding the Mathematical Seed: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya
One can thus see how, by helping one to read and understand a verse word for word the commentator, also, gives his own interpretation of it. In turn, by giving his own understanding Bh¯ askara sheds light on some of the mathematical functions of the ambiguities and puns within the verse, giving us a glimpse oﬀ what could have been a typical way of composing technical verses. c Elaborating a technical vocabulary As he comments on the words used ¯ by Aryabhat askara underlines and insists that the vocabulary employed is .
How does he, practically, put it into action? 3 ¯ Bh¯askara’s interpretation of Aryabhat . a’s verses. We will then look at how he transforms Aryabhat a’s rules into . mathematical procedures. 10, volume I, p. 51. infamous grammatical commentary authored by Pata˜ njali, that all educated Indian Pandit knew. See [Filliozat 1988b]. 4 in volume I, p. 20 sqq. 109 An C. 1 xliii Standard techniques of s¯ utra interpretation The history of mathematical commentaries in Sanskrit still needs to be written111 .
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.