By Agathe Keller
Within the fifth century the Indian mathematician Aryabhata (476-499) wrote a small yet recognized 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 offered in volumes.Subjects taken care of in Bhaskara's remark diversity from computing the quantity of an equilateral tetrahedron to the curiosity on a loaned capital, from computations on sequence to an problematic strategy to unravel a Diophantine equation.This quantity comprises an creation and the literal translation. The advent goals at delivering a common historical past for the interpretation and is split in 3 sections: the 1st locates Bhaskara's textual content, the second one seems to be at its mathematical contents and the 3rd part analyzes the kinfolk 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
This uncovers the existence of specialized reading methods which most probably respond to equally specialized ways of elaborating s¯ utras. Additionally, it highlights our indebtedness to the commentator. For indeed, we do not know these diﬀerent reading tools, nor do we know how to detect verses that would require specialized readings. S¯ utras, probably, were composed in order to be open to such multiple readings and interpretations. Thus, Bh¯askara’s commentary discusses alternative interpretations of a same verse.
This doubling of the function of one word is possible because the traditional order of words is modiﬁed in an elliptical sentence117 . In some cases the commentator connects (sambandh-) the words of a verse because the natural order of the sentence has been lost. t), a traditional commentarial technique in Sanskrit literature is sometimes applied. Thus, when commenting on the second half of verse 3, Bh¯askara recalls the area of a square, evoked in the ﬁrst half of the verse. This is the basis on which he constructs the computation of its volume, and probably also the cube itself118 .
We hope to provide someday a full-ﬂedged analysis of the diﬀerent meanings the word can take and examine its relations with similar paradoxical entities in connection with irrationals in Mesopotamia and in ancient Greece. 88 See B. The mathematical matter xxxvii √ are manipulated the value of N is what is used in computations, but N is in fact the quantity considered. This is the paradox which makes the notion diﬃcult to grasp. ¯ıs emerge when a computation using the procedure corresponding to the “Pythagoras Theorem” produces a square whose root cannot be extracted93 .