By Agathe Keller
In 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, supplies in its moment bankruptcy a precis of Hindu arithmetic as much as that point. 200 years later, an Indian astronomer referred to as Bhaskara glossed this mathematial bankruptcy of the Aryabhatiya.
An english translation of Bhaskara’s remark and a mathematical complement are awarded in volumes.
Subjects handled in Bhaskara’s statement variety from computing the amount of an equilateral tetrahedron to the curiosity on a loaned capital, from computations on sequence to an difficult procedure to unravel a Diophantine equation.
This quantity comprises motives for every verse observation translated in quantity 1. those supplementations talk about the linguistic and mathematical concerns uncovered by means of the commentator. quite worthy for readers are an appendix on Indian astronomy, difficult glossaries, and an in depth bibliography.
Read Online or Download Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies) PDF
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Additional resources for Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies)
Finally, it is read as a method to find the area of any field. 1 Procedure for the area of a rectangle The area of the rectangle may be seen as a direct application of the method given ¯ by Aryabhat ara) and length . a here, as the area is a product of its width (vist¯ (¯ ay¯ ama). Bh¯ askara seems to admit that this is a very well-known fact. A verse quoted in the general commentary states: vyaktam ¯yate yasm¯ at . phalam a since in rectangles the area is obvious However, the first example of the commentary concerns rectangles.
Hence, when the square of the base is subtracted from the square of the hypotenuse, the remainder is the square of the perpendicular. .. In other words EK 2 = EF 2 − F K 2 = EG2 − KG2 . e, its square root cannot be extracted without an approximation. Therefore, the length of half the base is squared so that it can enter F G2 ¯ the rule given by Aryabhat . a. In other words 4 is computed. Step 3 The rule given in the verse is applied: A2 = √ EK 2 × F G2 ⇔ A2 = 4 EK 2 × F G2 . ¯ı may take here. ah.
C. 63] 1976, p. 63] 21 [Shukla 1976; p. 63, line 19]. Please refer also to the Glossary for the translations we have adopted of these terms. 22 [Kaye 1908; p. 16] 18 [Shukla 36 Supplements of the parallel sides”. Both Clark24 and Shukla25 seem to understand svap¯ ata as relating to the orthogonality of the segments, and add the other understanding of the compound in parenthesis. In all cases, there is no ambiguity concerning the segments that this compound refers to. ¯ The correspondence between Aryabhat .
Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies) by Agathe Keller