By Agathe Keller
In the 5th century, the Indian mathematician Aryabhata wrote a small yet well-known paintings on astronomy in 118 verses referred to as the Aryabhatiya. Its moment bankruptcy supplies a precis of Hindu arithmetic as much as that time, and two hundred years later, the Indian astronomer Bhaskara glossed that bankruptcy. This quantity is a literal English translation of Bhaskara’s remark whole with an introduction.
Read Online or Download Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies) PDF
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Extra resources for Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies)
93; volume II, p. 107. C. The commentary and its treatise xlvii verses 32-33. To do so he uses almost all of the diﬀerent techniques that we have speciﬁed above. ¯ 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.
What are the reasonings that Bh¯ askara named in such a way? Let us note, that we have very few testimonies of them in the text itself. Many of the explanations seem to have been oral. Diagrams would be the only trace left of them in the written text. In certain cases, we have traces of a reasoning but they are fragmentary or remain puzzling. Some of these reasonings are part of the “general commentary”; others are put forth or intertwined with solved examples. Perplexing as these reasonings can seem, this is our hypothesis: An explanation or proof consisted in rereading a procedure by an independent algorithm, that would furthermore give a mathematical grounding to it137 .
From being chords, arrows and semi-diameters these segments become upright sides, bases and hypotenuses as he tries to compute their lengths130 . ab in volume I, p. 24. ab, op. cit. and [Keller 1995] on this subject. 32-33, p. 128 and its supplement in volume II, p. 142. 128 This has been described above, on p. xxviii. ab in volume I, p. 83; volume II, p. 100. 11 in volume I, p. 57; volume II, p. 54. 126 See l Introduction property of the ﬁgure (it contains right-triangles) and, simultaneously, states the way the procedure will be applied.