Abstract
In this paper, we study the extraction of roots as presented by Al-Kashi in his 1427 book “Key to Arithmetic” and Stevin in his 1585 book “Arithmetic”. In analyzing their methods, we note that Stevin’s technique contains some flaws that we amend to present a coherent algorithm. We then show that the underlying algorithm for the methods of both Al-Kashi and Stevin is the same.
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Notes
Stevin (1625 p. 118) “ ... by wanting to give a general rule (method), there is even more reason to add it than to leave it. It is true that there is no example which we can approximate it better by leaving it, but there also others which are to the contrary can be approached better by adding it.”
Stevin (1625 p. 125) “We will not give in this construction any verbal explanation but only the disposition of digits of the achieved Operation ...”.
References
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Communicated by: George Saliba.
Research partially supported by Great Lakes Colleges Association New Directions Initiative Program Grant.
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Aydin, N., Hammoudi, L. Root extraction by Al-Kashi and Stevin. Arch. Hist. Exact Sci. 69, 291–310 (2015). https://doi.org/10.1007/s00407-015-0150-3
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DOI: https://doi.org/10.1007/s00407-015-0150-3