Muslim extraction of roots
From the Indians one has methods for obtaining square and cube roots, methods which are based on knowledge of individual cases, namely the knowledge of the squares of the nine digits 1^{2}, 2^{2} , 3^{2} (etc.) and their respective products, i.e. 2 × 3 etc. We have written a treatise on the proof of the validity of those methods and that they satisfy the conditions. In addition we have increased their types, namely in the form of the determination of the fourth, fifth, sixth roots up to any desired degree. No one preceded us in this and those proofs are purely arithmetic, founded on the arithmetic of The Elements.
JOC/EFR March 2006
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