メナイクモス
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^ a b Boyer (1991). “The age of Plato and Aristotle”. A History of Mathematics. pp. 104?105. ISBN 9780471543978. https://archive.org/details/historyofmathema00boye. "If OP=y and OD = x are coordinates of point P, we have y2 = R).OV, or, on substituting equals, y2 = R'D.OV = AR'.BC/AB.DO.BC/AB = AR'.BC2/AB2.In as much as segments AR', BC, and AB are the same for all points P on the curve EQDPG, we can write the equation of the curve, a "section of a right-angled cone", as y2=lx, where l is a constant, later to be known as the latus rectum of the curve. [...] Menaechmus apparently derived these properties of the conic sections and others as well. Since this material has a strong resemblance to the use of coordinates, as illustrated above, it has sometimes been maintains that Menaechmus had analytic geometry. Such a judgment is warranted only in part, for certainly Menaechmus was unaware that any equation in two unknown quantities determines a curve. In fact, the general concept of an equation in unknown quantities was alien to Greek thought. [...] He had hit upon the conics in a successful search for curves with the properties appropriate to the duplication of the cube. In terms of modern notation the solution is easily achieved. By shifting the cutting plane (Fig. 6.2), we can find a parabola with any latus rectum. If, then, we wish to duplicate a cube of edge a, we locate on a right-angled cone two parabolas, one with latus rectum a and another with latus rectum 2a. [...] It is probable that Menaechmus knew that the duplication could be achieved also by the use of a rectangular hyperbola and a parabola."
参考文献
Beckmann, Petr (1989). A History of Pi (3rd ed.). Dorset Press
Boyer, Carl B. (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc.. ISBN 0-471-54397-7. https://archive.org/details/historyofmathema00boye
Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN 0-471-18082-3. https://archive.org/details/historyofmathema0000cook
外部リンク
⇒Menaechmus' Constructions (conics) at ⇒Convergence
O'Connor, John J.; Robertson, Edmund F., “メナイクモス”, MacTutor History of Mathematics archive, University of St Andrews, https://mathshistory.st-andrews.ac.uk/Biographies/Menaechmus/ .
⇒Article at Encyclopadia Britannica
⇒Wolfram.com Biography
Fuentes Gonzalez, Pedro Pablo, “Menaichmos”, in R. Goulet (ed.), Dictionnaire des Philosophes Antiques, vol. IV, Paris, CNRS, 2005, p. 401-407.
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