Geodesic
Ten Mean Values of Antique Mathematics and their Mathematical, Philosophical and Aesthetical Meaning
Matematičeskoe obrazovanie, Tome 45 (2008) no. 1, pp. 27-38.

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Reconstruction of a principle on which all of the ten possible mean values could be constructed in antique time. Some philosophical background of the interest in these mean values. 
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A. I. Shchetnikov. Ten Mean Values of Antique Mathematics and their Mathematical, Philosophical and Aesthetical Meaning. Matematičeskoe obrazovanie, Tome 45 (2008) no. 1, pp. 27-38. http://geodesic.mathdoc.fr/item/MO_2008_45_1_a2/