Smith, David Eugene, 1860-1944 · Boston, New York [etc.] Ginn and Company · leaf 331
and was, indeed, rediscovered by him and pub-lished in 1752, it was known to the great Frenchgeometer Descartes, a fact that Leibnitz mentions.1 This theorem has a very practical application in thestudy of crystals, since it offers a convenient check on thecount of faces, edges, and vertices. Some… … The first represents two truncated pyramids placedbase to base. Here £ = 20, f=103 v = 12, so thate + 2 =/+ v. The second represents a crystal formedby replacing each edge of a cube by a plane, with theresult that e = 40,/= 18, and v = 24. The third repre-sents a crystal formed by replacing each…
Geometry
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