to an error in Koenigãs calculation (of tanã₤ö¡ =ã₤ãÿ£¢2),ãthat is to say to the imperfection of his logarithmic tables,ãnot (as the books say30) ãto a mistake on the part of the Bee.ã ãNot to a mistake on the part of Maraldiã is, of course, all that we are entitled to say.
The theorem may be proved as follows:
ABCDEF, abcdef, is a right prism upon a regular hexagonal base. The corners BDF are cut off by planes through the lines AC, CE, EA, meeting in a point V on the axis VN of the prism, and intersecting Bb, Dd, Ff, at X, Y, Z. It is evident that the volume of the figure thus formed is the same as that of the original prism with hexagonal ends. For, if the axis cut the hexagon ABCDEF in N, the volumes ACVN, ACBX are equal. {331}
It is required to find the inclination of the faces forming the trihedral angle at V to the axis, such that the surface of the figure may be a minimum.